Intermediate Microeconomics Midterm 2 (Chapters 4-7, skip 5)

What is the unit of time we are referring to for amounts of labor/capital/output/production?

Assumption is that we are referring to amount of labor/capital used EACH YEAR; output produced EACH YEAR

When marginal product of labor is decreasing, what happens to average product of labor?

*APl could be increasing OR decreasing*- depends on how amount of MPl is in comparison to APl --> If MPl < APl = average product decreasing --> If MPl > APl = average produce increasing

With labor being the input on the x-axis and output on the y-axis, what happens to the production curve with technological improvement?

Curve shifts upward- MORE output can be produced with same amount of input/labor --> x remains the same, y increases!

If a price consumption curve is downwards U-shaped, with good x on the horizontal axis and good y on the vertical axis, what relationship do x and y have?

If it is u-shaped, then -As price of good x decreases, Qd of good x increases, and Qd of good y decreases. --> *So at high prices of x, the two goods are substitutes* -As price of good x decreases, Qd of good x increases, and Qd of good y increases. --> *So at low prices of x, the two goods are complements*

Labor increases from 9 to 10 units, and output increase from 199 to 211 units. What is the marginal product of labor? What is the average product of labor for 10 labor units?

MPl = change in output/change in input --> (211-199)/(10-9) = 12 units! APl = total output/total input --> 211/10 = 21.1 units!

How do you find marginal cost of labor? Marginal cost of capital?

Remember, MC = cost of increasing output by 1 unit! MCl = w/MPl = change in total cost/change in q output = derivative of total cost! MCk = r/MPk = change in total cost/change in q output = derivative of total cost!

Normal good vs. inferior good vs. Giffen good

Normal good- increase in income leads to increase in demand for these goods (veggies, books, etc.) Inferior good- increase in income leadds to decrease in demand for these goods (ramen noodles, crappy food, etc.) Giffen good- when good is very inferior, decrease in price will lead to decrease in Qd! (snobbishness, econified) --> Defies the Law of Demand! --> Very rare; strong income effect (decrease in price = more income = decrease in Qd) --> Big share of budget ie- potatoes in Ireland

1) What is the slope of the price consumption curve when goods are substitutes? 2) What is the slope of the price consumption curve when goods are complements?

PCC = cost of one good stays constant, while other is variable 1) Normal goods are substitutes- *PCC slope = downwards sloping* 2) Normal goods are complements- *PCC slope = upwards sloping*

What is the isoelastic demand curve? What is the unit elastic demand curve?

*Isoelastic demand curve*- SLOPE CHANGES, PED CONSTANT --> Convex, downward sloping curve; slope is changing but PED is constant! --> PED = 0 when P = 0; increases in magnitude until it becomes infinity, when price is so high Qd = 0 *Unit elastic demand curve*- SLOPE CONSTANT, PED = -1 --> Price increase = decrease in Qd, such that total expenditure on the good remains the same! --> Perfectly elastic to changes in price

Consider a firm that produces both flutes(x) and piccolos(y). 1) What will the​ firm's production transformation curve look like if it experiences economies of​ scope? 2) What will the​ firm's production transformation curve look like if it does​ not?

*Production Transformation curve = Production Possibilities Frontier* x-axis = flutes y-axis = piccolos 1) Economies of scope = curved line going downwards (CONCAVE downwards line) --> When 1 single firm can make more of 2 goods than 2 specialized firms!--> CAN PRODUCE MORE, so concave as opposed to flat! 2) Diseconomies of scope = linear/flat line going downwards --> No economies of scope/less that can be produced, so just a boring straight line :-/

What is the short run like for production inputs? What is the long run like for production inputs? What is a fixed input?

*Short run*- at least 1 fixed/constant input --> Amount of input cannot be changed --> Typically, capital is fixed in short run; labor variable! *Long run*- amount of all production inputs are variable! --> Both labor and capital are variable! --> It takes time to change amount of inputs in order to increase/improve production of outputs --> ie- takes time to acquire more expensive machinery(capital) in order to more efficiently produce output! *Fixed input*- production input that cannot be changed in order to increase/change amount of output; in short run --> ie- company/farmer can't change amount of land it has in the short run to increase yield of crops; can easily increase amount of land it has in the long run to increase yield of crops!

What is theory of consumer behavior? What is theory of the firm?

*Theory of consumer behavior*- deals with demand; how consumers make purchasing decisions (focuses on the idea that choices stem from rational thought) *Theory fo the firm*- deals with supply; how firm maximizes profit through cost minimizing production decisions, and unethical shit wow, sounds like late stage capitalism to me but okay...........

How does a change in the price of one input change the​ firm's long-run expansion​ path? If the price of an input​ changes, then the... A. slope of the isoquants will​ change, and the firm will substitute away from the relatively more expensive input​, pivoting the expansion path toward the axis of the relatively cheaper input. B. slope of the isocost lines will​ change, and the firm will substitute toward the relatively cheaper input​, pivoting the expansion path toward the axis of the relatively cheaper input. C. isoquants will shift in a parallel​ fashion, and the firm will substitute toward the relatively cheaper input​, pivoting the expansion path toward the axis of the relatively cheaper input. D. slope of the isocost lines will​ change, and the firm will substitute away from the relatively more expensive input​, pivoting the expansion path toward the axis of the relatively more expensive input. E. isocost lines will shift in a parallel​ fashion, and the firm will substitute away from both​ inputs, shifting the expansion path in a parallel fashion.

--> Recall that the long run expansion path is basically a line made up of the intersections/tangent points between isocost and isoquant lines! --> Isocost lines shift as DIRECT result of price change (if w of L increased, and L was on x axis, isocost would shift inward on x-axis, making isocost line steeper! all of this movement makes the isoquants shift, and changes the LR expansion path, but those are secondary results of isocost's initial change!) B. slope of the isocost lines will​ change, and the firm will substitute toward the relatively cheaper input​, pivoting the expansion path toward the axis of the relatively cheaper input.

1) Suppose a firm must pay an annual​ tax, which is a fixed​ sum, independent of whether it produces any output. --> How does this tax affect the​ firm's fixed,​ marginal, and average​ costs? 2) Now suppose the firm is charged a tax that is proportional to the number of items it produces.​ --> How does this tax affect the​ firm's fixed,​ marginal, and average​ costs?

1) --> Fixed cost- increases; you have to add fixed annual tax to original fixed cost! --> Marginal cost- stays the same; annual tax does not affect cost of producing each output --> Average cost- increases; higher TC/q = higher AC! 2) --> Fixed cost- stays the same; tax is variable so it would not be added to fixed costs! --> Marginal cost- increases; tax is increased with each additional output, so cost of producing each output increases! --> Average cost- increases; higher TC/q = higher AC! *Question is just dealing with how to categorize costs, not delving into anything deeper! you got this queen, don't overthink!*

1) What is a product transformation curve? 2) What is economies of scope? 3) What is diseconomies of scope? 4) What is degree of economies of scope?

