ECON 420 - Midterm/Final

Exercise - 05/20/19 (presentation) Consider a classical economy. The production function is Y=A(K+L). Economy is in equilibrium initially, A=2, K=10. THE FOLLOWING QUESTIONS ARE ALL WITHIN THE SAME ECONOMY AND SCENARIO!!! 1) If labor supply curve is characterized by W/P=1(1/5)Ls, determine the real wage, the equilibrium amount labor, and the level of production Y. 2) Suppose government spending is completely financed by lump sum income tax, such that T=G=10. The consumption equation is C=c0+c1(Y-T)+c2r, where c0=5; c1=0.5; c2=0. What is the amount of consumption? 3) The saving equation is S=s0+s1(Y-T)+s2r. Determine the values of s0, s1, and s2. What is the amount of saving? What is the amount of investment? Illustrate the loanable fund market. 4) Suppose there is a sudden technology shock, such that A changes from 2 to 3. What will happen in the labor market? Assume K is fixed. What are the new equilibrium levels of W/P, L, and Y? 5) Assume gov't spending remains the same. What is the new equilibrium level of C, S, and I? Illustrate the change in the loanable funds market.

Y=A(K+L); A=2; K=10 1) Ld is determined by equating real wage to MPl (MPl = w/p!). i. MPl = w/p = PARTIAL derivative of CB function with respect to L - In partial derivative: only keep variables directly multiplied or divided by target variable! The rest gets thrown in the derivation process! --> derivY/derivL=A(K+L)--> Y=A --> A = *2 = REAL WAGE!* ii. Plug real wage into Ls = w/p = 1/5(Ls) = Ld equation for equilibrium of labor! --> 2 = 1/5(Ls) = 1x5 = Ls = *10 = equilibrium L!* iii. Plug L=10; K=10; A=2 into production function Y=A(K+L) --> Y=2(10+10)= *40* 2) T=G=10; Y=10 from (1); c0=5; c1=0.5; c2=0 i. Plug into C=c0+c1(Y-T)+c2r --> C=5+0.5(40-10)+(0xr)=5.5x30 --> *C=20* 3) s0; s1; s2=? i. Recall that savings = investment --> S=I ii. Recall that Y=C+I+G --> Y=C+S+G iii. Recall that S=total income-taxes-consumption --> S=Y-G-C - G=T - C=c0+c1(Y-T)+c2r iv. Plug above equations into the savings function! --> S=Y-T-[c0+c1(Y-T)+c2r]! - Simplify and group Y-T together: --> S=(Y-T)(1-c1)-c0-c2r --> S=-c0+(1-c1)(Y-T)-c2r v. With the savings function in the same format as the C function, we can see that -c0=s0; (1-c1)=s1; -c2r=s2r! --> *s0=-5; s1=(1-0.5)=0.5; s2r=0* vi. Given that savings = investment, just plug numbers in to find both! --> S=-5+0.5(40-10)-0 --> *S=I=10* Graph: i. x-axis=loanable funds (LF) ii. y-axis=interest rate (r) iii. Downward sloping curve=investment (I(r)) --> Savings=10 iv. Vertical curve=savings --> Savings=10 4) A0=2; A1=3 i. Recall from (1) that MPl = w/p = dY/dL = A --> Since A rises to 3, *W/P now = 3* ii. Equilibrium L in this context = find new Ls with numbers plugged into given Ld equation --> Ld=w/p=MPl=(1/5)Ls --> 3=(1/5)Ls --> *Ls=15* iii. Plug these values into given Y equation=A(K+L) --> K is fixed = 10 --> A now = 3 --> L now = 15 --> Y=3(10+15) --> *Y=75* 5) G=T=10=stays fixed - New C, S, I as result of A changing from 2 to 3? - Recall that Y=C+I+G - Recall that S=I - Recall that new Y=75 i. Plug values into C equation to find C: C=c0+c1(Y-T)-c1r - Other variables don't change - the only thing that's changed is Y as a result of A --> W/P changing! --> C=5+0.5(75-10)-0 --> *C now=37.5* ii. Plug values into derived S equation to find S: S=-c0+(1-c1)(Y-T)-c2r --> S=-5+0.5(75-10)-0 --> *S now=27.5* --> Since S=I, *I now=27.5 as well!* (I 也现在等于27.5！） Loanable funds market: i. y-axis=r ii. x-axis=loanable funds (LF) iii. Downward sloping curve=Investments (I(r)) --> A shifts r from r0=2 to r1=3! iv. Vertical curve=savings (S) --> S shifts from S0=10 to S1=27.5!

OPEN ECONOMY MACRO: Define the following: a) Balance of Payments --> Formula? --> What constitutes "balanced" BOP? b) Current Account --> Formula? c) Official Reserve Transaction d) Capital Account --> Formula? 2) What constitutes a trade deficit and surplus? How does this affect the Current Account? 3) What can we rewrite the BOP as if BOP=0 (AND ONLY IF BOP=0!)? 4) What is the Trade Balance formula?

a) BOP - record of economic transactions between US and foreign residents from US both in G/S as well as financial assets --> CU+CA+ORT = BOP --> CU=-CA-ORT (ONLY IF BOP IS SPECIFIED TO=0!) - Accounting for errors in the BOP: CU+CA+ORT+SD=BOP (SD = standard deviation) --> BOP always = 0! ---> Assume SD=0 unless told otherwise! b) Current Account (I) - record of economic transactions between US and foreign residents in ONLY goods/services - ie - Unilateral transfers (foreign aid), exports, imports, profits, investment income paid OR received (IIP / IIR) --> Exports - Imports +Net Transfers --> Current account = -(capital + reserve account)--> balances out financial+reserve account c) Official Reserve Account (III)- record of economic transaction in assets between public US and foreign entities --> ONLY dealing with central banks! - ie - Fed buys currency to lower exchange rate and prevent $ depreciation = BOP surplus! d) Capital (AKA FINANCIAL) account (II) - assets between private US and foreign residents --> Capital inflows-capital outflows=net capital inflows --> Foreign investment in domestic - domestic investment in foreign = net foreign wealth OR investment - ie - China investing in US stock/bond = foreign investment!; real estate, bonds, etc. 2) Trade deficit = exports < imports = NEGATIVE current account! --> = positive capital AKA financial account Trade surplus = exports > imports = POSITIVE current account! --> = negative capital AKA financial account 3) BOP if BOP=0 - AND ONLY IF BOP=0!: -(CA+ORT)=CU Current account = -(capital or financial + reserve acct) 4) Trade Balance formula: i. (T-G)+(S-I)=exports-t --> T-G = PuS (gov't intake - gov't expenditure=gov't savings) --> S-I = PrS (what you keep vs. what you invest) = PuS + PrS = trade balance a) Total National Saving = PuS+PrS

Exercise - 05/30/19 Keynesian Model: Consider a closed economy that is well characterized by a standard IS/LM structure with perfectly sticky prices, but with the following modifications: - T=t0+t1(I) - I=i0-i1r-i2t1 - C=a+b(Y-t0) Suppose that the gov't wants to increase taxes on investment. The fiscal authorities are concerned that this will adversely impact economic activity Y. To counteract this effect, the fiscal authorities plan to alter lump sum taxes. By how much must they do so? [Note: Assume the economy is stuck in a liquidity trap, i.e. r is fixed at r(fixed).]

- IS/LM structure = goods and services / money market = demand / supply - Y=C+I+G - t0=taxes - t1=investment's sensitivity to taxes - Want change in TAXES in terms of change in investor sensitivity to taxes! (t0是主题） - Find dY/dt0, then dY/dt1; equate dY/dt0 = dY/dt1 to find dt0 in terms of dt1; convert to discrete terms to find change(t0) in terms of change(t1)! i. Plug in given equations to Y=C+I+G - DON'T plug in T equation - NOT specified that G=T! --> Y=a+b(Y-t0)+i0-i1r-i2t1+G - Simplify: --> Y(1-b)=a-bt0+i0-i1r-i2t1+G --> Y=[a-bt0+i0-i1r-i2t1+G]/[1-b] ii. Find dY/dt0 --> dY/dt0=-b/(1-b) --> Discrete version: changeY=[-b/(1-b)]xchanget0 iii. Find dY/dt1 --> dY/dt1=-i2/(1-b) --> Discrete version: changeY=[-i2/(1-b)]xchanget1 iv. Since both equations equal changeY, equate them together to find changet0 in terms of changet1! --> [-b/(1-b)]xchanget0=[-i2/(1-b)]xchanget1 - Isolate changet0: --> changet0={[-i2/(1-b)]xchanget1}/[-b/(1-b)] - Cross multiply to simplify: --> changet0=[-i2/-b]xchanget1 --> *changet0=[i2/b]xchanget1*

Exercise - 06/13/19 DYNAMIC AS-AD MODEL: Consider a standard Dynamic AS/AD model as presented in class. Suppose there is a Keynesian-style drop in animal spirits towards investment. How will equilibrium income in this economy respond to this shock?

- Recall the dynamic AS-AD equations: --> AS: Pit=Pit-1+o[Yt-Yt^]+Vt --> AD: Pit=Pit^-[(1+alpha(o)(Y))/(alpha(o)(Pi))][Yt-Y^]+[1/(alpha(o)Pi)][Et] - Recall that national income=Yt - Recall that shock to demand for G/s (which is what Keynesian-style drop in "animal spirits" in investment is)=Et - Equilibrium income = must equate AS and AD! - GOAL: find dYt/dEt! i. Equate dynamic AS and AD formulas to find Yt=f(x)! --> Pit-1 +o[Yt-Yt^]+Vt = Pit^-[(1+alpha(o)(Y))/(alpha(o)(Pi))][Yt-Y^]+[1/(alpha(o)Pi)][Et] - Group Yts together! --> Yt[o + [(1+alpha(o)Y)/(alpha(o)Pi)]] = Pit^+[(1+alpha(o)(Y))/(alpha(o)(Pi))][Y^]+[Et/(alpha(o)Pi)]+oYt^ - Pit-1 - Vt --> Yt = {Pit^+[(1+alpha(o)(Y))/(alpha(o)(Pi))][Y^]+[Et/(alpha(o)Pi)]+oYt^ - Pit-1 - Vt}/{o + [(1+alpha(o)Y)/(alpha(o)Pi)]} ii. Take dYt/dEt to find Yt's sensitivity to change in Et! --> *dYt/dEt = [1/(alpha(o)Pi)]/[o + [(1+alpha(o)Y)/(alpha(o)Pi)]]*

Exercise - 05/29/19 Suppose you have Keynesian economy characterized by the aggregate demand function, short run aggregate supply function and price expectations function as shown below: (1) Yt=x0+x1Pt+v (2) Yt=Y*+q(Pt-Pt^e)+n (3) Pt^e=woPt-1+w1Pt-s+w2Pt-3+w3Pt-4+w4Pt-5 How sensitive are today's prices to a change in price levels from: a) 3 periods ago? b) 5 periods ago?

- Want to find the relationship between change in prices t (today) and change in prices t-3 (3 periods ago); change in prices t-5 (5 periods ago) - Need to find EQUILIBRIUM relation wrt prices - must first equate AD=AS and then sub in Pt^e equation! - Need to take derivative of Pt with respect to Pt-3 and Pt-5 to find sensitivity! i. Solve for Pt by equating AD with SRAS --> x0+x1Pt+v=Y*+q(Pt-Pt^e)+n --> -qPt+x1Pt=Y*-(qPt^e)+n-v-x0 --> Pt=[Y*-(qPt^e)+n-v-x0]/(x1-q) ii. Plug Pt^e equation into just solved Pt equation! --> Pt=[Y*-q(woPt-1+w1Pt-s+w2Pt-3+w3Pt-4+w4Pt-5)+n-v-x0]/(x1-q) iii. Take partial derivative of Pt with respect to Pt-3 and Pt-5! - can leave out other constants that don't have direct (multiplicatory/division) relation to Pt-3 and Pt-5! --> *d(Pt)/d(Pt-3) = -qw2/(x1-q)* --> *d(Pt)/d(Pt-5) = -qw4/(x1-q)* iv. Convert to discrete change equation to find how much change of Pt-3 and Pt-5 affect Pt! --> changePt = [-qw2/(x1-q)] x changePt-3 --> changePt = [-qw4/(x1-q)] x changePt-5

Exercise - 06/11/19 FEDERAL FUNDS RATE: Consider an economy where the market for federal funds is described as SR = 100; DR = 120-400FFR. Note: All numbers are in decimal format, i.e. 3 perfect is written as 0.03. What is the equilibrium Fed Funds Rate (FFR)? If the Fed wanted to set the target FFR to 3% what would it have to do? The equilibrium FFR is ___, and it would have to ___ worth of securities if the FFR target was 3%. a) 0.55; sell $8 b) 0.55, buy $8 c) 0.05, sell $8 d) 0.05, buy $8

1) a) Recall that... - FFR = policy or interest rate of federal reserve (when Fed raises or lowers its rates, this is the rate being referred to!) i. For equilibrium, set SR=DR to find equilibrium FFR --> 100=120-400FFR --> *FFR=0.05* b) MEANS THAT FED WANTS TO TAKE FFR DOWN BY 2%! Recall that... - To achieve SR=DR equilibrium for this case, simply divide FFR by SR value: 120-400(FFR/SR) - ALWAYS KEEP FFR AS A PERCENTAGE WHEN FINDING SR AND TO TARGET FFR! i. Find out changeQR/changeFFR --> Recall that QR=DR=SR in equilibrium! --> dQR/dFFR=-400 --> changeQR=(changeFFR)(-400) --> changeQR=-0.02x-400 --> changeQR=8! - Positive 8 = Fed must BUY $8 reserves! ALTERNATIVE METHOD: i. Plug 0.03 as 3% into equilibrium equation into DR equation --> 120-400(0.03)=DR=SR=100 --> SR=DR=120-400(3%/100) --> SR=DR=120-400(0.03%) --> SR=DR=108! --> Supply of federal funds must be 108 in order to lower FFR down to target of 3%! ii. SR1-SR0 = amount Fed must buy/sell! (-=sell/+=buy) [new-old] --> SR1=108; SR0=100 --> 108-100 = 8 = Fed must BUY $8 worth! *d) 0.05, buy $8*`

MONETARISM: 1) What are the 4 theories of money demand? 2) What are the 4 tenets of Monetarism? 3) What is the monetarist formula for the LM curve? a) How do income elasticity of Md (a1) and interest rate elasticity of Md (a2) affect the LM curve? 4) How does change in r affect investment according to monetarists? How does this affect the monetarist ISLM graph? 5) How does change in r affect income? How does this affect the monetarist ISLM graph? 6) What is the increase of output in Keynesian vs. Monetarist model with FP? a) What are the arguments being pushed forward by these models? 7) What is the increase of output in Keynesian vs. Monetarist model with MP? a) What are the arguments being pushed forward by these models 8) What is Okun's Law? 9) What is the Monetarist Inflation equation from the Keynesian SRAS and Okun's Law? 10) What is the Phillips Curve formula?

1) 4 theories: i. Fisher: MV=PY ii. Cambridge: Md=kPY iii. Keynes: Md=L(r,Y) iv. Monetarists: Md=K(re, rb, rd)PY - re=return on equity - rb=return on banks - rd=return on durable goods 2) 4 tenets of Monetarism: i. Ms is the dominant factor for national income ii. In the long run - money influences prices and real variables (Y, E) iii. In the short run - Ms can also influence real variables (Y, E) iv. Economic instability is resultant of bad gov't policies --> Bad typically = gov't intervention 3) Monetarist formula for LM: L(r,y)=a0+a1Y-a2r a) LM curve becomes steep when... i. Income elasticity of Md (a1) = very high --> Small change in Md = big change in income ii. Interest rate elasticity of Md (a2) = very low --> Small change in Md = small change in interest rate 4) Small change in r = big change in investment --> Result of this = LM curve is steeper for monetarists vs. Keynesians 5) Small change in r = big change in income --> Result of this = IS curve is flatter for monetarists vs. Keynesian 6) Fiscal policy leads to... i. Keynesian ISLM model: - Large increase in output ii. Monetarists' ISLM model: - Much smaller increase in output --> This is due to flatter IS/steeper LM curves! a) Arguments: i. Keynes - fiscal policy is effective ii. Monetarists - fiscal policy SUCKS! 7) Monetary policy leads to... i. Keynesian ISLM model: - Smaller increase in output ii. Monetarists' ISLM model: - Large increase in output --> This is due to flatter IS/steeper LM curves! a) Arguments: i. Keynes - monetary policy is okay ii. Monetarists - monetary policy is EFFECTIVE! 8) Okun's Law: Formula that connects output and employment: 1/o(Yt-Y^) = -b[URt-UR^]--> output gap = unemployment gap - 1/o, b = coefficients - Yt = actual output today - Y^ = natural rate of output - URt = actual unemployment today - UR^ = natural rate of unemployment - Output gap = 1/o(Yt-Y^) - Unemployment gap = -b[URt-UR^] 9) Recall that Keynes' SRAS formula: Yt=Y^+o[Pt-Pt^e-1]+n - Y^ = natural rate of output - Pt=today's prices - Pt^e-1 = yesterday's expectations of today's prices o, n = coefficients - Pt-Pt-1 = today's inflation Recall that Okun's Law: 1/o(Yt-Y^) = -b[URt-UR^]--> output gap = unemployment gap - i. Solve for Pt from the SRAS formula --> Yt=Y^+o[Pt-Pt^e-1]+n --> -oPt=Y^+o[Pt-Pt^e-1]+n-Yt --> Pt=[Y^-Yt+o[Pt-Pt^e-1]+n]/-o --> Pt=1/o[Y^-Yt] + Pt^e-1 - (n/o) ii. Subtract both sides by Pt-1 to get [Pt-Pt-1] bc this = inflation, which is what we want! --> *MONETARIST INFLATION FORMULA: Pt-Pt-1=1/o[Y^-Yt] + Pt^e-1 - Pt-1 - (n/o)* - Pit = Pt-Pt-1 = inflation - Pit^e-1 = Pt^e-1 - Pt-1 = yesterday's expected inflation of today 10) Derive Phillips Curve equation by subbing unemployment gap into output gap within the Monetarist Inflation equation! - Recall that output gap from Okun's Law = 1/o[Y^-Yt] - Recall that unemployment gap from Okun's Law = -b[URt-UR^] - Recall that the Monetarist Inflation equation = 1/o[Y^-Yt]-Pit^e-1 +(n/o) i. Substitute output gap in Monetarist Inflation equation with unemployment gap --> Pit = 1/o[Y^-Yt] + Pt^e-1 - Pt-1 - (n/o) --> Pit = -b[URt-UR^]+Pit^e-1 -(n/o) --> *Pit = Pit^e-1 - b[URt-UR^] - (n/o)* - Pit = inflation - Pit^e-1 = yesterday's expected inflation of today - b, 1/o, n = coefficients - URt = today's unemployment - UR^ = natural rate of unemployment

CHAPTER 5: Budget Deficit and Nat'l Debt 1) What signifies a balanced budget? a) What is the deficit? b) What characterizes a budget deficit? 2) What are methods available to gov't to deal with the deficit? 3) How do you calculate the deficit of today? Define the variables. a) What is Bt-1? 4) How do you calculate the change in debt? 5) What is change in debt = to? 6) What is the net tax function? 7) Are debt and deficit the same thing?