1) *Product transformation curve*- different amounts of 2 OUTPUTS that can be produced, with fixed inputs ie- tractors vs. cars produced using labor and capital --> Same as the production possibilities frontier! wow 2) *Economies of scope*- joint output of single firm > output of 2 specialized firms that produce single product each 3) *Diseconomies of scope*- joint output of single firm < output of 2 specialized firms that produce single product each 4) *Degree of economies of scope*- % of cost savings when 1 firm produces 2+ products INSTEAD OF several specialized firms

What are the 3 approaches to determining/estimating demand? Explain them and their weaknesses.

1) *Statistical approach*- use stats + data to estimate demand --> Weaknesses: none. Stats is all powerful and all consuming!!! MUAHAHAHAHA 2) *Interview approach*- interview consumers about how much they would buy @ certain price to estimate demand --> Indirect approaches = "How would you respond if this good had a 10% discount?" --> Weaknesses: -Most difficult method -May not succeed due to interview bias from interviewer/ee 3) *Experimental approach*- real sales offers are imposed to measure how price change affects demand + competitors --> AKA direct marketing experiments --> Weaknesses: -Experiments can be costly -Too many external variables to account for -Response to temporary vs. permanent changes are different -Firm can only afford to try limited # experiments

1) What is the substitution effect? 2) What is the income effect? 3) What does higher income lead to? What does lower income lead to? 4) What is the total effect? 5) What are these effects resulting from?

1) *Substitution effect*- as prices rise/income decreases, consumers will *substitute* expensive goods with cheaper ones; *level of utility held constant* --> Always positive value --> Fall in price of a good = consumers consume more of that good; less of relatively more expensive goods 2) *Income effect*- change in demand of a good/service due to change in a consumer's discretionary income/purchasing power --> Occurs if level of income increases, or price of good decreases --> Fall in price of a good = more real purchasing power --> Magnitude of income effect depends on how much of your budget was spent on that good/utility level of IC2 --> Normal goods = positive income effect value (new demand as a result of income increase - old demand) --> Inferior goods = negative income effect value (new demand as a result of income increase - old demand) 3) *Higher income leads to... --> More Qd of normal good --> Less Qd of inferior good *Less income leads to... --> Less Qd of normal good --> More Qd of inferior good 4) *Total effect* = substitution + income effect (OCB1—OCB2) 5) Result from fall in price of good! --> Typically occur simultaneously

The AJAX corporation determines that at current prices, the demand for its computer chips has a PED of -2 in the short run, while the PED for its disk drives is -1. 1) If the corporation decides to raise the price of both products by 30%, what will happen to computer chip and disk drive sales? 2) What would happen to sales revenue for computer chips and disk drives? 3) Can you tell from the available info which product will generate the most revenue? Why/why not?

1) -2 x 30 = -60%--> Computer chips sales would decrease by 60%! -1 x 30 = -30%--> Disk drive sales would decrease by 30%! 2) Apply these percentage changes to hypothetical numbers! --> Suppose P = 100; Qd = 50--> *OG revenue = 5000* (for both C and D) --> Computer chip revenue: P' = 100(1.3) = 130; Q'd = 50(0.4) = 20--> *New chip revenue = 2600* --> Disk drive revenue: P' = 100(1.3) = 130; Q'd = 50(0.7) = 35--> *New drive revenue = 4550* Now, calculate how much the revenues have decreased, and the % of the OG revenue that =! --> % change in revenue for chips: (new revenue - old revenue)/old revenue = (2600-5000)/5000 = -48% = *decrease by 48% in chips revenue*! --> % change in revenue for disks: (new revenue - old revenue)/old revenue = (4550-5000)/5000 = -9% = *decrease by 9% in disk revenue*! 3) No, we can't tell which products will generate the most revenue without the products' initial prices and quantities--> do not know if demand was bigger for product with higher elasticity, if prices were lower for inelastic products! Don't overthink this!!! dialectical materialism doesn't do well on tests

1) What is the law of diminishing marginal returns? 2) What is the attached assumption regarding the quality of inputs?

1) As use of an input(labor, land, etc.) increases, marginal increases in output will eventually decrease --> More use of land = more output, but the amount the output increases by eventually decreases! 2) Assumption is that the input is all of the SAME quality- so marginal output returns does NOT decrease as a result of worse quality, but as a result of the law of diminishing marginal returns itself!!!!!

1) What is the average product of input? How do you calculate it? 2) What is the marginal product of input? How do you calculate it? 3) What can these equations be applied to?

1) Average product- output per unit of labor input APl = total output q/total input 2) Marginal product- additional output produced for every +1 unit of input! MP of input- change in output/change in input (typically change in output/change in labor) --> MP = slope of TP or production function! :D 3) These equations can be applied to labor (L) or capital (K)! --> Average product of labor = output per unit of LABOR input = total output q/total labor input --> Marginal product of labor = change in output/change in labor input

Describe the returns to scale, MPl, and MPk of the following production functions: 1) q = 3L + 2K 2) q = (2L + 2K)^0.5 3) q = 3L(K^2) 4) q = (L^0.5)(K^0.5) 5) q = 4(L^0.5) + 4K

1) Constant returns to scale (also perfect substitutes); L and K do not have sq. root/exponent to increase/decrease their MPs! --> MPl = constant; no sq. root/exponent -->MPk = constant; no sq. root/exponent 2) Decreasing returns to scale; whole function is decreasing by a lot due to the sq. root! --> MPl = decreasing; sq. root --> MPk = decreasing; sq. root 3) Increasing returns to scale; capital is squared, which makes q increase by a lot!--> If sum of exponents < 1 = decreasing; sum of exp = 1 = constant; sum of exp > 1 = increasing --> 1 + 2 = 3--> increasing --> MPl = constant --> MPk = increasing; exponent 4) Constant returns to scale; since both are sq. rooted and multiplied, offsets decreasing MPs!--> If sum of exponents < 1 = decreasing; sum of exp = 1 = constant; sum of exp > 1 = increasing --> .5+.5 = 1 = constant --> MPl = decreasing; sq. root --> MPk = decreasing; sq. root 5) Decreasing returns to scale; since 1 of them is decreasing and 1 of them is sq. rooted --> MPl = decreasing; sq. root --> MPk = constant; no sq. root or exponent!

Suppose that output q is function of single input, labor (L). Describe the returns to scale associated with each of the following production functions: 1) q = L/2 2) q = L^2 + L 3) q = log(L)

1) Constant returns to scale; q = L/2--> doubled = q = 2L/2 = L--> doubling L EXACTLY doubles q = constant returns to scale! 2) Increasing returns to scale; labor is not only squared, but also doubled = q MORE than doubles; there's no way for q to decline! --> Suppose L = 3 before doubling--> q = 3^2 + 3 = 12 After doubling, L = 6--> q = 6^2 + 6 = 42 --> q = MORE than doubles after inputs are doubled! 3) Increasing, then decreasing returns to scale; just remember that *logs go up, then down!!* --> log(2) = 0.301 --> log(4) = 0.602 --> log(8) = 0.903 (now q=decreasing/less than doubling) --> log(16) = 1.204

A firm produces output with capital and labor. Suppose currently the marginal product of labor is 15 and the marginal product of capital is 4. Each unit of labor costs ​$13 and each unit of capital costs ​$3. 1) Is the firm minimizing the cost of​ production? Explain. 2) If not, how could firm decrease the cost of production, holding output constant?

1) Cost minimizing--> MPl/MPk = w/r--> MPl/w = MPk/r MPl = 15 MPk = 4 w = 13 r = 3 --> See if MP/$ is equal for labor and capital! --> MPl/w = MPk/r = 15/13 = 4/3--> 1.15 < 1.33 --> *NOT minimizing costs, bc MPk/r > MPl/w* 2) Decrease cost of production by using more capital, and less labor!

1) What is an isoquant? 2) What is an isoquant map?

1) Curve showing all possible combos of inputs (typically (L,K)) that yield the SAME output --> Isoquant = convex, which means it has a negative slope/MRTS! (The production version of the indifference curve lol) --> q = F(L,K); where production version of utility = output! 2) Graph containing more than 1 isoquant; used to describe a production function (the production equivalent of the utility function)

1) What is economies of scale? 2) What is diseconomies of scale? 3) How does it differ from returns to scale? 4) What is cost output elasticity? How does it relate to EOS and DOS? 5) How are EOS and DOS at lower vs. higher output levels?

1) Economies of scale :) - doubled output = less than double the cost --> MC < AC (both decreasing) 2) Diseconomies of scale :( - doubled output = more than double the cost! --> MC > AC (both increasing) 3) Economies of scale = input proportions are variable/change! --> VS. Returns to scale = inputs increase proportionally 4) Cost output elasticity- % change in cost of production, as a result of 1% increase in output How economies of scale is measured: --> Ec = (% change in cost) x (% change in q output) = [(new cost - old cost)/old cost]x[(new q output - old q output)/old q output] = MC/AC = (change in output/change in input)/(total output/total input) = marginal cost/average cost! --> Ec < 1 = economies of scale (cost is less elastic/sensitive to change in output) --> Ec > 1 = diseconomies of scale (cost is more elastic/sensitive to change in output) --> Ec = 1 = no economies/diseconomies of scale 5) *Lower output levels = economies of scale* --> So to double output from low OG output, cost = less than proportional/doubled --> Doesn't cost a lot to increase from very little! *Higher output levels = diseconomies of scale* --> Have to pay more to increase from a lot! --> Costs more and more to produce the same amount of product (has to do with law of diminishing returns; MP decreases)

Are there economies of scale? 1) C = 15(q^2) 2) C(q) = 8 + 3q

1) Economies of scale = output or q DOUBLES--> cost LESS than doubles Double q--> C = 15(2q)^2--> C = (4)(15q^2) --> Since C = 15(q^2); (4)(15q^2) = 4C! Cost MORE than doubles, so NO economies of scale--> actually has diseconomies of scale! 2) C(q) = 8 + 3q--> double q! --> C = 8 + 3(2q)--> C = 8 + 6q --> (C-8)/3 = 2q --> Cost LESS than doubles!--> YES, has economies of scale :-) --> Just isolate 2q = double the outputs on ones side, compared to what C is!--> If C is less than 2C, it is economies of scale! --> *OR JUST PLUG IN VALUES FOR Q LIKE A NORMAL PERSON LMAO*

What are the 2 main causes of growth in labor productivity?

1) INCREASE IN CAPITAL: Growth in *stock of capital*- amount of capital available for use in production (more land, more machinery, etc.) 2) ADVANCEMENT IN TECHNOLOGY: Technological advancement- development of new technologies that allow labor, etc. to be used more effectively = more output!

w = 5; r = 10 1) What is the isocost line through (6,2)? Graph and label at least 3 points. 2) What is true of every point on this isocost line? 3) What is the slope of the line?

1) Isocost function = 5L + 10K *Asking for all the (L,K) points that have same cost as (6,2)!* --> Plug (6,2) into isocost line!--> 5(6) + 10(2) = 50 --> Now just plug and chug for values that plug into isocost line = 50! (6,2); (0,5); (10,0); (2, 4)--> Now graph! 2) Every point on the line has a cost = $50! 3) Slope of isocost line = w/r = 5/10 = -1/2 (the line is downward sloping!) --> or (y2-y1)/(x2-x1) = (5-2)/(0-6) = -1/2

1) What is an isocost line? 2) What is the production cost equation? 3) How do you calculate the isocost line's slope? 4) What is expansion path?

1) Isocost line- graph showing all possible combos of labor and capital(inputs) that can be used for same total cost --> Production version of the BUDGET LINE!!!!! --> oh god, we're going to have to find the optimal price minimizing production bundle...ugh 2) C = wL + rK --> w = wage rate; wL = labor cost --> r = capital rental rate; rK = capital cost --> The production budget line, essentially --> rK stays constant in short run! (wL is variable) 3) Slope = -change in wage of L/change in rental rate of K = change in capital/change in labor 4) Expansion path- curve passing through points of tangency/same slope/INTERSECTION between isocost lines and isoquants! (like a PCC!)

The production function for Company A is: q = 10(K^0.5)(L^0.5) The production function for Company B is: q = 10(K^0.6)(L^0.4) 1) If both companies use same amounts of capital and labor (K = L), which firm will generate more output? 2) If capital is limited to 9 machine hours, and labor is unlimited in supply...which company has a greater marginal product of labor? Why?

1) Just use dummy numbers for K and L! --> K = 2; L = 2 Now, plug into the equations: -Company A's q = 20 -Company B's q = 20 Both firms generate the same output! 2) Company A would have the greater marginal product of labor (when labor > 1, since 1 is the choke point for labor; 0^0.5 = 0 after all) --> This is bc the exponent of L is greater for Company A than Company B! Proof: --> Suppose K = 9; L = 20 qA = 10(9^0.5)(20^0.5) = 134.16 qB = 10(9^0.6)(20^0.4) = 123.87 --> Now, L = 21 qA = 10(9^0.5)(21^0.5) = 137.48 qB = 10(9^0.6)(21^0.4) = 126.31 A's MP = 137.48-137.16 = 3.32 B's MP = 2.44 --> Thus, A's MP is higher!

1) What is the long term average cost curve? 2) What is the short term average cost curve? 3) What is the long term marginal cost curve?

1) LAC- curve showing average cost of production, as output produced increases (both capital/K and labor/L are variable!) 2) SAC- curve showing average cost of production, as output produced increases (holding capital/K constant; labor/L is variable!) 3) LMC- curve showing marginal cost of production, as output produced increases *Output = x-axis; costs = y-axis!*

1) What is labor productivity? 2) What kinds of economists are typically concerned with this? 3) Why is labor productivity important?

1) Labor productivity- APl for entire industry/economy = RGDP (everything produced by economy)/hours worked 2) Macroeconomists care about this! 3) Important bc it determines the REAL standard of living a country can give to its citizens

1) What is marginal cost? What is slope for? 2) What is marginal cost in the short run? 3) What is average total cost? 4) What is average fixed cost? 5) What is average variable cost? 6) What are all cost functions = function of? 7) What happens to MC if MPl falls/rises?