1) Balanced budget (hardly ever the reality): when G=T a) Deficit = gov't spending - tax revenue for a particular year! b) Expenses > revenue = budget deficit 2) Two (2) methods to deal with deficit: i. Print money --> Downside: can lead to HYPERinflation ii. Sell bonds --> This leads to increased debt, however --> Big chunk of US bonds bought by CHINESE INVESTORS HAHAHAHA 我的祖国啊 3) Deficit of today (Dt) = spending - revenue --> Gt+Trt+Intt) - Txt --> *Gt+Trt+r(Bt-1) - Txt* - G = gov't spending - Tr = transfers (transfers of money) - Tx = tax revenue - r = nominal interest rate a) Bt-1 = all the bonds you issued last year that are now due interest! --> Bt-1 = gov't debt for period t-1 (last period) 4) Change in debt = Bt - Bt-1 --> t-1 = subscript, just signifies value from last period! 5) *Bt - Bt-1 = (Gt+Tr-Txt) + r(Bt-1)* i. Bt - Bt-1 = change in debt ii. r(Bt-1) = interest payment from last period that gov't needs to pay today iii. (Gt+Tr-Txt) = primary deficit (anything OTHER than interest debt) --> This is the important part of the spending from the country's perspective 6) Net tax function: *T=t0+t1Y* 7) Debt and deficit are NOT the same thing!

DYNAMIC AS-AD MODEL: 1) What is the dynamic AS-AD model? 2) What is the demand for goods/services equation? 3) What is the Fisher equation within this model? 4) What is the Phillips curve equation? 5) What is the Adaptive Expectations equation? 6) What is the Taylor Rule/Monetary Policy Rule equation? 7) What are the Dynamic AS/AD models? REAL BUSINESS CYCLE THEORY: 1) What is the max equation? a) What is this equation subject to? 2) What is the equation for output in this model? ?3) What is the sensitivity of output to change in consumption? ?4) What is the sensitivity of output to change in labor hours?

1) Dynamic AS-AD model: gives us insight into how economy works in the SHORT RUN! 2) D for G/S: Yt=Ytfixed - alpha(rt-P) + E - E=investment confidence 3) Fisher equation within this model: rt+Pit^et=it-Pit^et 4) Phillips curve: Pit = Pit^e-1 - b[URt-UR^] - (n/o) 5) Adaptive Expectations: Pit+1^et=Pit --> Best guess of tomorrow's inflation = today's inflation! 6) Taylor rule/MP rule: it=Pit+P+oPi(Pit-Pit^)+oY(Yt-Yt^) - Yt=today's output - Yt^=natural rate of output - o=coefficient - Pi=inflation - Pit^=natural rate of inflation 7) Dynamic AS, AD: i. AS: Pit=Pit-1+o[Yt-Yt^]+Vt ii. AD: Pit=Pit^-[(1+alpha(o)(Y))/(alpha(o)(Pi))][Yt-Y^]+[1/(alpha(o)Pi)][Et] REAL BUSINESS CYCLE THEORY: 1) Max: u(Ct)+Bu(Ct+1)+B2u(Ct+2)+B3u(Ct+3)+...Bnu(Ct+n) a) Subject to: Ct + Dt+1 = WtNt+[1+rt-1]Dt - Ct = consumption of today - Dt = bonds of today - Dt+1 = bonds of next period - Wt = wages - Nt = labor hours 2) Output equation: Y = B{u(Ct)+v(1-Nt)+入[wtNt+(1+rt-1)Dt-Ct+Dt-1]} ?3) Ct = consumption Use output equation to find sensitivity of Y to Ct! i. Group Cts together: --> Y = B{u(Ct)+v(1-Nt)+入[wtNt+(1+rt-1)Dt-Ct+Dt-1]} --> Y = Ct(Bu-B入) dY/dCt: B(u-入) ?4) Nt = labor hours Use output equation to find sensitivity of Y to Nt! i. Group Nts together: --> Y = B{u(Ct)+v(1-Nt)+入[wtNt+(1+rt-1)Dt-Ct+Dt-1]} --> Y = Nt(入wt-v) dY/dCt: (入wt-v)

1) What is the effect of a shock on G on: i. Y? ii. IS/LM output? iii. IS/LM interest rate? 2) What are the 2 features of the Keynesian model? 3) What are the 3 motives for Money Demand in the Keynesian model? 4) What are the Money Demand functions within Keynesian theory? What is its relation to the LM interest rate fxn? 5) What is the liquidity trap?

1) Effect of G on variable Y = find dY/dG i. Recall that Y=[a+i0-bT-i1r+G]/(1-b) --> dY/dG=1/(1-b) --> Discrete version: changeY=changeG/(1-b) ii. Recall that IS/LM Y^=[a+i0-bT+G+ i1/c2(M-c0)]/[(1-b)+ c1i1/c2] --> dY^/dG=1/[(1-b)+ c1i1/c2] --> Discrete version: changeY^=changeG/[(1-b)+ c1i1/c2] iii. Recall that IS/LM r^=[((1-b)(c0-M))/c2 + (a+i0+G-bT)c1/c2]/[(1-b)+ c1i1/c2] --> dr/dG=(c1/c2)/[(1-b)+ c1i1/c2] --> Discrete version: changer^=[changeGx(c1/c2)]/[(1-b)+ c1i1/c2] 2) i. Adaptive expectations ii. Sticky prices/wages 3) Motives for Md: i. Transactionary purposes - for G/S purchases ii. Precautionary - just in case, future savings iii. Speculative - want to sell currency in the market 4) Md=L(r,Y) Md=c0+c1Y-c2r - All parameters = positive! i. Connection to LM interest rate function - if you just find r in terms of Md then you have the LM interest rate function! --> r=[c0-M+c1Y]/c2 5) Liquidity trap - when consumers choose to avoid bonds and keep funds in savings due to the belief that interest rates (r) will soon rise = bond values decrease--> don't want to hold asset with value that's expected to fall! --> Rising interest rates push bond values down - inverse relationship --> Consumers don't want to hold an asset with value that's expected to decline!

Exercise - 06/17/19 1) Consider an open economy where capital is perfectly mobile and exchange rates are fixed. Assume that currently e is equal to its target rate. Suppose the central bank wants to weaken the currency by targeting a HIGHER value of e. Use the ISLMBP framework to analyze what would happen in the economy if the central bank initiated such a move, explicitly stating whether equilibrium output and interest rate falls, rises, or remains unchanged. 2) Consider the Mundell Fleming model characterized by the equations below: C=a+b(Y-T)-cr I=i0-i1r G=Gfixed T=Tfixed X=x0+x1Yf-x2(1/e)P-x3GP Z=z0+z1Y-z2ePf-z3GP M=c0+c1Y-c2r F=f0+f1(r-rf) Everything is the same as we saw in class except the term GP refers to 'geopolitical conditions' which is essentially trying to represent the idea that trade is hampered by growing political conflicts (think Sino-US trade war ie). Also, recall the national accounting identity: Y=C+I+G+X-Z a) Solve for r in the LM equation (money market) b) Solve for r in the IS equation (goods market) c) Now combine the 2 equations you derived and find an equilibrium expression for Y^. d) How sensitive is equilibrium output to geopolitical fragmentation?

1) Fed wants HIGHER exchange rate = depreciation of $ (MONETARY POLICY!) - Achievable through increasing Ms (selling DC) = decreases r = increases exchange rate = depreciation of $ - Perfect capital mobility = BOP is horizontal line (BOP doesn't shift in perfect CM of fixed exchange rate!) - *If Fed has a stated GOAL of changing exchange rate, it will allow fluctuation of the exchange rate/IS and LM system to achieve that goal!* - Fixed system! i. Fed sells DC = increase of Ms ii. LM increases/shifts right = r decreases; Y increases --> THIS MOVEMENT ACHIEVES FED'S GOAL! --> BOP deficit (iD low, Ms high) --> Increase of e = depreciation of $ iii. IS increases/shifts right = r returns to equilibrium, Y increases iv. *FINAL RESULT: increased Y, unchanged r!* --> Unchanged r bc of perfect CM! change of r depends on slope of BOP! 2) a) LM: M=c0+c1Y-c2r Solve for r: --> *r=(c0+c1Y-M)/c2* b) IS: Y=a+b(Y-T)-cr+i0-i1r+Gfixed+Tfixed+x0+x1Yf-x2(1/e)P-x3GP-z0-z1Y+z2ePf+z3GP Solve for r: --> Y(1-b+z1)+r(c+il)=a-bT+i0+Gfixed+Tfixed+x0+x1Yf-x2(1/e)P-x3GP-z0+z2ePf+z3GP --> r={a-bT+i0+Gfixed+Tfixed+x0+x1Yf-x2(1/e)P-x3GP-z0+z2ePf+z3GP-Y(1-b+z1)}/(c+il) Group: --> *r={a-bT+i0+Gfixed+Tfixed+x0+x1Yf-x2(1/e)P-z0+z2ePf-Y(1-b+z1)+GP(z3-x3)}/(c+il)* c) Equilibrium for Y^ = equate r's from IS and LM framework: --> {a-bT+i0+Gfixed+Tfixed+x0+x1Yf-x2(1/e)P-z0+z2ePf-Y(1-b+z1)+GP(z3-x3)}/(c+il) = (c0+c1Y-M)/c2 Simplify/group Ys: --> {a-bT+i0+Gfixed+Tfixed+x0+x1Yf-x2(1/e)P-z0+z2ePf-Y(1-b+z1)+GP(z3-x3)}/(c+il) = (c0+c1Y-M)/c2 --> *Y^ = {[a-bT+i0+Gfixed+Tfixed+x0+x1Yf-x2(1/e)P-z0+z2ePf-Y(1-b+z1)+GP(z3-x3)-(c0/c2)+(M/c2)]/(c+il)}/[(1-b+z1)/(c+i1))+c1/c2]* d) Need dY^/dGP: --> Y^ = {[a-bT+i0+Gfixed+Tfixed+x0+x1Yf-x2(1/e)P-z0+z2ePf-Y(1-b+z1)+GP(z3-x3)-(c0/c2)+(M/c2)]/(c+il)}/[(1-b+z1)/(c+i1))+c1/c2] *dY^/dGP = {z3-x3}/{(c+i1)(c1/c2 -[(1-b+z1)/(c+i1)]}* *changeY = changeGP x {z3-x3}/{(c+i1)(c1/c2 -[(1-b+z1)/(c+i1)]}*

CHAPTER 5: 1) What is fiscal policy? --> Federal budget? --> Fiscal year? 2) What are the 2 actions of fiscal policy? 3) What is the impossible trinity within economic policy? 4) What happens to exchange rate when capital inflows/K increases? 5) What should the gov't do to keep the exchange rate fixed when capital inflows increase?

1) Fiscal policy - use of gov't spending/revenue collection to influence economy --> Federal budget = plan for reception/spending of gov't revenues --> Fiscal year = 12 mo period, begins on any date 2) 2 actions: i. Expansionary policy - encourages economic growth --> Higher spending, tax cuts ii. Contractionary policy - reduces economic growth --> Lower spending, higher taxes 3) Impossible trinity - impossible to have these 3 policies in place concurrently: i. Free capital flows/perfect K mobility ii. Fixed exchange rates iii. Independent monetary policy 4)Capital inflows/K increase = exchange rate decrease (=interest rate increase) --> Financial account surplus = BOP surplus = Ms too low, interest rate too high! 5) To keep exchange rate fixed: sell domestic currency, buy foreign currency = Ms increases, interest rate decreases, exchange rate increases --> LM curve shifts right/increases bc Ms increased!

HW 1 (pt. I) 1) Suppose Peuzo produced 500 of its popular new city car in the fourth quarter of 2014. Peuzo has two production costs: labor and intermediate goods. Peuzo pays its workers $30 per hour, and they employed 9,000 work hours. Intermediate goods were bought from Engin for $5000 per car. Engin's only input was labor, which cost $200,000 total. In the fourth quarter, Peuzo sold 200 cars to consumers at a price of $10,000 EACH. - In the first quarter of 2015, Peuzo produced 480 cars. Peuzo's wage per hour went up by 35%. Peuzo employed the same number of work hours. Also, Engin's labor costs were the same as in the previous quarter. Peuzo sold to consumers all cars produced in the first quarter of 2015 and the cars left in inventory from the previous quarter. However, Peuzo raised the price of the car to $12000 after a successful marketing campaign that made the new model very popular. - What was Peuzo and Engin's total contribution to National Income in the fourth quarter of 2014? - - - What was GDP in the first quarter of 2015? A. N IQ4:2014 = $3,192,000; GDPQ1:2015 = $7,698,000 B. N IQ4:2014 = $3,662,000; GDPQ1:2015 = $7,698,000 C. N IQ4:2014 = $3,662,000; GDPQ1:2015 = $9,360,000 D. N IQ4:2014 = $3,192,000; GDPQ1:2015 = $9,360,000 2) Consider a simple economy with two companies: Fresh Juice, and Organic Oranges. Organic Oranges do not sell oranges directly to consumer; rather it supplies its entire harvest to Fresh Juice as an intermediate good. Fresh Juice sells its juice directly to consumers. As juice is perishable, juice produced in Q1 cannot be sold in Q2. Suppose Fresh Juice produced 2,000 gallons of juice in Q1. The two inputs used were oranges, which cost $9,000 total, and labor, which cost $22 per gallon of juice. Organic Oranges's only input is labor, which costs $6,000, total. Fresh Juice sold 1,800 gallons of juice in the first quarter at a price of $55 each. - Which of the following correctly matches total corporate profit and wages in the economy in Q1? A. ProfitTotal = 49,000; WagesTotal = 50,000 B. ProfitTotal = 49,000; WagesTotal = 44,000 C. ProfitTotal = 55,000; WagesTotal = 50,000 D. ProfitTotal = 55,000; WagesTotal = 44,000 3) Which one of the following Cobb-Douglas production functions exhibits diminishing returns to labor? A. F (K,N) = AK^0.4 x N^1.5 B. F (K, N) = AK^0.5 x N^0.4 C. F (K,N) = AK^1.4 x N^1.5 D. F (K, N) = AK^0.5 x N^1.4 4) Suppose a shock hits the economy that abides by a Classical model and you observe the following changes: - Overall output increases - Marginal productivity of workers decrease Which of the following could lead to these observations? A. Flood in Minnesota, which destroyed the production facility. B. Invention of personal computers C. A huge lake was drained and new fertile land was revealed D. Immigrants get working visas and join the labor force.

1) GDP OR nat'l income = C+I+G+NX (I includes inventory unsold) = GNI = wages+firm P! *RMR FOR GNI: PROFITS = (R-C per good) x #sold*!!! Q4 2014: GNI--> rmr to multiply profits by AMOUNT SOLD for the specific company! PROFITS - P i. Labor cost per good = 9000hrs per 500 cars = 18 hrs per car = 18x30 = 540 labor cost per good ii. Capital cost per good 5000 capital cost per good iii. Revenues per good = 10k per car iv. Profits - P = (10k-5540)x200 sold = 892k PROFITS - E i. Labor cost per good = 200k total per 500 sold = 400 per good ii. Revenues per good = 5k per car iii. Profits - E = (5k-400)x500 sold = 2.3m TOTAL PROFITS - P+E i. 892k+2.3m = 3.192m WAGES - P i. Labor wages = 9000 labor hrs x 30 per hr = 270k WAGES - E i. Labor wages = 200k Total wages: i. 200k+270k = 470k GNI: *i. 3.192m+470k = 3.662m* Q5:2015: GDP = C+I+G+NX P: i. C: only from consumers! --> 480+(500-200 left in inventory) sold = 780 sold x 12k = 9.36m ii. I: sold from inventory = negative! --> 300 x 5540 cost per good = -1.662m GDP: 9.36m-1.662m = 7.698m --> IF YOU'RE NOT SURE, CALCULATE GNI AND GDP TO DOUBLE CHECK! --> *B. NIQ4:2014 = $3, 662, 000; GDPQ1:2015 = $7, 698, 000* 2) P = TR-TC GDP or nat'l income = C+I+G+NX OO supplies oranges to FJ as intermediate good! *Q1: PROFITS* i. Costs - FJ --> Labor cost 22/unit output x 2000 gallons = 44k --> Capital cost 9000 total = 9k ii. Costs - OO --> Labor cost 6000 total = 6k iii. TOTAL COSTS: 44k+9k+6k = 59k - - - - - - - - - - - - - - - i. Revenues - FJ --> Sold 1800 gallons x 55 each = 99k ii. Revenues - OO --> Sold 9000 worth oranges to FJ = 9k ii. TOTAL REVENUES: 108k - - - - - - - - - - - - - - - TOTAL PROFITS = 108k-59k = 49k --------------------------------- *Q1: WAGES* i. Wages - FJ --> Labor cost 22/unit output x 2000 gallons = 44k ii. Wages - OO ---> Labor cost 6000 total = 6k TOTAL WAGES: 50k *A. ProfitTotal = 49,000; WagesTotal = 50,000* 3) Recall that Y=Kfixed^a x L^(1-a) Diminishing returns to labor = when 0<(1-a)<1 --> *B. F (K, N) = AK^0.5 x N^0.4* 4) ACCORDING TO CLASSICAL MODEL: Output increased WHILE MPl decreased = labor force increasing faster than employment? MPl = w/p, if this decreases it means P > W Mathematically: Output increasing but prices also increasing? i. OUTPUT SIDE: recall that Y=A(K^a)L^(1-a) --> Increase in L = increase in output! ii. MPL SIDE: recall that MPl=w/p=[(1-a)AK^a]/L^a --> Increase in L = decrease in MPl! Conceptually: i. L increase = decrease in MPl = each additional worker yields decreasing increases in output!) --> More workers = aggregate output increases, but each worker doing less ii. A or K increase = increase in MPl --> *D. Immigrants get working visas and join the labor force*

1) What is the Keynesian theory of the relationship between government spending and output? 2) What is the mathematical proof for this Keynesian theory? 3) a) What is b? b) What is the relationship between b and output? 4) a) What is i1? b) What is the relationship between i1 and output? 5) a) What is c0? b) What is the relationship between c0 and output? 6) a) What is c1? b) What is the relationship between c1 and output?

1) Gov't spending KICKSTARTS employment i. Higher income leads to higher marginal propensity Higher MPc = higher output = this is all resultant of higher government spending! --> Leads to HIGHER interest rate! 2) This is all backed up by changeY/changeG i. *changeY/changeG = 1/[(1-b)+c1(i1/c2)]* 3) a) From Keynesian consumption model: C=a+b(Y-T) --> Amount change of consumption PER 1 unit increase in disposable income (Y-T) --> Marginal propensity to consume! b) i. Higher b = higher demand for output ii. Higher demand for output = the more effective government spending for raising output (Y) is! 4) a) From investment equation I = i0+i1r i1 = interest rate elasticity of investment --> Amount of investment change PER 1 unit increase in interest rate (r) b) i. Higher i1 = higher elasticity/sensitivity to interest rate changes = Y increases by less with increased gov't spending ii. Government spending increases interest rate (r) iii. High elasticity of investor sensitivity to interest rate increase = less investment (loans now cost more for investors) iv. Less investment = less output (Y)! 5) a) From the Md equation: Md = c0+c1Y-c2r --> c1 = Income elasticity of Md --> Amount of Md change PER 1 unit increase in income b) i. Higher c1 = the less effective government spending for raising Y (output) is! --> Higher c1 = smaller Y 6) a) From Md equation: Md = c0+c1Y-c2r --> c2 = interest rate elasticity of Md --> Amount of Md change PER 1 unit increase in interest rate b) i. Higher c2 = the more effective government spending for raising Y (output) is! ii. Higher interest rate elasticity of Md = higher interest rate resultant from gov't spending = Md drops at faster rate than interest rate is rising = more output!