1) MC- increase in cost resulting from increasing output by 1 unit --> = change in cost/change in quantity of output = change in total cost/change in quantity of output = change in variable cost/change in quantity of output --> ALSO = slope of TC = slope of VC 2) MC in short run = wage rate/MPl = wage rate/[(change in quantity of output)/(change in labor)] 3) ATC- total cost/quantity of output 4) AFC- fixed cost/quantity of output 5) AVC- variable cost/quantity of output 6) All cost functions = function of output or q! 7) --> If MPl falls, MC rises! (takes more money to get same amount of output) --> If MPl rises, MC falls! (takes less money to get same amount of output)

1) What is the marginal rate of technical substitution (MRTS)? 2) How do you calculate it? 3) How do you find the firm's cost minimizing/profit maximizing choice of inputs (L,K)? 4) Is the MRTS the same at different areas along the isoquant curve? 5) Why is the MRTS always negative?

1) MRTS/slope of isoquant!- amount you reduce of quantity for input A + increase by 1 unit of quantity for input B, while keeping output(production utility) constant! (always negative!) 2) MRTS of x for y = -change in y/change in x --> MRTS of labor for capital = -change in capital(K)/change in labor(L) 3) Set MPl/MPk = -change in K/change in L = MRTS--> find variable A in terms of B and plug into production version of BL (remember, its marginal x/marginal y!) 4) No, the MRTS is different for different areas of the isoquant- just like the MRS for the indifference curves This is because isoquants are convex (bowed inwards) 5) MRTS is always negative bc productivity of any ONE input is limited (remember, MRTS is how much of input A you can decrease, while INCREASING input B to maintain same output--> productivity of input B is limited!) --> Production needs a balanced mix of both inputs

1) What do isoquants look like when inputs are perfect substitutes? 2) What do isoquants look like when inputs are fixed proportions?

1) Perf substitutes- downward sloping parallel lines --> MRTS is constant along the isoquant! --> ie- musical instruments can be made entirely with machines (capital); or with no tools and just highly skilled labor! 2) Fixed proportions/perf complements- outward facing right angles (L's, literally lmao) --> MRTS = undefined/infinity along vertical part of isoquant; MRTS = 0 along horizontal part of isoquant --> ie- nutty oat crunch cereal requires exactly 1 oz nuts for every 4 oz oats in every serving! lmao

Consider a market with network externalities, where Qd = 100-P. At P = $45, current demand without network externalities is Qd1 = 77.50-0.50P. At P = $35, demand without network externalities would be Qd2 = 82.50-0.50P. 1) With network externalities, how much would the price change increase/decrease Qd? 2) Without network externalities, how much would the price change increase/decrease CURRENT Qd? 3) Therefore, how much did the network externality change the Qd?

1) Plug $45 and $35 into the Qd equation with network externalities! --> Qd = 100-P--> 100-(45) = 55, original Qd --> Qd = 100-P--> 100-(35) = 65, new Qd --> With network externalities, Qd increases by 10! 2) Plug $45 and $35 into CURRENT Qd equation withOUT network externalities! --> Qd1 = 77.50-0.50P--> 77.50-0.50(45) = 55, original Qd --> Qd1 = 77.50-0.50P--> 77.50-0.50(35) = 60, new Qd --> WithOUT network externalities, Qd increases by 5! 3) The network externality increased Qd for P = 35 by 5!

1) Price increase in sugar = what kind of income and substitution effect? 2) Price increase in housing = what kind of income and substitution effect? 3) Price increase in theater tickets = what kind of income and substitution effect? 4) Price increase in all food = what kind of income and substitution effect?

1) Price increase in sugar = --> Small income effect- makes up small portion of budget, so income not too affected --> Small substitution effect- no need to substitute, because it does not take up huge portion of budget 2) Price increase in housing = --> Large income effect- income = less valuable with inflation of housing prices --> Small substitution effect- what to substitute housing with? 3) Price increase in theater tickets = --> Small income effect- makes up small portion of budget, income not too affected; purchasing power not weakened --> Large substitution effect- many substitutes for theater tickets/other ways to spend money and time (also bigger ticket item than sugar, so you would want to substitute) 4) Price increase in all food = --> Large income effect- makes up large portion of budget, income purchasing power decreased --> Small substitution effect- what to substitute food with?

1) What is the returns to scale rate? 2) What are the 3 different types of returns to scale rate? How do they look on graphs? (*referring to the isoquants*)

1) Rate that output increases, as inputs are increased proportionally (same amount across the inputs; typically double the inputs) ie- output = ? if we put 2 farmers to work with 2 machines on 2 acres of land? 2) i. *Increasing returns to scale*- if inputs double, outputs MORE than double --> For Cobb Douglas function (L, K are multiplied): if exponents' sum > 1--> IRTS --> *Isoquants move closer together as inputs are increased along the line (line slices down from the origin)* ii. *Constant returns to scale*- if inputs double, outputs EXACTLY double (output change = linear to input change) --> For Cobb Douglas function (L, K are multiplied): If exponents' sum = 1--> CRTS --> *Isoquants are equally spaced apart; isoquants are still convex though!* iii. *Decreasing returns to scale*- if inputs double, outputs LESS than double --> For Cobb Douglas function (L, K are multiplied): If exponents' sum < 1--> DRTS

1) If demand is inelastic, what happens to expenditures if.... a) Price increases? b) Price decreases? 2) If demand is elastic, what happens to expenditures if... a) Price increases? b) Price decreases? 3) If demand is unit elastic, what happens to expenditures if... a) Price increases? b) Price decreases?

1) Relationship between inelastic demand and expenditures = linear!!!!! a) Price increases = spending increases b) Price decreases = spending decreases 2) Relationship between elastic demand and expenditures = inverse a) Price increases = spending decreases b) Price decreases = spending increases 3) Relationship between unit elastic demand and expenditures = nonexistent a) Price increases = spending unchanged b) Price decreases = spending unchanged *Unit elastic = adjust consumption of goods so that expenditures remain the same*

A firm has a fixed production cost = $1,000 and constant marginal cost of production = $400 per unit produced. 1) What is the firm's total cost function? 2) What is the firm's ATC of production? 3) If the firm wanted to minimize the average total​ cost, would it choose to be very large or very​ small? Explain.

1) Remember TC = variable cost + fixed cost = wL + rK! (wL is variable)--> write in terms of q --> FC = 1000 --> MC or VC = 400 per output, or 400q --> *TC = 1000 + 400q* OR 1000 + 400L (since L is typically variable) 2) ATC = TC/q--> (1000 + 400q)/q--> *ATC = 1000/q + 400* 3) Very large, bc large firms are able to produce more(q), and ATC goes down with higher q of output(since it's the denominator)!