FOREIGN EXCHANGE MARKET GRAPH: 1) What must happen for internal and external equilibrium to be achieved? 2) How does value of domestic currency affect net exports? 3) What happens to output, interest rate, BOP, foreign currency, and exchange rate when government spending increases? 4) What happens to the ISLM-BOP graph when G increases? Explain graphically and in words. 5) Flexible exchange rate vs. fixed exchange rate? 6) Suppose the Fed sets the level of $ at 1.0, while the equilibrium of foreign exchange is at 1.25. Draw the graph and discuss the implications of this. 7) Advantages of flexible and fixed exchange rates? 8) a) Suppose G increases. What happens to IS, interest rate/output, exchange rate, domestic currency? b) What does the Fed do in response within fixed exchange rate system? c) What happens to LM as a result?

1) INTERNAL/EXTERNAL EQUILIBRIUM: BOP = IS = LM (x-axis=Y; y-axis=r) Graph: standard ISLM graph+BOP curve i. BOP curve = upward sloping; goes through both sides of X https://www.google.com/url?sa=i&source=images&cd=&ved=2ahUKEwi4x_Kj3tLiAhXKjFkKHYUQBLIQjRx6BAgBEAU&url=https%3A%2F%2Fslideplayer.com%2Fslide%2F6985355%2F&psig=AOvVaw1IHfLkbiMcWe7Wqsdk2iAx&ust=1559837659620230 2) i. Domestic currency appreciation = net exports decrease (more expensive for buyers) --> Foreign buyer pays in foreign currency; foreign currency < domestic currency = when foreign currency is converted back to domestic currency, exporters get back LESS dollars! ii. Domestic currency depreciation = net exports increase (less expensive or buyers) --> Foreign buyer pays in foreign currency; foreign currency > domestic currency = when foreign currency is converted back to domestic currency, exporters get back MORE dollars! 3) G increases: i. IS curve increases/shifts right ii. Y increases iii. r increases iv. Dfx decreases/Sfx increases iv. exchange rate decreases = domestic currency appreciates --> Recall that e and r have inverse relationship! v. Net exports decrease - due to domestic currency appreciation vi. Output decreases, BUT not in the aggregate - this is because IS increased! SO in general, OUTPUT INCREASES! --> Magnitude is just decreased 4) Graph: x-axis=Y; y-axis=r https://drive.google.com/open?id=1ynquBROnseB6Ji6vwYPSzzZG_IZwz_k3 i. IS originally shifts from IS(G1e1) to IS(G2e1) ii. IS decreases to IS(G2e2) - due to r increase=e decrease=domestic currency appreciates=exports decrease=output decreases --> NOTE: IS(G2e2) still > IS(G1e1) iii. BOP increases from BOP(e1) to BOP(e2) to meet at new equilibrium (c) with IS(G2e2) and LM curves!! 5) i. Flexible exchange rate: market 做主 --> northern countries can afford to do this ii. Fixed exchange rate: controlled by central bank+government regulatory institutions; set exchange rate at (perceived) appropriate level for country --> REGARDLESS of Dfx or Sfx --> Southern countries 6) https://drive.google.com/open?id=16OEJnoRKizWpx5-V7LaZAUDxD0quV9IT FOREIGN EXCHANGE MARKET GRAPH: i. y-axis=e(D/F); x-axis=Qfx ii. Target horizontal line=1.0 (fixed rate) iii. Fx market equilibrium=1.25, which is > target rate IMPLICATION: *TARGET RATE OF 1 DOMESTIC CURRENCY PER 1 FOREIGN CURRENCY UNDERVALUES FOREIGN CURRENCY AND OVERVALUES DOMESTIC CURRENCY!* 7) Advantages of... FLEXIBLE EXCHANGE RATES - colonizer countries do this!: Advantages of Flexible Exchange Rates i. Allows policy makers to focus on domestic goals. --> Removes potential conflicts that arise between internal balance (domestic goals) and external balance (BoP equilibrium). ii. Insulate domestic economy from external shocks - your economy is already implemented into global capitalism! FIXED EXCHANGE RATES - colonized countries tend to choose this!: i. ENCOURAGES international trade! --> Fluctuating exchange rates create risk=which discourages international trade - something Southern countries rely on more heavily and northern countries rely on less! ii. ENCOURAGES foreign investment/borrowing! --> Fluctuating exchange rates=instability=frictional unemployment as labor is shifted to/from production for home & foreign markets = political instability iii. DISCOURAGES speculation/instability! --> Fluctuating exchange rates=speculation=exacerbates i. and ii.! 8) G increase= i. IS(G1,e1) shifts right/increases to IS(G2,e1) ii. r increases/Y increases iii. e decrease/domestic currency appreciation iv. TO CONTROL THIS: Fed buys foreign currency to increase exchange rate/sells domestic currency (increase domestic Ms)=decrease iD=increases e --> This decreases domestic currency value! - prevent inflation! v. Decrease in Sfx=increase in supply of domestic Ms=results in... vi. LM(M1) shifts right/increases to LM(M2) *THIS IS THE NEW EQUILIBRIUM, at intersection of IS(G2,e1) and LM(M2)!*

1) What do monetary variables refer to? 2) What do fiscal variables refer to? 3) What does 4) What happens to (r) and Y when taxes increase? Draw the IS graph to demonstrate. 5) Define the investment equation. i. What happens when i0 decreases? Draw the investment-interest rate and IS graphs to demonstrate. 6) What happens to interest rates and output when taxes decrease? Draw the IS and LM curves to demonstrate.

1) Money supply 2) Gov't spending, taxes, etc. 4) When taxes increase... -RMR THAT T=/=G UNLESS SPECIFICALLY SPECIFIED!! gov't expenditure=public works; taxes=taking away from your pockets and tends to turn off consumers, they're not simply the same unless specified so! --> y-axis=r; x-axis=Y --> IS curve = downward sloping i. IS (output) shifts left/down ii. Interest rates decrease iii. Output decreases 5) I = i0-i1r i. Recall that i0 = other variables that affect interest rates - but NOT directly! ii. When i0 falls, investment as a whole DECREASES! Investment-interest rate graph: r=y-axis; investment=x-axis i. Investment curve (downward sloping) shifts left (down) ii. Interest rate falls iii. Investment falls. IS graph (deals with r and Y!) r=y-axis; output=x-axis i. IS curve (downward sloping) shifts left (down) ii. Interest rate falls iii. Output falls 6) When taxes decrease... --> y-axis=r; x-axis=Y --> IS curve = downward sloping --> LM curve = upward sloping i. IS curve shifts right/up --> r0 increases to r1 --> Y0 increases to Y3 ii. To offset this, LM curve shifts right/down --> r1 increases to r2 --> Y3 decreases to Y2

Exercise 3: 1) Consider a simple economy with only 1 company: Bakery. Bakery sells cakes directly to consumers. These cakes are perishable; the DOH will not permit Bakery to sell a cake produced in Q1 to be sold in Q2. Suppose Bakery produced 500 cakes in Q1. The only input into the production process was labor, which cost $13.5 per cake produced. The company sold 450 cakes in the 1st quarter at a price of $25 each. Which of the following is an accurate depiction of the NIPA? You may assume that the level of inventories in Q4 were 0. a. C=11250; I=0; W=6750; P=4500 b. C=11250; I=675; W=6750; P=5175 c. C=12500; I=0; W=5750; P=6750 d. C=12500; I=675; W=6750; P=4500 2) Consider an economy with only 2 companies: A and B. A sells plastic at $8/unit. B purchases 100 units of plastic rom A, and uses each unit of plastic to create 1 widget. B sells 90 widgets to consumers at a price of $10 each. You may assume A has no costs to product eh plastic, B incurs not other costs in the production process, and that the widgets/plastic are durable. a. C=900; I=0; W=0; P=900 b. C=900; I=0; W=80; P=900 c. C=980; I=80; W=800; P=180 d. C=900; I=80; W=0; P=980 3) Define the population(P) as the sum of those in the labor force (LF) and those not in the labor force (NILF). Now define the employment (L) to population (P) ratio as the fraction of the population that's employed. Find an analytical expression to represent how the employment to population ratio changes with an increase in the #unemployed (U) individuals. You may assume the #employed, #unemployed, and those not in the labor force are independent from one another for ease of exposition. a. -UxNILF! b. -L(U+L+NILF)^-2 c. (U+L+NILF)^-2 d. -L(LF+NILF)^-1

1) NIPA = national income Consumption = 450 x 25 Inventory investment = 0 (what's left in inventory) P = 25 each TR = 25 x 450 = 11250 TC = 6750 + RK = 6750 --> Profit = 4500 Wages = 13.5 x 500 = 6750 *a. C=11250; I=0; W=6750; P=4500* 2) Company A: P=8 each Company B: i. Inventory remaining = 10 --> Inventory investment = #remaining x cost per unit --> 10 x 8 = 80 --> I = 80 --> subtract from profits? ii. Profits = TR-TC --> Cost of K = 8x100 = 800 --> Creates 100 widgets (1 piece plastic = 1 output) --> TR = 90x10 = 900 --> Profits = 900-800 = 100 iii. C = 90 sold x 10 each = 900 iv. Wages = 0 TOTAL NIPA: i. Profits = 100+80+800 = 980 --> Since GDP = 980, national income = profits of these companies must also = 980! ii. C = 90 sold to consumers by B x 10 price = 900 --> Rmr, cost of capital (RK = what B buys from A for $8 x 100) does NOT count as consumption! Counts as cost of input! iii. Wages = 0 iv. I = 10 x 8 = 80 --> *d. C=900; I=80; W=0; P=980* 3) Population = LF+NILF = people capable of working+people incapable (children, elderly) --> U=unemployed; L=employed i. Implement variable U into L/Pop function - break down "Pop" variable! - Pop = labor force(LF)+not in labor force(NILF --> L/(LF+NILF) - Labor force = unemployed+employed --> L/[(U+L)+NILF] = L[(U+L)+NILF]^-1 ii. Take dL/Pop / dU--> assuming independence, increase unemployed=increased Pop so take dL/Pop / dPop - to find sensitivity of L/Pop to U! - Pop=[U+L+NILF]^-1 --> d(L/Pop)/dPop = -L[U+L+NILF]^-2 --> *b. -L(U+L+NILF)^-2*

Real Business Cycle (RBC) STRUCTURE: - Won't be on final but could have a qualitative question on this 1) Profit function? 2) What is the maximized profit function? 3) What is capital equal to? 4) What is the Lagrangian profit function?

1) Profit function: AtF(Kt, Nz)-WtNt-It+Et+1-(1+rt-1)Dt - AtF(Kt, Nz)=output=profit - -WtNt-It+Et+1-(1+rt-1)Dt=cost --> Profit = revenues-costs 2) Maximize: Nt, Kt+1, It, Dt+1 3) Kt+1 = It+(1-S)Kt - Kt+1=tomorrow's capital - (1-S)=undepereciated capital - It=today's investment 4) Lagrangian profit function: L=E(t=0) Mt: AtF(Kt,Nt)-wtNt-It+Dt-1-(1+rt-1)Dt+

Exercise - 5/23/19 1) Below you are given info for a hypothetical economy (note that Ms is the nominal Ms). Using this info, obtain an equation for the aggregate demand curve, expressing P as a function of Y. - C=200+0.75(Y-T) - I=1000-25r - G=T=100 - Ms=1000 - L(r,Y)=0.5Y-100r a. P=((3/2000)Y-4.9)^-1 b. P=(666(2/3))(1/Y)-0.2) c. P=0.0045Y-5.1 2) Imagine a Keynesian economy in recession. The consumption function is given as C=a+b(Y-T). Marginal propensity to consume = 0.7 in this economy, and the gov't plans to increase its spending in order to raise output, as measured by Keynesian Cross, by $1000. However, last minute consumer survey estimates that autonomous private consumption in consumer attitudes, has fallen by $150. How much of a total change in gov't expenditures should be implemented to meet the targeted increase of $1k? - - Hint: the gov't spending must meet 2 objectives: overcome the consumer shock and increase output. Analyze these separately, then combine. a. $300 b. $150 c. $450 d. $1000 3) This question asks you to gather data and to use it in a fixed wage, flexible price Keynesian model. Suppose the economy is characterized by the following: C=1895+0.94(Y-T) I=3000-i1r G=T Md=0.16Y-100r What are the IS and LM functions? Be sure to write Y as a function of r.

1) RMR THE SIMPLIFY FIRST, THEN PLUG IN! Y SIDE (IS - output and r): i. Plug in all expressions for C, I, G into C+I+G=Y function! --> Y = 200+0.75(Y-100)+1000-25r+100 --> Y = 200+0.75Y-75+1000-25r+100 --> 0.25Y = 200-75+1000-25r+100 --> 0.25Y = 1225-25r --> Y = 4900-100r = THIS is the base equation you'll be plugging the equation for P in! ii. Now find r in terms of P - will use this to plug into Money Side equation! --> Y = 4900-100r --> r = Y-4900/-100 --> r = 49 - Y/100 iii. Equate Ms/P with Md to yield equilibrium Money Market equation! - Recall that L(r,Y)=real Md in Keynesian model! --> Ms/P=0.5Y-100r --> 1000/P=0.5Y-100r iv. Plug r=f(Y) into Money Market equation! (LM) --> 1000/P=0.5Y-100(49-(Y/100)) --> 1000/P=0.5Y-4900+Y --> 1000/P=1.5Y-4900 v. Find P in terms of Y! - Cross multiply terms to simplify: --> 1000/1.5Y-4900 = P - Simplify: --> P = 666.66667/(Y-0.2041) --> This is also equivalent to *a. P=((3/2000)Y-4.9)^-1*! - 1/(3/2000)=666.66667 - 1/4.9=0.2041! --> REMEMBER TO CHECK THE WHOLE PROBLEM! B IS INCORRECT BC 666.67/Y=/=666.67Y! 2) Start with Keynesian output equation: Y=(1/(1-b))(a+i0+G-bT)-(i1r/(1-b))--> NOT given any values from money market side so don't need to use LM equation! --> Assume all other variables=0 i. Recall that b = MPc = 0.7 ii. Recall that a = private consumption; a falls by 150 iii. To find how much Y needs to CHANGE by, take the derivative of Y with respect to a from output equation--> 1/(1-b) = dY/dG iv. Convert this derivative to discrete (change in) equation: changeY/changea = 1/(1-b)--> changeY = changea/(1-b) --> changeY = -150/(1-0.7) --> changeY = -150/0.3 --> Y changes by -500! v. Gov't needs to increase output by 1000+(decrease in output)=1500 to achieve net 1000 increase! vi. Since gov't needs to achieve Y=1500, need to find out how much G needs to increase to achieve 1500! - find derivative of Y with respect to G --> dY/dG = 1/(1-b) v. Convert deriv of Y with respect to G to discrete (change in) equation: changeY = changeG/(1-b) vi. Y value into changeY = changeG/(1-b) to find changeG! --> 1500 = changeG/(0.3) --> changeG = 450!--> *c. $450* 3) DON'T OVERTHINK IT! Just asking for simple IS (Output in terms of r) and LM (Output in terms of M) functions--> ALL YOU NEED TO DO IS A LITTLE SIMPLE ALGEBRA TO FIND Y=f(r) for IS; Y=f(M/P) for LM!!!!!!! - Remember: assume Md and Ms are NOMINAL unless otherwise notified! IS FXN - 从东西(Y)开始！！！！！！: i. Start with Y=C+I+G equation - since you're given values for these equations! Plug all expressions to Y function. --> Y = 1895+0.94(Y-G)+3000-i1r+G--> subbed out T for G bc G=T! --> Y = 4895+0.94Y-0.94G-i1r+G = 4895+0.94Y+0.06G-i1r --> *Y=(4895+0.06G-i1r)/0.06* = Y is a function of r! LM FXN - 从钱(M)开始！！！: i. Convert Md equation to REAL Md by dividing Md equation by P --> Real Md = (0.16Y-100r)/P ii. Solve for Y! --> 0.16Y = MP + 100r --> *Y=[MP + 100r]/0.16* = Y is a function of M!

Exercise 4: 1) Suppose that the aggregate production function for an economy is given by Yt=(Kfixed^a)(Ld^b). Under what conditions will this production function exhibit diminishing returns to capital, but not negative returns to capital? a. 0<a<1 b. a<1 c. a>1 d. a+b=1 2) Suppose that an economy is characterized by a Cobb-Douglas production function and that capital's share of GDP is 1/3. What is the production function? a. Yt=(Kfixed^1/3)(Ld^2/3) b. Yt=(Kfixed^2/3)(Ld^1/3) c. Yt=(Kfixed^1/3)(Ld^1/3) d. Yt=(Kfixed^2/3)(Ld^2/3) 3) What is the labor demand function of the economy mentioned in the previous question? a. Ld = 8/27(Kfixed) x ((w/p)^-3) b. w/p = 2/3(Kfixed^(1/3))(Ld^(1/3)) c. w/p = Kfixed^(1/3)(Ld^(2/3)) d. Ld = w/p 4) Disposable income (Y-T) can be consumed(C) or saved(S). Formally, we have: Y-T=S+C=(s0+s1(Y-T)+s2(r)) + (c0+c1(Y-T)+c2(r)) where r=real interest rate. Let s0,s1,s2,c0,c1,c2 = real numbers. If s0=-c0—which is assumed for simplicity—which one of the following is always true? a. s1 is less than or equal to 0. b. The supply curve of loanable funds is vertical when the quantity of loanable funds is measured on the horizontal axis. c. A unit increase in disposable income, ceteris paribus, leads to c1 units of change in consumption. d. A unit change in tax, ceteris paribus, leads to s1 units of increase in saving. 5) Suppose that you're a classical economist. You're given the following info about economy x: - V=0.5 - M=$1000 - Positive linear relationship btwn labor and output such that 1 unit labor produces 10 units output - There is another positive linear relationship between Ld and the real wage such that Ld = 0.2(w/p) Denote the level of output by Y, and solve for the equilibrium of economy X as a classical economist (hint: start by deriving the AD curve). Which one of the following is false for economy X? a. Equilibrium is characterized by (P,Y) = (25, 20) b. Equilibrium is characterized by (L,W) = (2, 250) c. If the total money supply suddenly and exogenously increases to $2000 when economy X is at equilibrium, this leads to a new equilibrium at which labor supply is higher. d. The slope of the AD curve is not constant.