You manage a plant that​ mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function: q = 20KL q = the number of engines produced per​ week K = the number of assembly​ machines L = the number of labor teams Each assembly machine rents for r = ​$20,000 per​ week, and each team costs w = $4,000 per week. Engine costs are given by the cost of labor teams and​ machines, plus ​$2,000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design. FOR THE SHORT TERM: 1) What is the TC function, in terms of q? 2) What is the AC function, in terms of q? 3) What is the MC function, in terms of q? 4) How do average costs vary with output? 5) How many teams are required to produce 500 engines? 6) What is the AC per engine for producing 500 engines? 7) Suppose you're asked to make recommendations for the design of a new production facility. What capital/labor(K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output q?

1) TC = FC + VC = rK + wL --> r = 20,000 --> w = 4,000 --> K = 5 --> Cost for each production of engine = 2,000 TC = 100,000 + 4000L + 2000q--> need to find L in terms of q! --> q = 20(5)L--> L = q/100 --> TC = 100,000 + 4000(q/100) + 2000q--> *TC = 100,000 + 2040q* 2) AC = TC/q--> (100,000 + 4000(q/100) + 2000q)/q--> 100,000/q + 40 + 2000--> *AC = 100,000/q + 2040* 3) MC = change in cost of producing output/q of output = derivative of TC --> *MC = 2040* 4) As q of output increases, AC goes down! 5) Basically L = ? when q = 500 --> Recall from (1) L in terms of q of output--> L = q/100 --> L = 500/100--> *L = 5 teams!* 6) AC = 100,000/q + 2040--> plug in q = 500--> *AC = $2240* 7) This is asking for the cost minimizing RATIO (not the actual bundle) which = setting MRTS = cost ratio! :-D (they already gave you MRTS which = K/L, lol) --> MRTS = MPl/MPk = w/r --> Recall that q = 20KL--> MPl = 20K; MPk = 20L--> MRTS = K/L --> w = 4,000; r = 20,000--> Now set MRTS = cost ratio! --> K/L = 4000/20,000 = 1/5 = 0.2/1--> *0.2 K for every 1 unit of L OR 5 L for every 1 unit of K*

When Ajax Co. produced 3 units of output per​ week, its total fixed cost was ​$120 and total variable cost was ​$45. When output increased to 4 units per​ week, total fixed cost remained at ​$120 and total variable cost increased to ​$70. 1) With output at 4 units/week, TC = ? 2) With output at 4 units/week, AVC = ? 3) With output at 4 units/week, AFC = ? 4) With output at 4 units/week, ATC = ? 5) MC of producing the 4th unit = ?

1) TC = FC + VC--> 120 + 70 = $190 2) AVC = VC/q--> 70/4 = $17.5 3) AFC = FC/q--> 120/4 = $30 4) ATC = TC/q--> 190/4 = $47.5 5) MC = change in total cost of output/change in q of output--> (190-165)/(4-3) = $25

q = 8(L^0.5)K w = 7 r = 3 K = 1 1) What is the total cost function? 2) What is the fixed cost? 3) What is the variable cost? 4) What is the total cost function, in terms of q? 5) What is the marginal cost?

1) TC = wL + rK --> 7L + 3 2) FC = 3 3) VC = L; find what L = from production function! --> q = 8(L^0.5)(1) = 8(L^0.5)--> L = q^2/8^2 = *q^2/64* 4) TC = (7q^2)/64 + 3 5) MC = derivative of TC! --> *MC = 7q/32*

1) What happens to total product as MP is increasing and positive? 2) What happens to total product as MP is decreasing and positive? 3) What happens to total product as MP is decreasing and negative?

1) Total product is increasing at an increasing rate! 2) Total product is increasing at a decreasing rate! 3) Total product is decreasing!

1) What is user cost of capital? 2) What is rental rate of capital? 3) What is their relationship, if capital market is competitive as is the assumption?

1) User cost of capital- annual cost of owning/using capital asset/opportunity cost of capital = economic depreciation + (interest rate x value of capital) = economic depreciation + forgone interest 2) Rental rate of capital- annual cost of renting one unit of capital 3) Rental rate = user cost --> Most textbooks assume that capital is rented at rental rate r --> Capital that is purchased can be treated as if it were rented at rental rate = user cost ie- if you bought K for $100, assume that it's the same as renting K for $10 for 10 weeks = $100 user cost --> Simplify the capital cost and labor cost functions!

Suppose that a​ firm's production function​ is: q = 10(L^0.5)K^0.5 Its marginal product functions​ are: MPl = 5(K^0.5)/L^0.5 = 0.5q/L MPk = 5(L^0.5)/K^0.5 = 0.5q/K The cost of a unit of​ labor, w = ​$20 and the cost of a unit of​ capital, r = ​$80. Isoquants for output of 140 and 280 are illustrated in the figure to the right. ​Initially, the firm is producing 140 units of output and has determined that the​ cost-minimizing quantities of labor and capital are 28 and 7​, respectively. 1) Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short​ run, how much labor will the firm​ require? 2) What are the optimal levels of capital and labor in the long run, if the firm wants to increase output to 280 units? 3) What is the isocost line for q = 140? 4) What is the isocost line for q = 280?

1) When q = 280, K = 7, L = ? --> q = 280; K is fixed at 7!!!--> THIS IS NOT ASKING FOR COST MINIMIZING INPUTS!!! STOP OVERTHINKING! --> Set 280 = production function to find L! --> 280 = 10(L^0.5)(7^0.5)--> 280/(7^0.5) = 10(L^0.5)--> 280/(10 x 7^0.5) = L^0.5--> [280/(10 x 7^0.5)]^2 = L--> [280^2/(10^2 x (7^(0.5 x 2))) = L-->78400/700 = L--> *L = 112* (Remember that (x(y^0.5))^2 = (x^2)(y^0.5)^2!!!) 2) NOW asking for cost minimizing inputs! --> q = 280 i. Set MRTS = w/r--> MPl/MPk = w/r--> (0.5q/L)/(0.5q/K) = 20/80--> K/L = 1/4--> K = 0.25L ii. Plug K in terms of L into production function!--> 10(L^0.5)(0.25L)^0.5 = 280--> 280/10 = (L^0.5)(0.25^0.5)(L^0.5)--> 28 = 0.5L--> *L = 56!* iii. Plug L into K = 0.25L to find K!--> K = 0.25(56)--> *K = 14!* 3) q = 140 has the bundle (28,7), use this to find cost of q = 140 (since everything on the isoquant = same output) TC = 20L + 80K--> 20(28) + 80(7) = 1120 = TC --> 1120 = 20L + 80K --> L intercept = 56; K intercept = 14 4) q = 280 has the bundle (56,14), use this to find cost of q = 280 (since everything on the isoquant = same output) TC = 20L + 80K--> 20(56) + 80(14) = 2240 = TC --> 1120 = 20L + 80K --> L intercept = 112; K intercept = 28