1) Recall cobb douglas fxn: Yt=(Kfixed^a)(L^(1-a)) Diminishing returns to capital = when 0<a<1 Increasing returns to capital = when a>1 Negative returns to capital = when a<0 Positive returns to capital = when a>0 --> *a. 0<a<1* 2) Recall for cobb douglas fxns that exponents must add up to 1! --> Yt=(Kfixed^a)(L^(1-a)) --> K share = 1/3; L share = necessarily 2/3 (1-1/3) --> *a. Yt=(Kfixed^1/3)(Lf^2/3)* 3) Previous question (prod fxn): Yt=(Kfixed^1/3)(Lf^2/3) - Recall that MPl = w/p - Recall that MPl = w/p = dY/dL - Want Ld=f(w/p)--> only requires 2 steps: find w/p, isolate Ld! i. Take dY/dLd to get w/p which contains Ld in the equation! --> Bring over exponent of Ld to front of the function; subtract exponent 2/3 - 1 (just derivative stuff) --> 2/3(Kfixed^1/3)(Ld^[2/3-1]) --> 2/3(Kfixed^1/3)(Ld^-1/3) - This is equal to MPl = w/p! --> w/p = 2/3(Kfixed^1/3)(Ld^-1/3) - 别多想！ ii. Isolate Ld to find Ld=f(MPl) or Ld=f(w/p) - Divide both sides by Ld^-1/3: --> (MPl)(Ld^1/3) = 2/3(Kfixed^1/3) - Divide both sides by w/p --> Ld^1/3 = [2/3(Kfixed^1/3)]x((MPl)^-1) --> Keep w/p in its current form, p/w has no meaning! iii. Simplify: - Cube each side to get rid of exponents - this means every variable gets cubed! --> [Ld^1/3]^3 = [[2/3(Kfixed^1/3)]x(MPl^-1)]^3 --> Since MPl=w/p, the answer is *a. Ld = 8/27(Kfixed) x ((w/p)^-3)* 4) Aggregate disposable income = Y-T (national income - national taxes) --> Assume that savings = s0+s1(Y-T)+s2(r); consumption = c0+c1(Y-T)+c2(r) --> Y-T = S+C = (s0+s1(Y-T)+s2(r))+(c0+c1(Y-T)+c2(r)) - In this case, disposable income=y-axis; interest rate=x-axis - This means that s2 and c2 are slopes of the supply curve! - s1 and c1 = units change in savings and consumption, RESPECTIVELY, when Y-T increases by 1 unit! --> If s0=c0, is a, b, c, or d true? i. Debunk/confirm a. --> s2(r) = saving's relationship to interest rate; r=x and --> s2 is not necessarily 0 - in general, saving can be positive depending on interest rate (if interest rate is higher = savings is higher (incentive to keep savings in pocket)) --> a. is false! ii. Debunk/confirm b. --> s2 and c2 = slopes of supply curve; not necessarily = undefined (x/0), as is necessary for a vertical curve! --> without restrictions placed on s2 and c2, this is false! --> b. is false! iii. Debunk/confirm c. --> Unit increase (Y-T) AKA disposable income = c1 units CHANGE in consumption --> s1 and c1 denote the unit change per 1 unit increase in Y-T for savings and consumption, respectively! --> Thus, 1 unit increase in disposable income = c1 units change in consumption! (would also mean = s1 units change in savings!) --> *c. is correct!* iv. Debunk/confirm d. --> Unit change in tax = s1 units INCREASE in savings? --> This would depend on whether tax is positive or negative! - not given in d. --> ie: 1 unit increase in T = s1 units change in savings--> as 1 unit INCREASE in T = 1 unit decrease in (Y-T) = s1 units change in savings! --> d. is false! 5) Classical AD formula = dealing with P(y-axis) and Y(x-axis) --> P=xY Classical AS formula = dealing with Y(y-axis) and L(x-axis) --> Y=xL - REALISTICALLY, ONLY NEED TO DEAL WITH AD AND Ld EQUATIONS HERE! - IF IT DOESN'T DEAL WITH VARIABLES IN FORMULA, DON'T NEED TO DERIVE THE FORMULAS! i. Derive demand function from QTM, MV=PY! --> M=1000; V=0.5; P=?; Y=? --> 1000x0.5=PY--> 500=PY --> *AD: P=500/Y* ii. Derive supply function from MPl=w/p equation! (MPl = w/p (real wages) = 10) --> Given that MPl = 10; 1 L = 10Y --> Thus, *AS: Y=L/10* iii. Debunk/confirm a. --> AD: P=500/Y --> Equilibrium is when P=25; Y=20 --> a. is true! iv. Debunk/confirm b. - JUST DEALS WITH LD EQUATION! --> Ld = 0.2(w/p) - Recall that P=25, from (a) - Just plug in values of (b) to confirm or deny! --> 2=0.2(250/25)--> 2=2! --> b. is true! v. Debunk/confirm c. - If M rises = PY rise (p x output) = AS increases = actual labor supply of equilibrium decreases --> *c. If the total money supply suddenly and exogenously increases to $2000 when economy X is at equilibrium, this leads to a new equilibrium at which labor supply is higher is false = the answer!* --> Increased M=increased P--> L=0.2(w/p), increased P=decreased L! vi. Debunk/confirm d. - AD slope is NOT constant! Changes with every movement. --> d. is true!

Exercise - 06/10/19 1) (An expansionary tax policy) Imagine an economy described by the following: C=a+b(Y-T) T=t0+t1Y I=Ifixed-i1r G=Gfixed L(Y,r)=c0+c1Y - c2r Ms=Mfixed In this economy, the price level is perfectly sticky and normalized to unity: P=1. The economy is initially in its ISLM equilibrium, and the policy maker of this economy has a given target of changeY>0, ceteris paribus. Find the sensitivity of income to a change in the fixed amount of the tax function (t_0). What is the sign of change? 2) (The multipliers revisited) Consider the simple Keynesian cross model. The consumption founction and the tax revenue are defined as: C=a+b(Y-T) T=t0+t1Y where b is between 0-1, t0>0 is the lump sum tax, and t1 (between 0-1) is the marginal income tax rate. Assume that the private investment I and the gov't expenditure G are exogenous. *Definition: the fiscal multiplier is the ratio of a change in national income to the change in gov't spending that causes it. Find the fiscal multiplier - that is, the sensitivity of income to a change a in the gov't spending.

1) Recall that Y=C+I+G - Solve for r in the goods and money markets - then get an EQUILIBRIUM IS=LM expression for Y=f(t0) - FOR EQUILIBRIUM YOU CAN'T JUST PLUG! MUST FIND EQUILIBRIUM EQUATIONS! - Want to find change in Y in ISLM equilibrium! - Then take dY/dt0! GOODS MARKET (IS): i. Plug in given equations to Y=C+I+G --> Y=a+b(Y-(t0+t1Y))+Ifixed-i1r+G ii. Group rs and Ys together (since they're what we're solving for!) --> ilr=a-bt0+Ifixed+G-Y[1-b+t1b] --> r={a-bt0+Ifixed+G-Y[1-b+t1b]}/i1 MONEY MARKET (LM): i. Equate Md and Ms (Md=L(Y,r); Ms=M*) and solve for r! --> (c0+c1Y-c2r) = M --> r=(c0+c1Y-Mfixed)/c2 IS=LM EQUILIBRIUM: i. Equate r equations from IS and LM! --> (c0+c1Y-Mfixed)/c2 = {a-bt0+Ifixed+G-Y[1-b+t1b]}/i1 ii. Isolate rs and Ys together (to get Y=f(x)) --> Y[1-b+tlb+c1/c2] = {[a-bt0+Ifixed+G-Y[1-b+t1b]]/i1} - c0/c2 + Mfixed/c2 --> Y = [{[a-bt0+Ifixed+G-Y[1-b+t1b]]/i1}-c0/c2+Mfixed/c2]/[1-b+tlb+c1/c2] --> {[a-bt0+Ifixed+G-Y(1-b+t1b)]/i1}-c0/c2+Mfixed/c2]/[1-b+tlb+c1/c2] iii. NOW, take dY/dt0 to find sensitivity of Y(national income) to change in taxes! THIS IS YOUR TAX MULTIPLIER! --> *dY/dt0 = -b/[ilc1/c2 +1+b(1+t1)]* = TAX MULTIPLIER! - *Sign of the change = negative!* --> changeY = [changet0] x [-b/[ilc1/c2 +1+b(1+t1)] 2) Want sensitivity of Y to G--> need dY/dG - Recall that Y=C+I+G - NO money market! - only for how Y changes in the goods market! i. Plug all given equations into Y equation, simplify for Y=f(G) --> Y=a+b(Y-(t0+t1Y))+I+G --> Y(1-b+bt1)=a-bt0+I+G ---> Y=[a-bt0+I+G]/[1-b(1+t1)] ii. Find dY/dG to find sensitivity of Y to change in G! --> *dY/dG = 1/[1-b(1+t1)]* = FISCAL SPENDING MULTIPLIER! --> *Sign of change = positive!* --> changeY = changeG/[1-b(1+t1)]

CHAPTER 5: LUMP SUM TAX REDUCTION IN CLASSICAL VS. KEYNESIAN MODELS 1) What is the Ricardian equivalence? a) What is the lump sum tax reduction effect on consumption/savings in the classical model WITHOUT Ricardian equivalence? Graph. b) What is the lump sum tax reduction effect on consumption/savings in the classical model WITH Ricardian equivalence? Graph. 2) What is the lump sum tax reduction effect on consumption/savings in the Keynesian model? a) What is the mathematical equation for determining change in lump sum tax reduction effect? (tip: Y=f(x))

1) Ricardian equivalence - laissez faire incorrect rationalization LMAO; gov't cannot stimulate consumer spending! - Economic theory - when gov't tries to stimulate an economic by increasing debt-financed gov't spending (ie. bonds)... i. Taxes go down ii. Gov't debt goes up iii. Gov't pays off debt by increasing future taxes iv. Everyone is perfectly informed and perfectly rational, thus consumers save excess money to pay for expected future tax increases that gov't will use to pay off its debt v. Thus, demand remains unchanged! CONCLUSION: GOV'T INTERVENTION BAD LAISSEZ FAIRE/CAPITALISM GOOD a) WITHOUT Ricardian equivalence: Taxes decrease = total taxes decrease = consumption increase = savings decrease --> Graph: x-axis=S,I; y-axis=r --> I=downward sloping; S=upward sloping --> S1 shifts left to S2 = r increases/S,I decreases b) WITH Ricardian equivalence: Total taxes decrease = future taxes increase = no change in consumption --> Graph: x-axis=S,I; y-axis=r --> I=downward sloping; S=upward sloping --> No change in either! 2) Recall the IS graph: x-axis=Y (output); y-axis=consumer expenditure - Expenditure (IS) curve = flat, upward sloping - 45 degree equilibrium line i. Decrease in lump sum tax = increase in consumption ii. Expenditure shifts upward = increased output, increased expenditure! a) MATHEMATICAL PROOF: - E=C+I+G - C=a+b(Y-T) - T=t0+t1Y i. Sub in formulas to E! --> E=a+b(Y-(t0+t1Y))+I+G ii. Simplify! --> *Y=[a-bt0+I+G]/[1-b(1-t1)]*

1) What is wealth equal to? 2) What are 3 motives for holding onto money? 3) What is a bond? 4) What is the equation for price with respect to the bond market? 5) What is the money demand function (graphing+mathematical)? 6) Equilibrium for money demand and money supply? 7) Classical LM curve? 8) What is a liquidity trap? 9) Describe the liquidity graph and its connection to the LM graph. 10) Describe real Ms and interest rate graph.

1) Wealth = Money + Bonds (assumption that carries over to portfolio approach in int'l econ!) 2) 3 motives: i. Transactions - need to buy goods/services in the future (education, retirement, etc.) ii. Precautionary purposes - what if the economy tanks, or I lose my job? iii. Speculative purposes - will it be worth more in the future? will it be better used in the future? 3) Bond - loan made by investor to borrower (low risk) 4) P with respect to bond market = future value [of bond]/(1+r)^m --> Increase in interest rate = decrease in prices! 5) GRAPH EQUATION: Md = L(r, Y) --> L = nominal Md MATHEMATICAL EQUATION: Md = c0+c1Y-c2r 6) In equilibrium: Md=Ms=M - Md = c0+c1Y-c2(r) i. Solve for c2r! --> c2(r) = c0+c1Y-M --> r=c0/c2 + c1/c2(Y)-1/c2(M) 7) Classical LM curve assumptions: - LM = relationship between liquidity preference and Ms --> How much cash you want to hold and how much money is in the system - Md=c0+c1Y-c2r - c2=0 - We are in equilibrium! i. LM curve = vertical ii. r=y-axis; Y=x-axis --> Y=(M-c0)/c1o 8) Liquidity trap - central bank keeps raising Ms AKA liquidity of economy, but can't get out of recession --> bc consumers keep on holding onto money! --> Only applicable to recessions i. No matter how much interest rate drops and real cash supply becomes = you still want to hold onto money BC they expect that following such low interest rates, the only direction for interest rates to move is up - which will devalue their bonds! ii. At low levels of r, Fed convinces households to buy their bonds - households feel that bonds they buy today will be worth less in the future 9) Liquidity graph connects to LM curve Sensitivity of consumer's demand for money is very high --> CONSUMERS WILL STILL HOLD MONEY AT VER LOW LEVELS OF OUTPUT/NATIONAL INCOME! 10) Ms = constant Recall that real Ms = Ms/P! - r=x-axis; Ms/P=y-axis i. Downward sloping curve = L(r,Y) --> Increase in L(r,Y) = increase in r ii. Ms/P = vertical curve --> Increase in Ms/P = decrease in r

FLEXIBLE NOMINAL PRICES AND FLEXIBLE NOMINAL WAGES! 1) a) Draw the flexible wage-labor graph. Describe elements. b) Draw the output-labor graph. Describe elements. c) Draw the SRAS graph. Describe elements. d) How does increase of prices affect fixed wage system vs. flexible wage system? e) Does supply curve matter in flexible system?

1) a) i. y-axis = nominal wages ii. x-axis = Qlabor b) i. y-axis = output ii. x-axis = Qlabor c) i. y-axis = nominal P ii. x-axis = output d) Increase of prices = decrease in REAL wages = increase in Ld... i. Fixed wage system = has HIGHER increase in output --> All wages are fixed, so decrease in P undoubtedly decreases real wage = labor demand increases for sure! - While in flexible system, if nominal wages increase by P decreases, direction of real wage not as sure = labor demand increase not as sure/or increases by less! --> Effect on employment is HIGHER in fixed system ii. Flexible wage system = has LOWER increase in output e) Yes - Ls curve DOES matter in flexible system! --> NOMINAL wages/prices are FLEXIBLE, making supply curve affect flexible i. Increase in Ld = increase in nominal wages = increase in output = increase in labor

FIXED NOMINAL PRICES AND FIXED NOMINAL WAGES! 1) a) Draw the flexible prices/fixed wage labor market b) Suppose prices increase. Graph the effects of this on Ld and output. (draw the wage-labor and output-labor graphs). c) When prices increase, what happens to real wages, Ld, wages', and output? d) What is the SRAS curve? Define x and y-axes. e) Does the supply curve matter for labor in the fixed system? 2) What are the 2 types of labor contracts within Keynesian nominal sticky wage system? 3) What is the Keynesian Ls function? 4) What is Pt*e? i. What does Pt mean? ii. What about Pt-1? iii. What about Pt-2?

1) a) THIS IS ALL NOMINAL! i. y-axis: fixed nominal wages ii. x-axis = Qlabor iii. Ld = MPl x P --> Downward sloping b) NOMINAL wages DON'T change, but increase of P results in decrease of REAL WAGES (AKA purchasing power) = Ld curve shifts right (cheaper to hire more labor) i. Ld0 = Qlabor0 (old equilibrium) ii. Ld1 = Qlabor1 (new equilibrium, > Qlabor0) Move from wage-labor graph to output-labor graph! (draw it below wage-labor graph, as a continuation of vertical Qlabor lines 0 and 1) - y-axis = output (Y) - x-axis = Qlabor - Upward sloping curve i. Qlabor0 = lower output due (Y1) to lower labor (relatively) ii. i. Qlabor 1 = higher output (Y2) due to higher labor c) P increase = real wage falls = cheaper to hire workers, Ld RISES! = increased L = increased output. --> Nominal wage DOESN'T CHANGE in sticky wage system! Real wage changes, but that's a matter of purchasing power d) SRAS = Short Run Aggregate Supply Curve. i. y-axis = Prices ii. x-axis = output --> Shows that increase in P = increase in output (circa econ 101) e) No - since nominal prices/wages are STICKY/fixed, supply curve does not affect labor in the fixed system. 2) Two types of labor contracts within Keynesian sticky wage system: i. Institutional labor contracts (ON PAPER) - labor unions negotiate and set contractual wage for an amount of time (6 mtts, year, etc.) with firms ii. Implicit labor contracts (VERBAL) - verbal negotiation to set and establish wage for an amount of time 3) Ls=f(w/P^e) = Keynesian labor supply function --> wages/expected prices --> Also a function for expected real wages! 4) Pt^e = wt1Pt+wt2Pt2+...wtnPtn --> wtn = specific weight on specific day's price --> Ptn = a specific day's price! i. Pt = today's price ii. Pt-1 = yesterday's price (price from 1 period prior) iii. Pt-2 = day before yesterday's price (price from 2 periods prior)

Exercise 1 - 05/15/19 1. Consider the demand function: Qd=a0+a1P a. Interpret the economic meaning/sign of parameter a0 b. Interpret economic meaning/sign of parameter a1 c. Compute/plot demand curve d. Identify slope/y-intercept of demand curve 2. Consider the demand function: Qs=b0+b1P a. Interpret the economic meaning/sign of parameter b0 b. Interpret economic meaning/sign of parameter b1 c. Compute/plot supply curve d. Identify slope/y-intercept of demand curve 3. Find the equilibrium price and quantity from the S and D curve described above. 4. Identify the parameter that changes in order to facilitate a leftward parallel shift in the supply curve. Identify the direction of change in that parameter and describe what happens to the equilibrium values of price and quantity. 5. We will now work with partial derivatives: 6. Sensitivity Analysis: Consider the D/S specifications from Q1 and Q2. a. How sensitive is the equilibrium price of 1 unit change in b0? b. Suppose b0 drops by 2 units. By how much will the equilibrium price change? 7. Expand the object E3/i-1^xi 8. Expand the object E2/i=1^xi 9. Find the solution Einf/i=1^xi where |x|<1

1) a) a0=constant (can be positive or negative) --> Should this be positive or negative? - a0=Qd if P is 0 —> a0=positive b) a1=slope of demand curve (can be positive or negative) --> How demand changes with respect to price --> For every 1 unit increase in P, Qd decreases by 1 unit of a1 c) Downward sloping d) y=mx+b form of Qd function: P=(1/a1)Qd-(a0/a1) - Slope = 1/a1 --> a1 is negative! (from law of demand) - Y-intercept = -a0/a1 - Since a1 is negative, y-intercept is POSITIVE! (-a0/-a1) 2) a) b0=constant (can be positive or negative) --> Should this be positive or negative? --> b0=Qd if P is 0 —> b0=positive b) b1=slope of supply curve (can be positive or negative) --> How supply changes with respect to price --> For every 1 unit increase in P, Qs increases by 1 unit of b1 c) Upward sloping d) y=mx+b form of Qs function: P=(1/b1)Qs-(b0/b1) --> EXAMPLE: at origin of (0,0), b0=0 but b1=/=0 as that would make the y-intercept undefined - Slope = 1/b1 --> b1 is positive! (from law of supply) - Y-intercept = b0/b1 --> Since b1 is positive, y-intercept is NEGATIVE! (-b0/b1) 3) Equilibrium when Qd=Qs —> a0+a1P=b0+b1P —> P=[(b0-a0)/(a1-b1)] --> ALWAYS START WITH Qd=Qs, find it in terms of P (as P can be merged first!) and then plug back into D and S functions to find equilibrium quantity! --> NOW PLUG BACK INTO Qd AND Qs FUNCTION = should be equal to both Qd and Qs --> *Qd=a0+a1[(b0-a0)/(a1-b1)]=Qs* 4) When b0 falls below 0 = causes supply to shift leftwards 1. Assumptions: 1. b1=positive (based on law of supply) 2. y-intercept=-b0/b1 3. If y-intercept increases=supply shifts left 4. Since b1 is necessarily positive if b0 becomes negative that makes -(b0/b1) POSITIVE! = increase = leftward shift of supply - P increases, Q decrease 5) a) Partial derivative of a0+a1P —> a1 (bd/bf(constants) = 0) b) Derivative of a0+a1P^2 —> take 2 down so it's 2a1(P^(2-1) = 2a1P c) Derivative of a0+a1X(P) OR a0+a1eP = a1e --> Remember that X is FUNCTION - need to convert to constant first! 6) a) Just asking for derivative - derive with respect to b0 in Qs equation --> P=[(b0-a0)/(a1-b1)] —> distribute b0 and a0=[(b0/(a1-b1))-(a0/(a1-b1))]—> fraction w/o b0 is cancelled by derivative; derivative of [b0/(a1-b1)]=[1/(a1-b1)] --> Sensitivity = [1/(a1-b1)] b) Convert to discrete equation from p[(b0-a0)/(a1-b1)] 1. Change in P/Change in b0 = (1/(a1-b1)) 2. Move b0 to other side, wants to know how P changes as b0 moves 3. b0 drops by 2 units so b0=-2b 4. End up getting (-2b/(a1-b1)) 5. Derivative of (-2b/(a1-b1)) = [-2/(a1-b1)]! 7) = x1+x2+x3 8) =(x1+x2)(y1+y2) 9) Never went over in class

Suppose there is a shock that increases government spending. What happens to the IS, LM, and IS-LM graphs? Make sure to include both a mathematical and graph explanation.

1) https://drive.google.com/open?id=1y2ruP2PSRbNvxwZWincOv6eG63ehkqzf Shock to G - increase most likely: a) IS effect i. IS equilibrium equation: Y*=[a+i0-bT+G+(i1/c2)(M-c0)]/[(1-b)+ c1i1/c2] --> dY/dG = 1/[(1-b)+ c1i1/c2] --> Increase G = increase Y; decrease G = decrease Y ii. IS Graph = exp-output graph: - exp=y-axis; Y=x-axis - Expenditure = flat upward sloping curve - 45 degree equilibrium curve --> *Exp curve overshoots from E(r1, G1) to E(r1, G2) then settles down at a point below E(r1, G2) yet above E(r1, G1) at E(r2, G2)* --> *Expenditure and output follow this overshooting and then settling* b) LM effect i. LM equilibrium equation: r*=[((1-b)/c2)(c0-M)+ c1/c2 (a+i0+G-bT)]/[(1-b)+ c1i1/c2] --> dr/dG = [c1/c2]/[(1-b)+ c1i1/c2] ii. LM Graph = real money-interest rate graph - interest rate=y-axis; real money=x-axis - Ms = vertical curve - Md = downward sloping curve --> *Md curve increases/shifts right as result of shock to G* --> *Interest rate increases from r1 to r2!* c) IS-LM interaction Graph = how investment savings and money liquidity interact! --> IS curve: Y*=[a+i0-bT+G+(i1/c2)(M-c0)]/[(1-b)+ c1i1/c2] --> LM curve: r*=[((1-b)/c2)(c0-M)+ c1/c2 (a+i0+G-bT)]/[(1-b)+ c1i1/c2] - y-axis=interest rates - x-axis=output - *IS curve, rises from IS(G1) to IS(G2)* - *Output and interest rates behave as shown in the LM and IS graphs!* 2) IS=downward sloping; LM=upward sloping a) IS decreases/shifts left = AD decreases/shifts left b) IS decreases/shifts left = AD decreases/shifts left c) IS decreases/shifts left = AD decreases/shifts left d) LM decreases/shifts left = AD decreases/shifts left e) LM decreases/shifts left = AD decreases/shifts left 3) Increase in G= IS curve increases/shifts right --> From Y1 to Y2! Perfectly sticky prices = AS curve is horizontal line --> AD increases (increasing Y from Y1 to Y2) - increase matches the output increase from IS shift!

HW 1 (pt. II): 5) Consider the Classical model from class. Which of the following would make the aggregate demand curve flatter? A. A technological breakthrough that decreases production costs. B. A decrease in the velocity of money due to companies paying on a monthly rather than bi-weekly basis. C. A plague epidemic decreases size of labor force. D. An increase in money in circulation due to the buying of bonds by the Federal Reserve Bank. 6) Consider classical model with following assumptions: - Ls=x(w/p) - CB prod function - QTM accurately describes AD - Theory of distribution holds as accurate [x, a, A, K, M, V]=[30, 0.3, 100, 700, 3000, 40] Find the approximate equilibrium output level: a. Y= 98,865.24 b. Y= 113,183.13 c. Y= 126,476.40 d. Y= 142,163.06 ?7) Consider the classical model described in previous question. Suppose the economy experiences a negative technology shock and technology level goes down by 3. Find the approx level of inflation: a. 4.62% v. -4.62% c. 9.62% d. -9.62% 8) Consider a classical economy with the following characteristic: - Investment fxn: I=i0-i1(r)+i2(IC) - where IC=investor confidence - Consumption fxn: C=a+b(Y-T)-cr - All model parameters are positive Suppose that the investor confidence (IC) has increased. How does this change in IC affect the classical model? Be sure to mention what happens to Y, N, P, r, C, S, PrS, PuS. Note: Assume that change in investment does not impact the capital stock. Written discussion and/or graphs are required.

5) Recall that AD curve: P=MV/Y i. Slope = deriv of P with respect to Y (target variable!) = deriv(P)/deriv(Y)--> --> derivP/derivY = (-1MV)/Y^2 = slope --> ALWAYS RMR TO MOVE EVERY TERM TO THE NUMERATOR IF DEALING WITH A FRACTION PRIOR TO DERIVATIVE!! ii. What will reduce ABSOLUTE VALUE of slope of AD curve? --> Decrease in M, V = absolute value of slope becomes smaller! --> Increase in Y (income/output) = ab`solute value of slope becomes smaller! --> *B. A decrease in the velocity of money due to companies paying on a monthly rather than bi-weekly basis.* 6) Need to find Y (output level) which is = to AK^aL^(1-a), but don't have the value for L. Find L first! LABOR SIDE: i. Solve for Ls by finding Ld first! Recall that Ld=w/p=MPl=derivative of CB function (AK^aL^(1-a)) --> (1-a)AK^aL^-a = Ld = w/p = MPl ii. Recall that Ls = gamma(w/p)--> plug derived CB MPl into Ls! --> gamma[(1-a)AK^aL^-a] = Ls = L in general iii. Isolate L on one side - move L ^-a to other side! - ALWAYS ISOLATE TARGET VARIABLE TO 1 SIDE --> [gamma(1-a)AK^a]/L^-a = L/L^-a --> Recall that 1/L^-a = L^+a/1! --> [gamma(1-a)AK^a] = L^(1+a) iv. Get rid of ^(1+a) by raising both sides to the ^[1/(1+a)]! --> [gamma(1-a)AK^a]^[1/(1+a)] = [L^(1+a)]^[1/(1+a)] --> [gamma(1-a)AK^a]^[1/(1+a)] = L v. Now plug L into CB function (Y=AK^aL^(1-a))! PRODUCTION SIDE: i. Plug L into output CB function!: --> Y = AK^a[(gamma(1-a)AK^a)^(1/(1+a))]^(1-a) ii. Recall the parameter values - just plug the parameter values into this equation to get the approximate equilibrium output level! --> Y = [(100)(700^0.3)][[(30(0.7)(100)(700^0.3)]^(1/(1+0.3)]^(1-0.3) = (713.722539376)[[14988.1733269]^(1/1.3)]^0.7 --> Y = 126476.396924 ~= *c. 126476.40* 7) Recall that Inflation rate = (new price-old price)/old price - WON'T BE ON EXAM! --> Inflation = movement of prices--> deals with QTM! i. Recall that QTM is MV=PY ii. As inflation primarily deals with the movement of prices, isolate P to one side! --> P=MV/Y iii. A = variable for technology; recall that A = 100 from (6). A decreases by 3, making A in (7) = 97-100=-3! iv. Plug expression for Y from (6) into P=MV/Y! --> P = MV/{(AK^a)[gamma(1-a)AK^a]^[1/(1+a)]^(1-a)} v. Take derivP/derivA --> to find amount P changes PER 1 unit A --> First, combine As thru multiplication in the equation: REMEMBER THAT AK^a MEANS a IS THE EXPONENT FOR K, *NOT* A!!!!!!! IT'S NOT DISTRIBUTED! - MV/all other constants x [(A^(1/(1+a)))^(1-a)]x[A^1] = A^[((1-a)/(1+a))+(1+a)/(1+a))] = A^[(2)/(1+a)] --> Second, move A to the top; exponent becomes negative (all other variables are constants so leave them alone): P = [MV x A^(-2/(1+a))]/{(K^a)[gamma(1-a)K^a]^[1/(1+a)]^(1-a)} --> Next take the derivative of A!: {[-2/(1+a)]MVA^[(-2/(1+a))-((1+a)/(1+a))]}/all other constants --> Simplify: {[-2/(1+a)]MVA^[(-3-a)/1+a)]/{(K^a)[gamma(1-a)K^a]^[1/(1+a)]^(1-a)} --> changeP = {[-2/(1+a)]MVA^[(-3-a)/1+a)]/{(K^a)[gamma(1-a)K^a]^[1-a/(1+a)] x changeA --> okay to just leave function as answer here; focus is on work moreso than answer! v. Now, plug all parameter values (changeA=new-old=97-100=-3 now) into this formula! --> 0.01459682 x -3 = -0.04379046 x 100 = -4.379046% --> Closest to *b. -4.62%* v. Recall that inflation rate = (new price-old price)/old price - new A=97; old A=100 vi. Plug all numbers into P equation using the old A value! - old A = 100 --> (3000x40)/{100x700^0.3[(30x(1-0.3)100x700^0.3)^(1/1.3)]^(0.7)} = 120k/126476.39692413 = 0.94879363 = Old P vii. Plug all numbers into P equation using the new A value! - new A = 97 --> (3000x40)/{97x700^0.3[[30(1-0.3)97x700^0.3]^(1/1.3)]^0.7} = 120k/[(14538.53)^(1/1.3)]^0.7 =120k/120686.39279168 = 0.99431259 = New P v. Plug values for New P and Old P into inflation equation - (New P - Old P)/Old P --> (0.99431259-0.94879363)/0.94879363 = 0.04797561 = 4.79756% =~ *a. 4.62%* 8) Recall that S = I in classical model! - Y=income; N=labor; P=price; r=interest rate; C=consumption; S=savings; PrS=private savings; PuS=public savings Increase in IC LEADS TO... i. *Increase in interest rates (r)* --> Increase in investor demand (since all model parameters are positive!) = increase in interest rates ii. *Increase in PrS (PrS)* --> Increase in interest rates = priv savings increase iii. *Decrease in consumption (C)* --> PrS increase = consumption decreases (you either save OR eat with income) iv. *No change in PuS (PuS)* --> Since we're not told anything about taxes of changes in gov't spending v. *Increase in general S (S)* --> Since S = PrS+PuS and PrS increases, while PuS stays constant vi. *No change in output (Y)* --> Y = C+I+G+NX; not told anything about G or NX so Y = C+I in this case! --> Since change in investment exactly = change in savings (5% decrease in investment = 5% increase in savings in Classical model), Y doesn't change! vii. *No change in labor (L)* --> Since we're not told about a change in prices or wages, L doesn't change! viii. *No change in prices (P)* --> Since we're not told about a change in prices, there is no change in prices LMAO

1) How do you connect the investment savings (Is) graph with the r graph? 2) Equilibrium of LM curve for interest rates vs. Is expression for interest rates

Derive Is curve from Keynesian supply equation: Y=(1/1-b)(a+i0+G-bT)-(i1r)/(1-b) --> Solve for r to derive Is expression for interest rates equation! Is expression for interest rates: r = 1/i1[a+i0+a-bT]-(1-b/i1)(Y) 2) Equilibrium of LM curve for interest rates + Is expression for interest rates i. Recall that LM curve for interest rates is r=(c0/c2) - (1/c2)(M)+(c1/c2)(Y) ii. Is curve for interest rates is r = 1/i1[a+i0+a-bT]-(1-b/i1)(Y) iii. 1/i1[a+i0+a-bT]-(1-b/i1)(Y) = (c0/c2) - (1/c2)(M)+(c1/c2)(Y) iv. Solve for Y

MONEY: 1) What is Money? 2) What are the 3 components of Money? 3) What constitutes "savings"? 4) What is monetary policy? 5) What are its 3 goals? 6) What are the 3 tools of monetary policy? 7) What is the Required Reserve Formula? 8) What is the monetary base formula? 9)What is the impact of MP on money supply? MONEY MULTIPLIER: 1) What is the deposit multiplier formula? 2) What is the deposit multiplier's relation to the bank reserve rate? 3) What is the money multiplier equal to? 4) Simplifying assumption that allows for the money multiplier? 5) What is C/D? TAYLOR RULE: 1) What is the Taylor Rule? Define variables and formula.

MONEY: 1) Money = medium of exchange; store of value; unit of account 2) 3 components: i. Currency(C) or cash ii. M1 = cash + checkable deposits = C+D iii. M2 = M1+savings 3) Savings = broad term for "neare money" --> Mutual funds, time deposits=can be quickly converted to cash 4) Monetary Policy = what is the central bank does to affect interest rates/credit in the economy --> INFLUENCE DEMAND! 5) 3 goals: i. Promote maximum employment ii. Stabilize prices iii. Moderate long term interest rate 6) 3 tools: i. Discount rate - interest rate charged by Fed to depository institutions on short term loans ii. Reserve Requirement - % of deposits that banks are required to maintain in their vaults/on deposit at a Fed iii. Open Market Operations - buying/selling gov't securities to change the Ms 7) Required Reserves Ratio: --> rrd = Reserve/Deposit = R/D 8) Monetary Base Formula: --> MB = C+R - Cash + Reserves 9) Impact of MP on Ms--> higher interest rate = lower Ms; lower interest rate = higher Ms MONEY MULTIPLIER: 1) Deposit multiplier = changeD/changeR = change in deposits/change in bank reserves 2) rr = bank reserve rate changeD/changeR = 1/rr 3) Money Multiplier = changeMs/changeMB --> = changeD/changeR = = 1/rr 4) Cash is fixed 5) C/D = cash/deposits TAYLOR RULE: 1) Taylor Rule = formula for deciding what interest rate should be *it = r^+ n^ + qx[nt-n^]+qy[Yt-Ytf]* it = target interest rate r^ = natural rate of interest n^ = natural rate of inflation qx, qy = some coefficient nt = today's interest rate Yt = today's output Ytf = today's output under full employment

Exercise - 06/14/19 Assume the economy under investigation abides by an RBC structure with the following specifications: i. Yt=F(Kt,Nt)=Zt(Kt+Nt) ii. N^=2 for all t (N^ is the equilibrium level of employment) iii. It=sigma(Yt) iv. Kt+1=It+(1-S)Kt v. Z=2 for all t What is the effect of a current period capital shock (Kt) on Yt+1? Consider only the supply side of the system in your answer. a) 2(1-S) b) 4sigma+2(1-S) c) 4sigma-2S d) 2-4S

RBC structure with equilibrium - must use EVERY equation that has Kt and Yt in it, to ensure you have ALL possible Kts in equation! - Looking for dYt+1/dKt i. Iterate forward for Yt to get Yt+1! --> Yt+1 = Zt+1(Kt+1 + Nt+1) --> Yt+1 = Zt+1(Kt+1) + Zt+1(Nt+1) ii. Sub in equation for Kt+1 into Yt+1 equation --> Yt+1 = Zt+1[It+(1-S)Kt] + Zt+1(Nt+1) iii. Sub in equation for It into Yt+1 equation - Have to plug in bc It equation has a Yt in it, and Yt has a K in it! --> Yt+1 = Zt+1[[sigma(Yt)]+(1-S)Kt] + Zt+1(Nt+1) iv. Sub in equation for Yt into Yt+1 equation --> Yt+1 = Zt+1[[sigma(Zt+1(Kt+1) + Zt+1(Nt+1))]+(1-S)Kt] + Zt+1(Nt+1) v. Simplify/sub in Z=2! --> Yt+1 = 2{[sigma(2(Kt+1) + 2(Nt+1))]+(1-S)Kt} + 2(Nt+1) vi. Take dYt+1/dKt --> dYt+1/dKt = 2[2sigma+(1-S)] --> 4sigma+2-2S = 4sigma+2(1-S) *b) 4sigma+2(1-S)*

Exercise - 06/11/19 MONETARY POLICY: - Consider an economy with a standard money demand specification L=a0+a1Y-a2r where a0, a1, a2=6.25, 0.2, 5; Real GDP = 50k, i1=0, nominal Ms=10k, and the price level is fixed at 1. In addition, the demand for reserves is given by FFR=alpha0-alpha1(QR), where QR = quantity of reserves demand., with alpha0, alpha1=250,2; and the supply of reserves is 124.875. The required reserve ratio in this economy is 10% and the standard deposit-based money multiplier describes appropriately the money market. - Suppose the monetary authority wises to raise the interest rate r by 10 basis points. [Note: a basis point is one hundredth of a percentage point. For example, and increase from 1.00 to 1.10 is a rise of 10 basis points.] a) Which of the actions below would accomplish the central bank's goal? Moreover, which is an accurate depiction of the new interest rate r after the policy action? a) Sell 0.5 bonds, new r=1.15 b) Sell 0.05 bonds, new r=1.35 c) Purchase 0.5 bonds, new r=1.15 d) Purchase 0.05 bonds, new r=1.35 b) What is the change in FFR?