Marginal product of another worker = # customers that can be served by that worker in given time period. Juana the manager has 1 worker, but is considering hiring 2nd and 3rd. 1) Why would the marginal product of the 2nd and 3rd workers be higher than the 1st? a) workers can specialize at a separate task, and output will increase at increasing rate b) workers can take advantage of existing machinery, and total output will increase c) workers of higher quality can be hired, and output will increase at increasing rate d) workers can take advantage of existing machinery, and average output will increase e) company can purchase more machinery for additional workers, and output will increase at increasing rate 2) Why might you expect marginal product of additional workers to diminish eventually? a) company's equipment may become outdated/inefficient, output will increase at diminishing rate b) company may use less capital, and output will increase at diminishing rate c) they may get in each other's way, total output will decrease d) company may experience setbacks in technology e) they may no longer be able to specialize, output will increase at diminishing rate

1) a) workers can specialize at a separate task, and output will increase at increasing rate --> Workers hired can specialize on tasks, allowing them to serve more customers with different requests! 2) e) they may no longer be able to specialize, output will increase at diminishing rate --> There are only a number of types of requests customers will have that workers can serve! --> Law of diminishing marginal returns bih NOT c) they may get in each other's way, total output will decrease—total output may not necessarily decrease, but will increase at a decreasing rate

Production function--> q = 5LK MPl = 5K MPk = 5L wage rate = 7 rental rate = 3 K = 1 1) What is the total cost function? 2) What is the fixed cost? 3) What is the variable cost? 4) What is the total cost function in terms of q? 5) What is the marginal cost?

1) q = 5LK Cost function = wL + rK *Cost function = 7L + 3* 2) *Fixed cost or rK = 3* 3) Variable cost = must solve for L from q function! --> q = 5LK--> K = 1 --> q = 5L --> L = q/5--> now plug into cost function! --> 7(q/5) + 3--> *VC or wL = (7/5)q = L* 4) TC = 7L + 3 --> Plug in VC or wL which = (7/5)q --> TC = (7/5)q + 3 5) Marginal cost = derivative of total cost! --> Derivative of (7/5)q + 3 = *7/5 = MC*

If a firm hires a currently unemployed​ worker, the opportunity cost of utilizing the​ worker's services is zero. This statement is... A. false because the​ worker's time otherwise spent in unpaid household work has value. B. false because the​ worker's new wages are an implicit cost. C. true because the​ worker's new wages are a sunk cost. D. false because the​ worker's time otherwise spent in leisure activities has no value. E. true because the​ worker's time otherwise has no value.

A. false because the​ worker's time otherwise spent in unpaid household work has value. --> Referring to the worker's opportunity cost of going to work (so the worker themself could be doing household work, which is the opportunity cost of working instead of staying home)

A firm that has positive accounting profit does not necessarily have positive economic profit. This statement is... A. true because economic costs will be greater than accounting costs if implicit costs exist. B. false because economic costs will be greater than accounting costs if depreciation exists. C. true because economic costs will be greater than accounting costs if sunk costs exist. D. false because accounting costs will be greater than economic costs if implicit costs exist. E. false because economic costs will be greater than accounting costs if explicit costs exist.

A. true because economic costs will be greater than accounting costs if implicit costs exist. --> Implicit costs such as opportunity cost and whatnot! Economic costs = explicit(accounting) costs + implicit(opportunity) costs

What is accounting cost? What is economic cost? What is opportunity cost? What is sunk cost?

AC- actual expenses + depreciation charges for capital equipment; explicit --> Usually different from economic costs --> Backward looking EC- firm's cost of utilizing economic resources in production; implicit + explicit --> Forward looking OC- cost of foregone opportunities, when firm's resources not put to their best use; implicit SC- costs that have been made/incurred, cannot be recovered --> Opportunity cost = 0

Atiya quits her computer programming​ job, where she was earning a salary of ​$70,000 per​ year, to start her own computer software business in a building that she owns and was previously renting out for ​$26,000 per year. In her first year of business she has the following​ expenses: --> $45,000 salary paid to herself --> $0 rent --> $30,000 other expenses Find the accounting cost and the economic cost associated with​ Atiya's computer software business.

Accounting cost = explicit costs = 45k + 30k = $75k Economic cost = implicit costs + explicit costs = Implicit costs = (70k-45k, which is difference in salary that she's missing out on) + 26k Explicit costs = $75k --> (70k-45k) + 26k + 75k = *$126k* --> OR (70k-45k to get what she could be earning with the computer programming job) + 26k + 30k + 45k of what she has to pay herself) = not including 45k in the equation to begin with!

How does AC behave when MC > AC? How does AC behave when MC < AC? How does AC behave when MC = AC?

Basically the same relationship as AP and MP! When MC > AC, AC is increasing! When MC < AC, AC is decreasing! When MC = AC, AC is at minimum!

Jose rents office space for​ $20,000 per year. He uses the office to fill out tax returns for​ 1,000 clients per year. If the office rent increases to​ $25,000 per​ year, the marginal cost of filling out tax returns will... A. increase by​ $5,000. B. increase by​ $5. C. not change. D. increase, but we cannot determine the amount of the increase with the information given.

C. not change. --> REMEMBER, IT'S JUST CATEGORIZING COSTS! --> Rent increase = increased FC; MC stays the same; AC increases

Qd = 46-2P Qs = -14+P What is the consumer surplus? Calculate mathematically.

Consumer surplus = (1/2)(price intercept of Qd - equilibrium price)(equilibrium quantity) --> Qd = Qs--> 46-2P = -14+P--> *P = 20; Q = 6* --> Convert Qd equation into y=mx+b format to figure out y intercept! --> P = -1/2Qd + 23 -->(1/2)(23-20)(6) = *9 consumer surplus!*

Elizabeth babysits on the weekends for extra money. Suppose that 3 neighbors with children are interested in hiring Elizabeth as a babysitter. Brown family would pay $34 for Elizabeth to babysit. Smith family would pay $26 for Elizabeth to babysit. Jones family would pay $25 for Elizabeth to babysit. If Elizabeth offers to babysit each set of children for $25, what will be consumer surplus for the three families' children combined?

Consumer surplus = willing to pay - actual price --> Brown family = 34-25 = $9 --> Smith family = 26-25 = $1 --> Jones family = 25-25 = $0 Add the surpluses together! --> $9+$1 = *$10 consumer surplus*

1) What is consumer surplus graphically and definitively? 2) What is aggregate consumer surplus?

Consumer surplus- difference between what a consumer is willing to pay vs. amount actually paid -->Willing to pay - amount actually paid = surplus! --> Total benefit from consumption of product - cost of purchase --> Area under demand curve; above the price line --> Positive surplus = you saved! --> Negative surplus = you were robbed breh ie- student willing to pay $10 for textbook, but actually paid $150 --> $10-$150 = -$140 surplus, aka a deficit, aka the American education system 2) Aggregate consumer surplus- summation of consumer surpluses for all consumers

Suppose that quantities of L and K must be used in equal quantities. w = 8 r = 2 L = K = q Find cost function. What are (L,K) for q = 4? q = 5? Graph q = 4 and q = 5. What is the MC? What is the AC?