Recall that SR=DR=1/a1(a0-FFR) Recall that simple money multiplier (m) = changeD/changeR = changeMs/changeMB = 1/rrd - SR=125.875 - Ms=10k - Md=L=6.25+0.2Y-5r - RGDP=50k - Ms=10k; P=1--> Ms/P=10k - FFR=250-2(QR) - alpha0=250; alpha1=2 - rrd=10%=changeD/changeR a) Asking for changeMB(determines amount bonds Fed must buy/sell), new r! i. Derive r0 from Ms=Md equation! - Ms=10k; Md=6.25+0.2Y-5r; RGDP=Y=50k --> 10k=6.25+0.2(50k)-5r --> r0=0.0125=1.25% - *Since Fed wants to raise r by 10 basis points = 0.01x10 points, r1 = 1.35%!* ii. Now, find changeMs when interest rate (r) changes from 1.25 to 1.35! - Take dMs/dr: Ms=Md=6.25+0.2Y-5r-10k --> dMs/dr=-5 --> changeMs=-5(changer) --> changeMs=-5(0.1) = -0.5! DOUBLE CHECK: - Recall that Ms=Md=L=6.25+0.2Y-5r --> Ms at r0=1.25: 6.25+0.2(50k)-5(1.25) = 10k --> Ms at r0=1.35: 6.25+0.2(50k)-5(1.35) = 9999.5 - changeMs = new-old = 9999.5-10k --> changeMs = -0.5! iii. Find changeMB = amount of bonds the Fed must buy/sell! (+=buy/-=sell) - Plug into Money Multiplier fxn: m=changeD/changeR = changeMs/changeMB = 1/rrd - rrd=10%=0.1 - changeMs=-0.5 --> 1/0.1 = -0.5/changeMB --> *changeMB = -0.05 = Fed must SELL 0.05 bonds!* - changeMB= -x =economy is MISSING x amount of bonds, so Fed needs to bu chong thru selling! (or selling 0.05 bonds renders Fed's reserve supply 0.05 bonds less=-0.05!) - changeMB = x = economy is OVERFLOWING x amount of bonds, so Fed needs to take away thru buying *b) Sell 0.05 bonds, new r=1.35* b) Recall that FFR=alpha0-alpha1(QR) - Recall that QR=SR=DR! - Recall that changeQR=changeMB (bonds Fed sells/buys) --> Fed controls QR! i. Find changeFFR with respect to QR --> dFFR/dQR = -alpha1 --> changeFFR = -alpha1(changeQR) --> changeFFR = -alpha1(changeMB) - changeMB (how much Fed buys or sells) = how much quantity of reserves changes by! --> ie. Fed SELLS 0.1 bonds = there are 0.1 bonds LESS in the reserves = -0.1 = changeMB=changeQR! ii. Plug values into changeFFR equation to find changeFFR! --> changeFFR = -2(-0.05) --> *changeFFR = 0.1*

Exercise - 05/28/19 Consider the simple Keynesian expenditure-output model (aka the Keynesian cross). Our economy is closed. The consumption function is given as C=c1(Y-T) where 0<c1<1. Gov't makes purchases equal to G>0, which is fully financed by its total tax revenue T>0. In this economy, total planned investment comes in the form of new machinery and is equal to Ip>0. In other words, planned inventory investment is 0. If c1=0.5, G=T=$5 and Ip=$40, find a functional relationship between unplanned inventory investment and output.

Recall: - Realized investment = PLANNED investment+UNPLANNED investment (Ir=Ip+Iu) - All variables are positive! - No NX, closed economy - Y = C+I+G+NX - Just find functional RELATIONSHIP between Iu and Y, just need to have Iu in the equation! - Functional = simple y=f(x) function! - Sensitivity = derivative! i. Stick Ir into Investment variable of Y function to find Y! --> Y = C+Ip+Iu+G ii. Stick C function with numbers into Y function --> Y = 0.5(Y-5)+40+Iu+5 --> Y = 0.5Y-2.5+45+Iu --> *Y = (42.5+Iu)/0.5*

Loanable funds market: 1) What happens to loanable funds and interest rate when there's an increase in G? 2) Relationship between S and... i. Government spending (G)? ii. Interest rate (r)? 3) What is the change in total savings? 4) What is the change in total investment? 5) What is the change in total C? 6) What is the change in total Y? 7) What is the relationship between r and C? 8) What is the consumption equation?

Remember: - Savings OR national income = Y-C-G - Savings = supply curve of LF market - Investment = demand curve of LF market - Delta = change in - Y=national income or GDP - C=consumption - G=gov spending - r=interest rate 1) Increase in G = decrease in S = supply curve shifts left = increase in interest rate (r) 2) i. Inverse (S increases = G decreases) --> deltaS = -deltaG ii. Inverse (S increases = r increases) --> (deltaS) = (deltaR) x C 3) Change in total savings = -(deltaG)+(C x deltaR) 4) Change in total investment = -(deltaG)+(C x deltaR) 5) Change in total consumption = -C x (change in interest rate) 6) Change in total income = -C x deltaR - deltaG + c x deltaR + deltaG --> deltaY = deltaC+deltaI+deltaG 7) Relationship between r and C = inverse (r increase = C decrease) 8) C = a+b(Y-T)-cr a,b,c = constants Y,T,r = variables (targets of interest)

CHAPTER 5: What are tax payments? What are the 3 purposes of tax payments? What are the 7 sources of tax payments? What are the 4 different tax structures?

Tax payments = receipts paid to gov't in adherence with tax laws Purposes: i. Revenue ii. Redistribution --> Progressive tax = tax rich more! iii. Alter behavior (pollution tax, tax investments abroad to discourage foreign investments, etc.) Sources: i. Individual income - salary/capital gains ii. Corporate income iii. Social insurance iv. Excise v. Estate vi. Customs duties (import/export tariffs) vii. Property Tax structures: i. Lump sum - $ per person ii. Tax rates - % of income, tY (t x income) iii. Tax credit - reduction of tax liability iv. Tax rebate - reverse lump sum

1) Were classical economists able to explain WHY the GD happened (3)? 2) Why did GD happen, according to Keynes? 3) What is the solution, according to Keynes? 4) What are the assumptions of Keynesian model? 5) What are 3 equilibrium equations derived from Keynesian assumptions? Specify what Ir and I =. 6) Suppose Ir =/= I, and Y>E. Is Ir greater than or less than I? 7) How did Keynes define consumption (formula)? 8) a) What is the autonomous spending multiplier? b) What is the Keynesian supply equation (show your work)? 9) Graph of aggregate demand vs. output? 10) Say an increase in gov't spending increases E1 to E2 in the graph from (9). a) Find the relationship between Y and G (output and government spending). b) How does 1 unit increase of gov't spending affect output?

1) No, bc the classical model is so simplifying as to be false in nature lmao 3 reasons by classical economists: i. Demand side - according to QTM theory, Ms dropped = prices dropping ii. iii. Supply and demand - simultaneous supply/demand shocks are consistent with Y and P movements of GD....but doesn't explain WHY labor contracted! 2) Inadequate investment demand 3) Solution = spending on infrastructure - Need gov't intervention - contrary to classical economists' solutions - Need a model where prices are STICKY - Need MANAGED market/capitalist economy, NOT "free" market --> Money multiplier - gov't spending kickstarts economic expansion (employs people thru public projects=income increases=consumption increases/investment increases=economic expansion) 4) Assumptions/equations: --> Two sides of Y that are equal but have diff equations: output and national income i. Y = E --> Total output = aggregate demand OR planned expenditure ii. E = C+I+G --> Agg. demand = consumption+investment+gov spending --> Assume a closed economy FOR NOW! No net exports for this reason! iii. Y = C+S+T --> National INCOME = consumption+savings+taxes iv. Y = C+Ir+G --> S = Ir --> G = T 5) Goods and services market - 3 equilibrium equations derived from assumptions: i. Y=E=C+I+G ii. S+T=I+G iii. Ir=I --> Ir = business+finance+investment, housing/residential+ REALIZED inventory --> I = business+finance+investment, housing/residential+ PLANNED inventory 6) Recall that I=Ip; Ir=Ir. Y=C+Ir+G; E=C+I+G i. If Y>E, this means that C+Ir+G>C+I+G --> This means that Ir>I! ii. *Ir>I = unintended inventory accumulation!* --> This is bc Ir is REALIZED inventory, NOT planned = unintended! 7) For Keynes, C=a+b(Y-T) - a = all exogenous factors that affect consumption - Y-T = income - taxes = disposable income - b = slope; how many units C changes PER 1 unit increase in Y-T --> b = marginal propensity to consume 8) Keynesian supply = plug consumption into output=ag demand; plug investment into output=ag demand afterwards! a) i. Plug C equation into Y=E=C+I+G (output equation) --> Y=[a+b(Y-T)]+I+G--> Y=a+bY-bT+I+G--> Y-bY=a-bT+I+G--> factor out Y: Y(1-b)=a-bT+I+G--> move 1-b to other side! ii. *Y=(1/(1-b))[a-bT+I+G]* --> (1/(1-b)) = autonomous spending multiplier b) Plug investment into previous function from (a) to get supply function: i. Investment = i0-i1(r) ii. Y=(1/(1-b))[a-bT+(i0-i1(r))+G] --> Distribute 1/(1-b)! iii. *Supply function: (1/(1-b))[a-bT+G]+(1/(1-b))[i0-i1(r)]* 9) Graph of aggregate demand vs. output i. E=y-axis; Y=x-axis ii. Equilibrium line = 45 degree line going through midpoint of E1 (both upward sloping --> Every point of 45 degree line = equilibrium = where Y=E iii. Actual demand CURVE = E1 (ag demand) iv. Midpoint of E1 = (Y1, E1) iv. When E1 increases, Y1 increases! (when ag demand increases=output increases) v. Unintended inventory shortfall = when E1>45 degree equilibrium vi. Unintended inventory accumulation = when E1<45 degree equilibrium 10) Increase in gov't spending = increases E1 to E2 Find the value of Y1 and Y2 using the Keynesian supply function: a) i. Take derivative of Y with respect to G: --> derivY/derivG = 1/(1-b)--> take discrete version of deriv: changeY/changeG = 1/(1-b) ii. *Relationship between Y and G (output and gov spending): changeY=changeG(1/(1-b))* b) *THIS TELLS US ABOUT A 1 TIME GOV'T SPENDING SHOCK: 1 unit increase gov't spending = raises output by MORE than 1 unit!*

1) What is the SRAS of output formula?

1) SRAS = short run ag supply curve! --> *Y=Ybar+u(P-P^e)+v* i. Y = output ii. Ybar = natural rate of output --> Output rate - when you're able to utilize ALL factors of production (aka full employment, etc.) iii. u or theta = fraction of difference btwn actual prices and exp iv. P = prices v. P^e = expected prices vi. v = unexpected shocks NOT related to prices --> ie - tornados, technology shocks

Exercise 2 - 05/16/19 1) Dall is a direct-to-consumer manufacturer of PCs. In Q1: 2008, Dall produced 5 PCs. The only input was labor from its short term contract employees, which cost $2k for the quarter in total. Dall was able to sell 2 of these PCs to consumers for $2k each. The owner of the firm decided to keep the remaining PCs in inventory. In Q2:2008, Dall produces no more PCs and sells the balance of its inventory for $1500 each. Track the activity of Dall corporation in Q1:2008 and Q2:2008. - Detail the national income and product account logs for both GDp and NI. - Moreover, attribute each transaction to a component of GDP/NI (C,I,G etc.) 2) National Income Accounting: A US based manufacturer of electronics equipment produces 5 especially long lasting digital cameras in Q1: 2008. They have 2 inputs: 1) specialty metal imported from Taiwan for a total of $1500 and 2) labor, which costs the firm a total of $50 for each camera produced. The firm is able to sell 4 units to consumers at $1000 each. In the second quarter, they are able to sell the remaining camera for $950. The firm also produces 5 new cameras and sells 4 of these for $1000 each. The firm incurs the same cost structure in Q2 as it did in Q1. Detail the national income and product account logs for both GDP and NI in Q1 and Q2 2008. Moreover, to the extent possible, attribute each transaction to a component of GDP.

ALWAYS REMEMBER FOR INVENTORY: - IF SOLD = -#sold x original per good cost - IF LEFTOVER = #unsold x original per good cost 1) GDP = C+I+GE+NX Q1: i. C - --> = (2 sold x 2000) = 4000 ii. I (includes inventory!) = inventory = cost/good x #unsold (NEGATIVE = ITEMS FROM INVENTORY SOLD!) --> Cost/good = $2000 total cost/5 goods produced = 400 --> 400 x 3 = 1200 iii. GE = none iv. NX = no exp or imp v. GDP = 4000+1200 = *5200* GNI = wages + total P of firm i. Wages - --> 2000 total labor expenditures ii. Total P of firm = P/good x #sold --> P/good = (R/good)-(cost/good) = 2000 earnings per 1 PC - 400 cost per 1 PC = 1600 --> Total P = 1600 x 2 sold = 3200 iii. GNI = 2000 + 3200 = *5200* Q2: i. C - --> = (3 sold x 1500) = 4500 ii. I (includes inventory!) = inventory = cost/good x #unsold (decreased inventory=negative, vice versa) --> OG cost/good = $2000 total cost/5 goods produced = 400 --> 400 x -3 (negative bc 3 were sold!) = -1200 iii. GE = none iv. NX = no exp or imp v. GDP = 4500+(-1200) = *3300* GNI = wages + total P of firm i. Wages - no additional wages given for 3 goods sold from inventory (the wages were already paid!) ii. Total R of firm = R/good x #sold = none in this case --> P/good = (revenue/good)-(cost/good) - ALWAYS FIND (R-C) PER GOOD X #SOLD FOR NI! = 1500 earnings per 1 PC - 400 cost per 1 PC = 1100 --> Total P = 1100 x 3 sold = 3300 iii. GNI = 0 + 3300 = *3300* 2) GDP = C+I+GE+NX Q1: i. C - --> = (4 sold x 1000 price) = 4000 ii. I (includes inventory!) = inventory = cost/good x #unsold (NEGATIVE = ITEMS FROM INVENTORY SOLD!) --> Capital cost/good = $1500 total cost/5 goods produced = 300 capital cost/good --> Labor cost/good = 50 labor cost/good --> Total cost/good = 300+50 = 350 iii. GE = none iv. NX = total exp - total imp --> 0 - 1500 imp = -1500 v. GDP = 4000+350-1500 = *2850* GNI = wages + total P of firm i. Wages - --> 50 labor cost/good --> Total wages = 50 x 5 produced = 250 ii. Total P of firm = P/good x #sold --> P/good = (earnings/good)-(cost/good) = 1000 earnings per good - 350 cost per good = 650 --> Total profit = 650 x 4 sold = 2600 iii. GNI = 250+2600 = *2850* Q2: Cost per good stays the same! GDP = C+I+GE+NX i. C - --> = (1 sold from inv x 950)+(4 sold x 1000) = 950+4000 = 4950 ii. I (includes inventory!) = inventory = cost/good x #unsold (NEGATIVE = INVENTORY ITEMS SOLD!) - Total cost/good = 350 --> -1 camera sold + 1 camera remaining from this sale --> -350+350 = 0 iii. GE = none iv. NX = total exp-total imp --> 0-1500 total imp = -1500 v. GDP = 4950+0+(-1500) = *3450* GNI = wages + total P of firm i. Wages - labor cost/good x #prod --> Labor cost/good = 50 --> #prod = 5 --> Wages = 50x5 = 250 ii. Total P of firm = P/good x #sold --> P/good = sum of all (earnings/good)-(cost/good) - for sold, inv - (1000 earnings per 4 PCs sold - 350 cost/good) = 650 - (950 earnings per 1 inv PC sold - 350 cost/good) = 600 --> Total profits = (650 x 4 sold)+(600x1) = 3200 iii. GNI = 250 + 3200 = *3450*

Suppose Yt=At(Kt^alpha)(Lt^(1-alpha)) How do you iterate forward your CD equation?

Iterate forward: Yt+1=At+1(Kt+1^alpha)(Lt+1^(1-alpha))