Cost function = wL + rK --> C = 8L + 2K Since L = K = q--> C = 8q + 2q --> C = 10q for q = 4--> L and K = 4--> (4,4) --> Graph- would be outward facing right angles MC = derivative of total cost = 10 AC = TC/q = 10

If the owner of a business pays herself no salary, than the accounting cost is zero, but the economic cost is positive. This statement is... A. true because economic costs include opportunity costs such as expenditures that cannot be recovered. B. false because economic costs include explicit costs. C. false because economic costs include the same costs as accounting costs. D. true because economic costs include opportunity costs such as the value of the business​ owner's time. E. false because accounting costs include implicit costs such as the value of the business​ owner's time.

D. true because economic costs include opportunity costs such as the value of the business​ owner's time. Economic costs = implicit costs (time, opportunities) + explicit costs

The production function q = 22(K^0.7)(L^0.1) exhibits what kind of returns to scale?

Decreasing returns to scale (MPk = decreasing due to sq. root; MPl = decreasing due to sq. root) --> Or for Cobb Douglas functions, if sum of exponents < 1--> DRTS! --> 0.7 + 0.1 = 0.8 < 1--> DRTS!

What is speculative demand?

Demand driven by expectation of the good's price increasing --> Not a result of utility resulting from good --> This is literally me and mom.....always lmaooooo ie- inflation drives people to buy more (which just increases inflation...lmao) bc they think price/value of good will just continue increasing

What is the difference between economies of scale and returns to​ scale? A. Economies of scale define whether joint output of a single firm is greater than output that could be achieved by two different firms when each produces a single​ product, and returns to scale define how output changes with input usage for a single firm. B. Economies of scale are present when the expansion path is a straight​ line, and returns to scale are present when the expansion path is not a straight line. C. Economies of scale are present when the​ long-run average cost curve is decreasing​, and returns to scale are present when the​ long-run average cost curve is increasing. D. Economies of scale define how cost changes with​ output, and returns to scale define how output changes with input usage. E. Economies of scale define how cost changes with output in the short ​run, and returns to scale define how cost changes with output in the long run.

EOS = more general; dealing with how cost changes with output! (ECONOMIES of scale, deals with the cost!) RTS = what happens to outputs when inputs are doubled! D. Economies of scale define how cost changes with​ output, and returns to scale define how output changes with input usage.

Chapter 7 Paper HW 3) A firm has a fixed production cost of $2500. For the first 100 units of production, the firm has a constant marginal cost of production of $50/unit output. Producing more than 100 units has a constant marginal cost of production of $70. The firm cannot produce more than 150 units. a) What is the firm's total cost function? Derive the formula(s) and graph the function. b) What is the firm's marginal cost function? Derive the formula(s) and graph the function. c) What are the firm's ATC, and AFC functions? Derive the formula(s) and graph the functions. d) Describe the relationship between the marginal cost function and the ATC function.

FC = 2500 MC = 50 for first 100 units of output MC = 70 for 101+ units of output Cannot produce more than 150! (the graph will have 2 different lines!) a) TC = FC + VC--> 2 TC functions; 2 TC lines! --> VC1 = 50q for anything below 100 units of output --> VC2 = 70q for anything above 100 units of output Now plug VCs into TC functions: --> TC1 = 2500 + 50q --> TC2 = 500 + 70q Find TC2 by setting TC1 = TC2 when q = 100 (they must intersect at q = 100): --> b + 70(100) = 2500 + 50(100)--> TC2 = 500 + 70q! Graph: x = q output; y = cost --> Cost becomes infinite at capacity constraint of 150 --> REMEMBER THAT GRAPH HAS TO BE CONTINUOUS! --> TC1 and TC2 intersect at (100, 7500) --> TC1 = (10,3000); (50,5000); (100,7500) --> TC2 = (100,7500); (110,8200); (150,11000) b) MC = derivative of TC, or literally what they gave you lol...either way you get the same answer! --> MC1 = 50 for q less than or = 100 --> MC2 = 70 for q > 70 Graph: straight line for y = 50; y = 70 (connect them like a step on flight of stairs, NAHMEAN) c) ATC = TC/q = 2 ATC equations: --> ATC1 = 2500/q + 50 --> ATC2 = 500/q + 70 AFC = FC/q = *2500/q* d) ATC decreases when MC<ATC; MC pulls ATC down ATC increases when MC>ATC; MC pulls ATC up! (?)

A firm uses 80 hours of labor and 6 units of capital to produce​ 10,000 gadgets per day.​ Labor's marginal product is 4 gadgets per hour and the marginal product of capital is 20 gadgets per unit. Each unit of labor costs​ $8 per hour and each unit of capital costs​ $50 per unit. If the firm wants to continue producing​ 10,000 gadgets per day at the lowest possible​ cost, it should... A. use less of both inputs. B. continue using 80 hours of labor and 6 units of capital. C. use more labor and less capital. D. use more capital and less labor.

Find MP/$ to find out which one to use more of! --> MPl = 4; MPk = 20 --> w = 8; r = 50 MPk/r = 20/50 = 0.4 MPl/w = 4/8 = 0.5 --> Firm should use more labor and less capital! C. use more labor and less capital.

How do you find marginal cost from total cost? Suppose TC = 50 + 2q. Find the MC.

Find derivative cost of total cost--> to find marginal cost! --> MC = derivative(TC) MC = derivative(50+2q) --> Derivative(50+2q) = 2 --> So *MC = 2!*

Why are firms necessary, according to Pearson?

Firms provide means of coordination between different workers/jobs for the production of outputs --> Streamline the production process --> Allow goods/services to be produced far more efficiently than without --> Lets just pretend like collective ownership of the means of production doesn't exist! self satisfying rhetoric, steeped

What is the production function? What is the equation for it?

Function showing the *maximum output* firm can produce for a combination of inputs (L,K) --> Maximum amount for minimum effort bih! --> This is the production equivalent of the UTILITY FUNCTION! --> q = F(L,K) q = highest output firm can produce for inputs (L,K) L = labor K = capital ie- q describes how much the crops farmer could yield with specific amounts of labor (labor/L/x) and machinery(capital/K/y)

Chapter 4 Paper HW: 2) An individual consumes 2 goods, clothing and food. Given the info below, illustrate both the income consumption curve and the Engel curve for clothing and food. Budget = $100; 150; 200; 250 Pc = $10; 10; 10; 10 Pf = $2; 2; 2; 2 Qc = 6; 8; 11; 15 Qf = 20; 35; 45; 50

ICC: (only different in what is held being held constant; prices held constant here!) 1) Remember that the Qs corresponding to the prices are not intercepts for the budget line, but the point where MRS = Px/Py and thus the point where the BL and IC intersects! (utility maximizing Qs) --> Q consumed of F = x; Q consumed of C = y 2) Find the intersects for the different prices--> construct budget lines for each price! ie- 10C + 2F = 100, and so on. 3) The ICC is just the line that traces all the different points of Qs that are utility maximizing through the different budget lines/ICs :D --> BLs: a) (50,0); (0,10) b) (75,0); (0,15) c) (100,0); (0,20) d) (125,0); (0,25) --> IC's (and what ICC passes through) a) (20,6) b) (35,8) c) (45,11) d) (50,15) Engel curve: just curve with x = Q consumed of the good (NOT the budget line intercept!); y = corresponding income level --> Remember to do a separate Engel curve for each good! --> If Engel curve slopes upward = normal good (as income increases, consumption increases) --> If Engel curve slopes downward = inferior good (as income increases, consumption decreases) --> Engel curve for food: (20,100); (35,150); (45,200); (50,250) --> Engel curve for clothing: (6,100); (8,150); (11,200); (15,250)

MRS for higher Pf + low Qf vs. low Pf + high Qf on downsloping curve?