HW 3: https://drive.google.com/open?id=1D69dNe7SbZrEeT7ARXHGId55YXXKz4tp

1) Asking for Y in ISLM equilibrium! - try LM and the BOP; a, c, x0, z0, c0, F0=0; P=1 Y0 EQUATION: i. Solve for r=f(x) for IS: - Recall that Y=C+I+G+NX - Plug given equations into Y equation --> Y = b(Y-Tfixed) + Ifixed-i1r + G + x1Yf-x2(1/e)-z1Y+z2e(Pf) - Group Ys and rs together (to get r=f(x)) --> i1r = b(Y-Tfixed) + Ifixed-i1r + G + x1Yf-x2(1/e)-z1Y+z2e(Pf) - Y --> i1r = -bTfixed + Ifixed-i1r + G + x1Yf-x2(1/e)+z2e(Pf) - Y+bY-z1Y --> r = [-bTfixed+Ifixed+G+x1Yf-x2(1/e)+z2e(Pf)+Y(-1+b-z1)]/i1 ii. Solve for r=f(x) for LM: - Recall that Md=Ms in equilibrium! - Solve for r from Md equation --> M=c0+c1Y-c2r --> r=(c0+c1Y-M)/c2 iii. Equate the two r equations together (so you can solve for Y=f(r)) --> (c0+c1Y-M)/c2 = [-bTfixed+Ifixed+G+x1Yf-x2(1/e)+z2e(Pf)+Y(-1+b-z1)]/i1 iv. Group Ys and rs together so you can solve for Y=f(x)! --> (c0+c1Y-M)(i1) = (c2)[-bTfixed+Ifixed+G+x1Yf-x2(1/e)+z2e(Pf)+Y(-1+b-z1)] --> Y(i1c1+c2-c2b+c2z1) = (c2)[-bTfixed+Ifixed+G+x1Yf-x2(1/e)+z2e(Pf)+i1M] --> Y = [c2/(i1c1+c2-c2b+c2z1)][-bTfixed+Ifixed+G+x1Yf-x2(1/e)+z2e(Pf)+i1M] iii. Simplify - recall that a, c, x0, z0, c0, F0=0; P=1! --> *Y0 = [c2/(i1c1+c2(1-b+z1)][-bTfixed+Ifixed+G+x1Yf-x2(1/e)+z2e(Pf)+i1M]* r0 EQUATION: i. Solve for Y=f(x) for IS equation: --> Y = b(Y-Tfixed) + Ifixed-i1r + G + x1Yf-x2(1/e)-z1Y+z2e(Pf) --> Y = [-bTfixed+Ifixed-i1r+G+x1Yf-x2(1/e)+z2e(Pf)]/[1-b+z1] ii. Solve for Y=f(x) for LM equation: --> M=c1Y-c2r --> Y = (M+c2r)/c1 iii. Equate IS=LM and solve for r: --> (M+c2r)/c1=[-bTfixed+Ifixed-i1r+G+x1Yf-x2(1/e)+z2e(Pf)]/[1-b+z1] - Group rs and Ys: --> r(c1i1+c2-bc2+z1c2)=c1[-bTfixed+Ifixed+G+x1Yf-x2(1/e)+z2e(Pf)] - [M(1-b+z1)] --> r0={c1[-bTfixed+Ifixed+G+x1Yf-x2(1/e)+z2e(Pf)] - [M(1-b+z1)]}/(c1i1+c2-bc2+z1c2) --> *r0={c1[-bTfixed+Ifixed+G+x1Yf-x2(1/e)+z2e(Pf)] - [M(1-b+z1)]}/(c1i1+c2(1-b+z1)* CLOSEST ANSWER (only one that matches denominator: D. - prof said it's fine as long as we show our work! 2) Imperfect capital mobility = BOP curve is flat upward sloping (high capital mobility) OR BOP curve is steep upward sloping (low capital mobility) - Slope of BOP < slope of LM = high capital mobility - REMEMBER: IN ECON 420, "DEPRECIATION OF EXCHANGE RATE" MEANS INCREASED EXCHANGE RATE/DEPRECIATION OF DOMESTIC CURRENCY! FLEXIBLE SYSTEM: i. Increased iF=increased exchange rate=depreciation of domestic exchange rate/currency value ii. Increased exchange rate=depreciated domestic currency (aka depreciated domestic exchange rate) --> Domestic exchange rate depreciation (domestic exchange rate=domestic currency) = exchange rate ratio VALUE increase! iii. IS shifts right/increases - due to depreciated domestic currency value/domestic exchange rate iv. BOP SHIFTS RIGHT- depreciated domestic currency = cheaper domestic assets! --> *Domestic exchange rate [currency value] depreciates/actual ratio increases!* FIXED SYSTEM: BOP curve doesn't move in fixed system! - thus, shifts "leftwards" moreso than flexible system, since flexible system shifted right! *A. depreciate, less* 3) PERFECT capital mobility = BOP curve is horizontal - Effectiveness = which is more effective at increasing Y! - *RECALL: depreciation of exchange rate/depreciation of domestic currency value = INCREASE in ratio value of exchange rate!* OPEN ECONOMY = WITH EXPORTS i. LM INCREASES/SHIFTS RIGHT - due to expansionary monetary policy --> From e0 to e1; BELOW the BOP curve = BOP deficit (iD low/Ms high) ii. IS INCREASES/SHIFTS RIGHT (to new equilibrium)- decreased iD/increased e = depreciated dC = increased NX since it's cheaper for foreign buyers! --> Intersection between LM1 and IS0 = new interest rate iii. Y INCREASES - must compare to fixed system to see whether closed or open system is more effective at increasing Y! --> Increase in Y; no change in r! CLOSED ECONOMY = WITHOUT EXPORTS i. LM INCREASES/SHIFTS RIGHT - expansionary monetary policy (Ms increases, interest rate decreases) --> From e0 to e1; BELOW the BOP curve = BOP deficit (Ms too high, interest rate too low!) ii. IS DOESN'T MOVE! - decreased iD/increased e = depreciated dC = WOULD BE increased NX since it's cheaper for foreign buyers BUT CLOSED SYSTEM HAS NO EXPORTS! iii. Y INCREASES - BUT BY LESS THAN OPEN SYSTEM! --> Increase in Y; no change in r! v. *B. depreciate, more* 4) Goal: stimulate economic activity through increasing Ms (conventional open market operations) EXPANSIONARY MONETARY POLICY = increasing Ms, decreasing iD = increased consumption/output --> GOAL: INCREASE Y! - Recall that Fed canNOT affect IS directly! a) Sfx rises, domestic gov't spending rises i. Sfx rise = e falls/iD rises = $ appreciation ii. FIXED SYSTEM - Fed counteracts by selling cD/buying FX = Ms increase iii. Ms increase = LM SHIFTS RIGHT/INCREASES --> Increases Y, decreases iD (or r) iv. Domestic gov't spending rise = IS rise --> Increases Y, increases iD (or r) relatively v. OVERALL: large Y increase, r doesn't really change --> TRUE! *A. A foreign central bank increases the supply of its currency on the FX market (i.e. supply of FX goes up) and domestic government spending rises.* b) X falls, gov't spending falls i. IS SHIFTS LEFT/DECREASES - X decrease/decreased gov't spending --> = BOP deficit (low iD/high Ms) = Threatens decreased iD ii. FIXED SYSTEM - Fed counteracts by buying dC to increase iD = decreases Ms iii. LM SHIFTS LEFT/DECREASES - due to Fed buying dC to increase iD = decreased Y iv. OVERALL: decreased Y, unchanged r --> FALSE! c) Foreign price (Pf) level falls i. Pf falls = increased imports (Z) ii. IS SHIFTS LEFT/DECREASES - increased imports = decreased Y (X-Z) --> = BOP deficit (low iD/high Ms) = Threatens: iD fall; e rise/dC dep; Ms rise iii. FIXED SYSTEM - to counteract, Fed buys dC = iD rises to original point, e falls to original point, Ms decreases iv. LM SHIFTS LEFT/DECREASES - due to decreased Ms v. OVERALL: decreased Y, unchanged r --> FALSE! d) Foreign central bank raises its local interest rates/iF increase = capital outflows/Sfx decreases = e increases = $ depreciates i. Sfx decrease threatens: e increase/$dep; iD decrease; Ms rise ii. FIXED SYSTEM - Fed counteracts by buying dC/sells fC --> Domestic Ms decreases iii. LM INCREASES/SHIFTS left - due to domestic Ms decrease - Recall that the only curve that shifts resultant of Fed's actions is the LM curve (Ms)! iv. OVERALL: Y decrease, decreased r --> FALSE! 5) NOT SPECIFIED THAT BOP IS IN BALANCE INITIALLY! - IN BALANCE: CU=-(CA+ORT) (but not specified that BOP=in balance!) FOR MOZAMBIQUE: i. (I) exports +3m ii. (I) imports -5m iii. (II) capital inflows (FDI; increased F holdings of D assets) +1m iv. (II) capital outflows (increased D holdings of F assets) -0.5m CU = -2 CA = 0.5 ORT = N/A (CU only=-(CA+ORT) if specified that BOP=in balance prior!) SD = 0 BOP = CU+CA+ORT = -2+0.5+0 = *-1.5* 6) Fiscal debt equation: Bt= Gt + Trt - Txt + (1+i)Bt-1 - Txt = today's lump sum tax - Bt = today's deficit Sensitivity of primary deficit (which depends entirely on Txt change) to deficit change = dBt/dTx Sensitivity of interest cost to deficit change = dBt/diBt-1 PRIMARY DEFICIT: - Recall that primary deficit = Gt+Trt-Txt - CAN ALSO get the same answer by taking dBt/dTxt = -1 = inverse relationship between deficit and lump sum tax! i. Primary deficit: --> Txt rises = primary deficit falls --> *Txt falls = primary deficit rises* INTEREST COST: - IS-LM system! Cannot use derivative for this, since derivative doesn't take sticky prices into account! i. Decrease in lump sum taxes = increase in consumption = IS increases/shifts right ii. Increase in IS = BOP surplus (high iD/lowMs) = increase in interest rate iii. Increase in interest rate = increase in interest cost! --> Txt falls = interest rate rises = interest cost rises --> *B. Primary deficit rises; interest cost on the debt rises*

OPEN ECONOMY MACRO - determinants of CU and CA!: 1) What is the ISLM-Mundell Fleming Framework for the Current Account? 2) What is the ISLM-Mundell Fleming Framework for the Capital Account? 3) What is the relationship between the capital account and the domestic interest rate? What about the foreign interest rate? 4) Is the Official Reserve Account exogenous? 5) What happens to exchange rate and value of domestic currency when demand of foreign currency increases? Explain graphically. 6) Suppose Brexit doesn't happen. This causes investors to feel more confident about UK and the interest rate of UK to increase. What happens to the Qfx, exchange rate, and the value of the RMB (supposing the RMB is the domestic currency)? 7) What are the 3 assumptions of the ISLM-Mundell-Fleming model? What are the 7 formulas of this model? 8) Suppose demand of FX increases and supply of FX decreases. Does Qfx increase or decrease?

1) ISLM-Mundell Fleming Framework for Current Account: --> CU = X[Y^f, (1/e)P] - Z[Y,eP^f] --> NOTE: outside the ISLM-Mundell framework, CU=X-Z+Net Transfers - BUT net transfers are exogenous and CANNOT be modeled by this framework! - X=exports - Z=imports - Y=domestic income - P=domestic price level - Y^f=foreign income, exogenous - P^f=foreign price level, exogenous - e=$/f nominal exchange 2) ISLM-Mundell Fleming Framework for Capital Account: --> CA = F(r-r^f) - r=domestic REAL interest rate --> Rate of return on domestic financial assets - r^f=foreign REAL interest rate, exogenous --> Rate of return on foreign financial assets 3) i. dCA/dr = dF/dr > 0 --> Domestic rate increase = capital inflow increase = capital account increase --> Relationship between capital account and domestic exchange rate = positive ii. dCA/dr^f = dF/dr^f < 0 --> Foreign interest rate increase = capital outflow increase = capital account decrease --> Relationship between capital account and foreign exchange rate = negative 4) YES, ORT is exogenous - meaning we assume it is in a vacuum from the rest of the system! 5) Graph: i. x-axis=Qforeign exchange (Qfx) ii. y-axis=exchange rate (domestic/foreign currency) iii. Dfx increase/shifts right = increase in Qfx = increase in exchange rate (D/F) = domestic currency value falls/depreciates (1 D currency = LESS F currency!) 6) Increased IC IN UK = increased interest rate in UK = increased investment in UK = demand for foreign exchange increases! Graph: i. x-axis=Qforeign exchange (Qfx) ii. y-axis=exchange rate (domestic/foreign currency) iii. Dfx increase/shifts right = increase in Qfx = increase in exchange rate (D/F) = domestic currency value falls/depreciates (1 D currency = LESS F currency!) --> Thus, RMB depreciates! 7) *Assumptions of ISLM-M-F Model* (really a continuation of Keynesian model for int'l econ): i. Flexible exchange rate (NOT a fixed exchange rate system!) ii. Imperfect capital mobility (some barriers/restrictions to production capital flows) iii. Sticky prices (prices aren't perfectly fluid) *Formulas:* i. C=a+b(Y-T)-cr - a=investor confidence - b=MPc - Y-T=disposable income ii. I=i0-i1r - i0=investment - i1=changes in r with 1 unit change in I iii. G=Gfixed; T=Tfixed iv. Exports=X=x0+x1Y^f - x2(P/e) - x0=exports - x1=foreign income change in response to 1 unit export change - x2=domestic price/e change in response to 1 unit export change --> Likely measuring real domestic prices v. Imports=Z=z0+z1Y-z2(P^f)e - z0=imports - z1=change in domestic income in response to 1 unit import change - z2=foreign prices x exchange rate change in response to 1 unit import change vi. Md=c0+c1Y-c2r - c0=consumption - c1=change in domestic income in response to 1 unit change in Md - c2=change in interest rate in response to 1 unit change in Md vii. F=f0+f1(r-rf) - f0=financial assets - f1=change in (domestic int rate-foreign int rate) in response to 1 unit change in financial assets 8) Not certain - depends on the magnitude of the increases of demand and supply curves for FX! --> If demand increase > supply decrease = Qfx increases --> If demand increase < supply decrease = Qfx decreases

Exercise - 06/07/19 Solving for e in the Mundell-Fleming model Suppose that an economy is well characterized by a standard Mundell-Fleming model with a fixed exchange rate and imperfect capital mobility. The local central bank is able to maintain its target (ie. the exchange rate is currently at its target fixed e, but the forces described by the model below suggest otherwise). Given the information below, the equilibrium exchange rate is ___ and the economy's exchange rate is ___. (Hint: you may need to use the quadratic formula in order to get the solution.) - Y=14 - Yf=10 - r=0 - rf=5 - P= 2Pf = 1 - efixed=1 - X=0.15Yf-50(1/e)P - Z=0.3Y-0.5e(Pf) - F=100+6(r-rf) *efixed = the target exchange rate a) 20.5, undervalued b) 20.5, overvalued c) 0.74, undervalued d) 0.74, overvalued

Recall that: - Exchange rate < 1 = domestic currency is undervalued! --> When asking for economy's exchange rate vs. equilibrium, asking for whether domestic cD is under/overvalued! - BOP = CU+CA+ORT+SD=0 --> CU = X-Z --> CA = capital inflows-outflows = F --> ORT=0; SD=0 --> Since P=2Pf=1, Pf=1/2=0.5 --> efixed=/=e! - Quadratic formula: x (or e)=[-b±(b^2 - 4ac)^0.5]/2a --> Plug in values to get exchange rate! (can ignore negative one, as e≠negative --> a+b+c=0 (a=highest exponent of 2; b=exponent of 1; c=exponent of 0) i. Plug all these values into the BOP function! --> BOP=0=0.15Yf-50(1/e)P-0.3Y+0.5e(0.5)+100+6(r-rf) ii. Plug given values into equation --> 0=0.15(10)-50(1/e)-0.3(14)+0.5e(0.5)+100+6(-5) iii. Simplify --> 0=1.5-50(e^-1)-4.2+0.25e+70 --> 0=0.25e+67.3-50e^-1 - Get rid of e^-1 (the -1 exponent specifically), multiply both sides by "e" --> e(0)=(0.25e+67.3-50e^-1)e --> 0=0.25e^2 +67.3e-50 iv. Plug in a, b, c from this quadratic function into quadratic equation to find e! --> e= {-67.3±[67.3^2 - 4(0.25x-50)]^0.5}/(2x0.25) --> *e=0.74* (can ignore negative value!) --> *1(current)>0.74(equilibrium) = domestic currency is UNDERVALUED at current!* *c) 0.74, undervalued*

Suppose you have a Keynesian economy characterized by the AD function, short run aggregate supply function, and price expectations function as shown below: i. Yt=x0+x1Pt+v ii. Yt=Y*+q(Pt-Pt^e)+n iii. Pt^e=w0Pt-1 + w1Pt-2 a) How sensitive are today's prices to a change in last period's prices? b) How sensitive are today's output to a change in last period's prices?

a) Sensitivity of Pt to change in Pt-1 = dPt/dPt-1 (need to find Pt=f(x)) i. Equate two Yt equations and rearrange to find Pt=f(x) --> x0+x1Pt+v=Y*+q(Pt-Pt^e)+n --> Pt(x1-q)=Y*+q(-Pt^e)+n-x0-v --> Pt=[Y*+q(-Pt^e)+n-x0-v]/[x1-q] ii. Sub Pt^e equation into Pt equation to get Pt-1! --> Pt=[Y*+q(-(w0Pt-1 + w1Pt-2))+n-x0-v]/[x1-q] ii. Find dPt/dPt-1! --> *dPt/dPt-1= -qw0/(x1-q)* --> changePt= [changePt-1][-qw0/(x1-q)] b) REMEMBER YOU'RE ASKED FOR AN EQUILIBRIUM SOLUTION - MUST USE ALL EQUATIONS! --> Need dYt/dPt-1 i. Find Pt in terms of Yt from i. to sub into ii. --> Pt=[(Yt-x0-v)/x1] ii. Plug Pt equation from i. into ii. --> Yt=Y*+q([(Yt-x0-v)/x1]-Pt^e)+n iii. Plug iii. into Pt^e for ii.! --> Yt=Y*+q([(Yt-x0-v)/x1]-[woPt-1 + w1Pt-2])+n iv. Group Yts together so you can take derivative! --> Yt = Y*+q[(-x0-v)/x1 - w0Pt-1 - w1Pt-2]+n}/{1- q/x1} v. Take dYt/dPt-1 to find sensitivity of today's output to Pt-1! --> *dYt/dPt-1 = [-qw0/(1- q/x1)]* --> changeYt = [-qw0/(1- q/x1)] x changePt-1

1) What is the IS formula (define and formula)? 2) What is the LM formula (define and formula)? 3) Derive the IS/LM OUTPUT AND INTEREST RATE formulas in EQUILIBRIUM; show your work. GRAPHS: 1) What is the IS curve? a) What happens to the IS when there's an increase in G? 2) What is the LM curve? a) What happens to the LM when there's an increase in G?

1) IS = goods market equilibrium schedule - shows all combos of interest rates/output for which the goods market is in equilibrium *r = (1/i1)[a+i0+G-bT]-[(1-b)/i1]Y* --> Rmr that (-) only appears before the b's! 2) LM = money market equilibrium schedule - shows all combos of interest rates/levels of income for which Md=Ms (demonstrates M market equilibrium!) *r = [(c0/c2)-(1/c2)M]+(c1/c2)Y* 3) What we want to find: IS=LM--> equilibrium equation for output=M market i. IS equation has 2 unknown/target variables: Y, i ii. LM equation has 2 unknown/target variables: Y, i iii. Thus, we can use these equations together to solve for the equilibrium level of output (Y) and equilibrium interest rate (r) in the economy! STEPS: FIRST: Find function for Y by equating LM and IS equations (basing in IS function bc it deals with output!) i. Equate LM (interest rate) and IS (output) equations to derive function for Y --> [(c0/c2)-(1/c2)M]+(c1/c2)Y = (1/i1)[a+i0+G-bT]-[(1-b)/i1]Y ii. Isolate Y's on 1 side --> (c1/c2)Y+[(1-b)/i1]Y = (1/i1)[a+i0+G-bT]-[(c0/c2)-(1/c2)M] iii. Simplify Y side --> Draw Y out of equation: Y[(c1/c2)+((1-b)/i1)] --> Cross multiply to combine: Y[(c1/c2)+((1-b)/i1)] = Y[(c1i1+c2-c2b)/c2i1] --> Divide numerator, denominator by c2 to get rid of c2!: Y[((c1i1/c2)+1-b)/i1] iv. Now equation looks like this: --> Y[((c1i1/c2)+1-b)/i1] = (1/i1)[a+i0+G-bT]-[(c0/c2)-(1/c2)M] v. SIMPLIFY! - goal is to isolate Y on one side! --> [(c0/c2)-(1/c2)M] simplifies to (c0-M)/c2 --> Divide both sides by [((c1i1/c2)+1-b)/i1] to simplify Y side: Y = {(1/i1)[a+i0+G-bT]-[(c0-M)/c2]}/[((c1i1/c2)+1-b)/i1] --> Simplify: *Y = [1/[(1-b)+((c1i1)/c2)]][a+b+i0+G-bT+(i1/c2)(M-c0)]* SECOND: Plug equilibrium Y derived from IS equation and plug back into original LM equation to solve for r! i. Recall that LM equation is r=(1/i1)[a+i0+G-bT]-[(1-b)/i1]Y ii. Plug equilibrium Y function into Y of LM equation! --> r=[(c0/c2)-(1/c2)M]+(c1/c2){[1/[(1-b)+(c1i1/c2)][a+b+i0+G-bT+(i1/c2)(M-c0)]} iii. Distribute c1/c2 and [1/(1-b)+(c1i1/c2)] into rest of equation --> r=[(c0-M)/c2]+[c1[a+b+i0+G-bT+(i1/c2)(M-c0)]]/[(c2((1-b)+(c1i1/c2))] --> r=[(c0-M)+c1[a+b+i0+G-bT+(i1/c2)(M-c0)]]/[c2((1-b)+(c1i1/c2))] --> r=[(c0-M)[(1-b)+(c1i1/c2)]+c1(a+i0+G-bT)+c1b+(c1i1/c2)M-(c1i1/c2)c0]]/[c2((1-b)+(c1i1/c2))] - Distribute c0 and -m out to each term! --> r=[c0(1-b)+(c1i1c0/c2)-M(1-b)-M(c1i1/c2)+c1b+(c1i1/c2)M-(c1i1/c2)c0+c1(a+i0+G-bT)]/[c2((1-b)+(c1i1/c2))] --> -M(c1i1/c2) and +(c1i1/c2)M cancel out --> +(c1i1c0/c2) and -(c1i1/c2)c0 cancel out --> r=[c0(1-b)-M(1-b)+c1b+c1(a+i0+G-bT)]/[c2((1-b)+(c1i1/c2))] - Now take (1-b) out and group c0 and M together! --> r=[(1-b)(c0-M)+c1(a+b+i0+G-bT)]/[c2((1-b)+(c1i1/c2))] - Now take [(1-b)+(c1i1/c2)] out of the fraction! --> *IS/LM output and interest rate equilibrium equation is: r=[1/((1-b)+(c1i1/c2)][((1-b)/c2)(c0-M)+(c1/c2)(a+b+i0+G-bT)]* GRAPHS: 1) IS curve = all combos of (r, Y) that = G/S market equilibrium - Downward sloping - r=[a+i0-bT+G-(1-b)Y]/i1 (not in equilibrium) - Points come from exp-output graph! --> output=x; exp=y; Exp line=upward sloping; 45 deg equilibrium line a) IS curve=connected to exp-output graph! i. Exp-Output graph: - exp=y-axis - output=x-axis - 45 degree upward sloping eq line where all exp=output --> Increase G = expenditure curve (upward sloping) increases/shifts left = increase Y ii. IS graph: - r=y-axis - output=x-axis --> Increase G = IS curve (downward sloping) increases/shifts rights = increase Y 2) LM curve = all combos of (r, Y) that = money market equilibrium - Upward sloping - r=(co-M+c1r)/c2 - Points come from a) Nothing happens to LM, increase in expenditure affects IS (G/S) curve! - Recall that IS curve=connected - Points come from real money-interest rate graph! --> M/P=x; r=y; L(r,Y)=Md=downward sloping; Ms/P=vertical line

HW 2: https://drive.google.com/drive/folders/1R49p_x90rWjowm16M9oSzzm2WidpTHXF

1) Looking for dY/dM WITH wealth vs. dY/dM WITHOUT wealth - greater or less? - Consumption function: C = a+b0(Y-T)+b1((B+M)/P) --> 0<b1<1 - Recall that investments=i0-i1r--> relationship between interest rate and investments - Looking for Y's relation to wealth! - P = 1!!! i. Plug C function into Y function; investments equation into Y function --> Y = [a+b0(Y-T)+b1((B+M)/P)] + i0-i1r + G ii. Plug LM (money mkt) equation into (r) of simplified Y function: r = [(c0-M+c1Y)/c2] --> Y = [a+b0(Y-T)+b1(B+M)] + i0-i1[(c0-M+c1Y)/c2] + G - SIMPLIFY/CONSOLIDATE Y - recall that xa+xb=x(a+b)! --> Y=[a-b0T+b1B+M(b1 + i1/c2)+i0 - i1c0/c2 + G]/[1-b0 + c1i1/c2] iii. Take derivative of Y in terms of M --> *dY/dM = [b + i1/c2]/[1-b0+ c1i1/c2]* - Discrete form: *changeY = (changeM) x [b1 + i1/c2]/[1-b0+ c1i1/c2]* iv. NOW take out b1(B+M) and repeat the derivation! --> Y function (with C and I eqxns plugged in) WITH wealth: Y = [a+b0(Y-T)+b1(B+M)] + i0-i1[(c0-M+c1)/c2] + G --> Y function (with C and I eqxns plugged in) WITHOUT wealth: Y = [a+b0(Y-T)+ i0-i1[(c0-M+c1)/c2] + G - SIMPLIFY/CONSOLIDATE Y's and M's! --> Y = [a-b0T+i0- i1c0/c2 + i1M/c2 +G]/[1-b0 + c1i1/c2] vii. Take derivative of Y in terms of M --> *dY/dM = [i1/c2]/[1-b0+ c1i1/c2]* --> Discrete form: *changeY = changeM x [i1/c2]/[1-b0+ c1i1/c2]* viii. Compare the derivative WITH wealth vs. derivative WITHOUT wealth --> WITH wealth: [b1 + i1/c2]/[1-b0+ c1i1/c2] --> WITHOUT wealth: [i1/c2]/[1-b0+ c1i1/c2] viv. WITH wealth has (b1)/(1-b0+ c1i1/c2) MORE sensitivity to change in Y than WITHOUT wealth! --> Thus, answer is *A. [b1 + i1/c2]/[1-b0+ c1i1/c2], greater* 2) C=c1(Y-T) - All variables positive! - Ir = Ip+Iu - Recall that Y=C+I+G+NX (but no NX bc closed economy) - Need relationship between Iu and Y! i. Plug Ir into Y function --> Y=C+Ip+Iu+G ii. Plug C function into Y function --> Y=0.7(Y-10)+40+Iu+10 iii. Simplify --> Y=0.7Y-7+50+Iu --> Y=0.7Y+43+Iu --> 0.3Y=43+Iu --> *Y=(43+Iu)/0.3* iv. Test each answer to find right one - IN EQUILIBRIUM: a) Y<210 = Iu is negative? --> 200=(43+Iu)/0.3--> Iu=positive --> a) is FALSE! b) Regardless of what Y=n, Iu>0 --> Say Y=10--> 10=(43+Iu)/0.3--> Iu=negative --> b) is FALSE! c) Iu = 0 in equilibrium --> Need to find equation for equilibrium d) Y>210 = Iu>20-->Iu=always>20 --> *d) is TRUE!* 3) Recall that MPc = b - C=a+b(Y-T) - Recall that Keynesian output equation: Y=(1/(1-b))(a+i0+G-bT)-(i1r/(1-b))--> NOT given any values from money market side so don't need to use LM equation! --> Assume all other variables=0 i. Recall that b = MPc --> MPc = 0.7 ii. Recall that a = private consumption --> a falls by 150 iii. To find how much Y needs to CHANGE by, take the derivative of Y—with respect to a—from output equation --> Y = [a/(1-b)] iv. Convert this derivative to discrete (change in) equation: changeY = changea/(1-b) --> changeY = -150/(1-0.7) --> changeY = -150/0.3 --> Y changes by -500! = output DECREASES by 500 as result of decreased PrS v. Gov't needs to increase output by [1000+(decrease in output)] to achieve net 1000 increase! --> 1000+500 = 1500 vi. Since gov't needs to achieve Y=1500, need to find out how much G needs to increase to achieve 1500! vii. Find derivative of Y with respect to G --> Y=(1/(1-b))(a+i0+G-bT)-(i1r/(1-b)) --> derivative of Y with respect to G = G/(1-b) v. Convert deriv of Y with respect to G to discrete (change in) equation --> changeY = changeG/(1-b) vi. Plug how much gov't needs to INCREASE output by into: changeY=changeG/(1-b) to find changeG! --> 1500 = changeG/(0.3) --> changeG = 450! --> *c. $450* - gov't needs to increase spending by $450 to increase output by 1500! *Expenditure-output graph:* i. y-axis = expenditure ii. x-axis = output iii. 45 degree equilibrium line = where E=Y at every point --> Hypothetical line where D=S at every point! iv. Demand curve = planned expenditure iv. Increase in G = increase in expenditure AKA demand curve (shifts left) --> Expenditure = C+I+G+NX --> output0 < output1 --> output1-output0 = 1500 increase in output as RESULT of G increasing by 450 4) Y=100+100M-10P --> Increase of M by 3 units; P1=? - At equilibrium0 (e0): Y=1000; P=100 - Recall that in the Classical model, money is neutral and Y NEVER CHANGES! - All discrete values - so just convert variables to changeX! i. Convert AD function to delta discrete function to find changeP--> (Y1 function for M1 and P1) - (Y2 function for M2 and P2) = to find the marginal change in P --> (100+100M1-10P1) - (100+100M2-10P2) --> Y = 100M1-100M2-10P1-10P2 --> Y = 100(changeM)-10(changeP) ii. Plug in values for changeM to get the changeP!--> recall EVERY variable becomes delta/change in! --> changeY = 100(3)-10(changeP)--> changeY=0 --> 0 = 300-10(changeP) --> -300/-10 = changeP --> P changes by 30! iii. Since P1 = 100 and P changes by 30, find new P! --> New P = 100+30 = *130* 5) - All parameters = positive - Standard demand curve = a1 aka slope=negative; a0=positive - Positive relationship between Y and P - Pt = today's price; Pt-1 = yesterday's price i. Solve for P by equating AD with SRAS --> a0+a1P=Yfixed+u(P-P^e)+v ii. Plug given Pt^e expression into SRAS expression to substitute P^e --> a0+a1Pt = Yfixed+u(P-[w0Pt-1+w1Pt-2])+v --> a1Pt = Yfixed+u(Pt-[w0Pt-1+w1Pt-2])+v-a0 - Move Pts all to one side --> a1Pt-uPt = Yfixed+u(-[w0Pt-1+w1Pt-2])+v-a0 --> Pt(a1-u) = Yfixed+u(-[w0Pt-1+w1Pt-2])+v-a0 --> Pt = [Yfixed+u(-[w0Pt-1+w1Pt-2])+v-a0]/(a1-u) iv. Take derivative of Pt with respect to Pt-1=yesterday - can leave out other constants that don't have relation to Pt-1 --> Pt = [u(-[w0])/(a1-u) --> Pt = -u(w0)/(a1-u) v. Convert derived equation to discrete change equation --> changePt = {-u(w0)/(a1-u)} x changePt-1 --> *b) rise by [-uw0/(a1-u)] x changePt-1* --> CONCEPTUALLY: Pt is positively related to Pt-1

1) Draw a graph demonstrating effects on IS, LM, BOP curves/position from expansionary monetary AND fiscal policy. Which policy works better in these cases? a) Perfect capital mobility, fixed exchange rate b) Perfect capital mobility, flexible exchange rate c) High capital mobility, fixed exchange rate d) High capital mobility, flexible exchange rate e) Low capital mobility, fixed exchange rate f) Low capital mobility, flexible exchange rate 2) Which exchange rate system is monetary policy (MP) more effective in? Which exchange rate system is fiscal policy (FP) more effective in? 3) What notates a BOP deficit on the ISLM-BOP graph? What notates a BOP surplus? 4) What does the BOP slope represent? What does it look like for... a) High capital mobility b) Low capital mobility c) Perfect capital mobility d) Imperfect capital mobility

--> x-axis=Y; y-axis=r --> BOP and IS shifts will typically be coordinated so that they end up in same equilibrium --> https://drive.google.com/open?id=1pcDLrHHxyf4ywrHUbgKBl3Racx8yCsLM 1) a) FIXED R, PERFECT CM SYSTEM: >Monetary Policy< i. LM increases/shifts right - due to expansionary monetary policy (Ms rises) --> Increased Ms=decreased iD=increased e=depreciated dC ii. FIXED SYSTEM - Fed counteracts by buying cD = decreases Ms=increased iD=decreased e=appreciated dC iii. LM decreases/shifts left - due to Fed decreasing Ms iv. RESULT: no change in Y or r! --> MP is ineffective under fixed/perfect CM system. >Fiscal Policy< i. IS increases/shifts right - due to increased gov't expenditure --> iD increases = decreased e = appreciated dC value ii. FIXED SYSTEM - Fed counteracts by selling dC to decrease iD --> Incrased Ms = decreased iD = increased e = depreciated dC value iii. LM increases/shifts right - due to increased Ms --> Rmr that BOP doesn't shift under fixed system OR perfect capital mobility! iv. RESULT: increased Y, no change in r! --> FP is effective under fixed/perfect CM system! b) FLEXIBLE R, PERFECT CM SYSTEM: >Monetary Policy< i. LM increases/shifts right - due to increased Ms --> Increased Ms=decreased iD=increased e=depreciated dC=increased NX ii. IS increases/shifts right - due to increased NX --> Recall that BOP doesn't shift under perfect K mobility! iii. RESULT: increased Y, no change in r --> MP is effective under flexible system! >Fiscal Policy< i. IS increases/shifts right - due to increased gov't expenditure --> Leads to increased iD=decreased e=appreciated $=less NX ii. IS decreases/shifts left - due to less NX iii. RESULT: no change in Y or r --> FP is ineffective under flexible/perfect CM system. c) FIXED R, HIGH CM SYSTEM: >Monetary Policy< i. LM increases/shifts right - due to expansionary monetary policy (Ms rises) --> IS-LM equilibrium shifts below flat BOP curve=deficit=increased Ms=decreased iD=increased e=depreciated dC ii. FIXED SYSTEM - Fed counteracts by buying cD = decreases Ms=increased iD=decreased e=appreciated dC iii. LM decreases/shifts left - due to Fed decreasing Ms iv. RESULT: no change in Y or r! --> MP is ineffective under fixed/perfect CM system. >Fiscal Policy< i. IS increases/shifts right - due to increased gov't expenditure --> IS-LM equilibrium shifts above flat BOP curve=surplus=decreased Ms=increased iD=decreased e=appreciated dC ii. FIXED SYSTEM - Fed counteracts by selling dC to decrease iD --> Increased Ms = decreased iD = increased e = depreciated dC value iii. LM increases/shifts right - due to increased Ms --> Rmr that BOP doesn't shift under fixed system OR perfect capital mobility! iv. RESULT: increased Y, no change in r! --> FP is effective under fixed/high CM system! d) FLEXIBLE R, HIGH CM SYSTEM: >Monetary Policy< i. LM increases/shifts right - due to increase in Ms --> IS-LM equilibrium shifts below flat BOP curve=deficit=increased Ms=decreased iD=increased e=depreciated dC=increased NX ii. IS increases/shifts right - due to increased NX iii. BOP shifts right/increases - due to depreciated DC=cheaper dAssets! iv. RESULT: increased Y, slightly decreased r! --> MP is effective in flexible/high CM system! --> Higher CM, more effective! >Fiscal Policy< i. IS shifts right/increases from is0 to is1 - due to increased gov't expenditure --> IS-LM equilibrium shifts above flat BOP curve=surplus=decreased Ms=increased iD=decreased e=appreciated dC=decreased NX ii. IS shifts left/decreases to is2 (is2>is0) - due to decreased NX iii. BOP shifts left/decreases - appreciated dC=more expensive dAssets --> To new equilibrium point with is2-LM! iv. RESULT: small increase in Y and r --> FP not as effective in flexible/high CM system! --> Smaller CM=better effect e) FIXED R, LOW CM SYSTEM: >Monetary Policy< i. LM increases/shifts right - due to expansionary monetary policy (Ms rises) --> IS-LM equilibrium shifts below steeper BOP curve=deficit=increased Ms=decreased iD=increased e=depreciated dC ii. FIXED SYSTEM - Fed counteracts by buying cD = decreases Ms=increased iD=decreased e=appreciated dC iii. LM decreases/shifts left - due to Fed decreasing Ms iv. RESULT: no change in Y or r! --> MP is ineffective under fixed/perfect CM system. >Fiscal Policy< i. IS increases/shifts right - due to increased gov't expenditure --> IS-LM equilibrium shifts below steeper BOP curve=deficit=increased Ms=decreased iD=increased e=depreciated dC ii. FIXED SYSTEM - Fed counteracts by buying dC to increase iD --> Decreased Ms = increased iD = decreased e = appreciated dC value iii. LM decreases/shifts left - due to decreased Ms --> Rmr that BOP doesn't shift under fixed system OR perfect capital mobility! iv. RESULT: tiny increase in Y, increase in r! --> FP is more effective under fixed/high CM system!! f) FLEXIBLE R, LOW CM SYSTEM: >Monetary Policy< i. LM increases/shifts right - due to increase in Ms --> IS-LM equilibrium shifts below steep BOP curve=deficit=increased Ms=decreased iD=increased e=depreciated dC=increased NX ii. IS increases/shifts right - due to increased NX iii. BOP shifts right/increases - due to depreciated DC=cheaper dAssets! iv. RESULT: increased Y, slightly decreased r! --> MP is effective in flexible/high CM system! --> Higher CM, more effective! >Fiscal Policy< i. IS shifts right/increases - due to increased gov't expenditure --> IS-LM equilibrium shifts below steeper BOP curve=deficit=increased Ms=decreased iD=increased e=depreciated dC=increased NX ii. IS shifts right/increases - due to increased NX iii. BOP shifts right/increases - depreciated dC=cheaper dAssets --> IS increases slightly to meet new increased BOP point iv. RESULT: moderately large increase in Y and r --> FP not as effective in flexible/high CM system! --> Smaller CM=better effect 2) Monetary Policy = more effective in flexible exchange rate Fiscal Policy = more effective in fixed exchange rate RECALL: FP=fixed policy --> FP increase = expansionary fiscal policy --> FP decrease = contractionary fiscal policy 3) BOP deficit=anything BELOW the BOP curve BOP surplus=anything ABOVE the BOP curve 4) BOP slope = substitutability of assets across countries --> The flatter the BOP slope = the higher the substitutability! a) High CM=flat upward slope b) Low CM=steep upward slope c) Perfect capital mobility=horizontal slope --> AKA perfect substitutability, when r=rf d) Imperfect capital mobility=upward slope NON-horizontal slope, could be high OR low CM

1) What is real money expressed as? 2) Relationship between r and m/p? 3) Relationship between r and output?

1) Real money = Ms/P 2) Negative relationship! m/p = vertical line r = downward sloping i. Downward sloping lines = L (r1, y2); L (r1, y1) --> y1 and y2 = from LM graph that connects to it! 3) Positive relationship! r and Y graph: i. LM curve = combo of Y and r --> Connected to r and m/p graph; upward sloping ii. Points of Relationship between interest rates and income = positive As income grows, transaction demands grow

OPEN ECONOMY MACRO: BOP accounting problems: 1) Assume that the BOP is in balance initially. Suppose a US consumer purchases $100 worth of cement from a Mexican exporter. Then a MX exporter uses $100 to purchase a US tractor. How is this recorded in the BOP? 2) Assume that BOP is in balance initially. Suppose a US consumer purchases $100 worth of cement from Mexican exporter. The MX exporter then uses the $100 to purchase a US bond. How is this recorded in the BOP? 3) Assume BOP is in balance initially. Suppose US consumer purchases $100 worth of cement from MX exporter. The MX exporter exchanges $s for pesos with the bank, the bank trades $s for pesos with the Fed. How is this recorded in the BOP?

A BIT different than 460 - every transaction only warrants 1 recording! - does not take into account increased/decreased holdings of foreign currency for EVERY transaction - only where it's relevant! - Current = exports - imports + Net Transfers - Capital = foreign investment in US - US investment in foreign 1) Cement: Current account: -$100 (imports) Tractor: Current account: +$100 (export of US tractor) 2) Cement: Current account: -$100 (imports) Bond: Capital account: +$100 (increased MX holdings of US fin assets/capital inflows) 3) Cement: Current account: -$100 (imports) Fed: ORS: +$100 (decreased Fed holdings of pesos)

Suppose there's an increase in Ms. What is the effect on the foreign exchange rate? Draw the foreign exchange market graph.

DOMESTIC Ms increase: i. iD decreases ii. Exchange rate increases = domestic currency depreciates iii. Domestic investors move assets to foreign market instead since domestic interest decreased = Dfx increases iv. Foreign investors pull currency out of domestic market to convert back to foreign currency since domestic currency depreciated = Sfx decreases v. Qfx remains the same --> Cannot tell change unless we know magnitudes of Dfx increase/Sfx decrease vi. Exchange rate increases = domestic currency FURTHER depreciated!