Internal value/MRS of food is high when price is high and quantity is low (rare and expensive? MRS skyrockets) --> Slope is steeper on typical convex utility curve at top, so MRS is higher! Internal value/MRS of food is low when price is low and quantity is high (common and cheap? MRS falls faster than my respect for America:) --> Slope is flatter on typical convex utility curve at bottom, so MRS is lower!

How do you find market demand from 3 demand segments graphically?

It is the horizontal summation of the quantities demanded! So for a price, find the amount demanded--> add them up, create new point! --> *Basically, add Qd coordinates (or the x coordinates), keeping Price(y) coordinates constant. VOILA! --> Say price = $10. Demand curve A = (5,10); demand curve B = (7,10); demand curve C = (8,10)--> market demand point = (20,10) --> Use this method to construct new curve!

What are the 3 factors of production?

LCI: *Labor*- human inputs; skilled+unskilled workers/entrepreneurial efforts! *Capital*- NOT financial capital; physical capital like land, buildings, machinery, equipment, inventories that are kept for future use (investments) *Inputs/materials*- nonhuman inputs; natural/raw resources ie- steel, plastics, electricity, water, etc.

Chapter 6 HW: 5) Consider the production function q = (L^0.5) + 7(K^3). Starting from input combo (2,5), does production function exhibit increasing, constant, or decreasing returns to scale if inputs double?

MPl = decreasing due to sq. root MPk = increasing due to exponent of 3--> larger constant than labor! --> Staring with (2,5): q1 = (2^0.5) + 7(5^3) = 876.41 --> If inputs double = (4,10): q2 = (4^0.5) + 7(10^3) = 7002 *Production function exhibits increasing returns to scale when inputs double* Returns to scale = dependent on the calculation (since MPl is decreasing and MPk is increasing; depends on magnitude of MPl's decrease and magnitude of MPk's increase!--> plug (2,5) and play around with numbers to see if it's increasing/decreasing/constant!

MPl for production of cereal is 80 cereals per hour. MRTS of labor for machine capital (all in hours) = 0.10. What is the MPk?

MRTS = MPl/MPk --> MPl = 80; MRTS = 0.10--> Just plug and chug! --> 0.10 = 80/MPk--> MPk = 800 cereals per hour!!!!!

How do you derive marginal cost from MRTS = w/r?

MRTS = w/r--> MPl/MPk = w/r --> MPl/w = MPk/r, which is the marginal product per dollar --> w/MPl = r/MPKk is the cost per marginal product = marginal cost! :D

Suppose a chair manufacturer finds that the marginal rate of technical substitution​ *(MRTS) of capital for labor* in her production process is substantially less than the ratio of the rental rate on machinery​ (r) to the wage rate for​ assembly-line labor​ (w). How should she alter her use of capital and labor to minimize the cost of​ production?

MRTS of capital FOR labor = -change in L/change in K = MPk/MPl Ratio of r to w = r/w --> She finds that MPk/MPl < r/w = --> Substitute numbers for them that fit the inequality and find out which one has a higher MP/$! --> Suppose MPk/MPl = 1/2; r/w = 2/3 MPk/r = 1/2; MPl/w = 2/3--> MPl/w > MPk/r--> L has higher MP/$! --> Use more labor and less capital!

What is a price consumption curve? What is an income consumption curve? What is an individual demand curve? What is an Engel curve? What does it mean when Engel curve is a backwards C on a graph?

Market baskets: 1) *Price consumption curve*(price)- curve tracing utility maximizing market baskets as the price of one good changes 2) *Income consumption curve*(income)- curve tracing utility maximizing market baskets as consumer's income changes Individual goods: 3) *Individual demand curve*(price)- curve relating Qd of a good to that good's price changes 4) *Engle curve*(income)- curve relating Qc of a good to consumer's income changes 5) If Engel curve is backwards C... --> Top part of the backwards C = inferior good (income elasticity of demand is negative) -High income = lower demand -Low income = higher demand! --> Bottom part of backwards C = normal good (income elasticity of demand is positive) -High income = higher demand -Low income = lower demand! Consumption = mutual relationship between utility maximizing market baskets + Price/Income changes Demand/Engle = direct relationship between Qd + Price/Income changes

There are 500 people with demand of Q = 10-2P. What is the market demand equation? Is there a choke price? Is there a kink in the graph itself (ie, is it continuous?)?

Market demand = SUM of all demand curves within the market, which in this case is 500 of 10-2P--> 500(10-2P) = 5000-1000P Choke price, P = 5 (they won't buy anything higher than $5) --> 10-2(5) = 0 No, there isn't a kink in the graph itself because all the same people are buying—the choke price is the same! --> Yes, it is continuous! There is only 1 market demand curve in this case :D

What is the market demand curve? What is the individual demand curve?

Market demand curve- curve showing Qd demanded of a good by ALL consumers at certain price point --> Summation of individual demand curves in certain market Individual demand curve- curve showing Qd demanded of a good by individual consumer at certain price point

What is a network externality? What is the bandwagon effect? How is it related to price? What is the snob effect? How is it related to price? What are examples of bandwagon and snob goods?

Network externality- individual's demand depends on what other people purchase (peer pressure) *Bandwagon effect/positive network externality*- as other people's demand increases, individual Qd increases; linear relationship --> Prices dip, Qd SKYROCKETS --> Has MORE elastic demand! --> ie- children's toys, trendy clothing, social networks (twitter!!!!!) --> Firms then further exploit the bandwagon effect through lowering price, wow i love capitalism *Snob effect/negative network externality*- as other people's demand increases, individual Qd decreases; inverse relationship --> Prices dip, Qd actually drops! --> Raise prices, Qd actually rises! --> Has LESS elastic demand! --> ie- rare works of art, bespoke clothing, etc. --> Firms then further exploit the snob effect through increasing price

How would the linear demand curve be described algebraically?

Q = a - bP + cI P = price I = income!

Chapter 4 Paper HW: 7) Suppose milk and cookies are known to be perfect complements, where 1 milk is always consumed with 1 cookie. a) Draw the price consumption curve for a variable price of cookies. (Assume the price of milk is $1 per bottle and the income for this budget is $10.) b) Draw the income consumption curve. (Assume the price of milk is $1 per bottle and the price of cookies is $0.50.)

REMEMBER THAT THESE ARE PERFECT COMPLEMENTS! SO BOTH GOODS MUST BE CONSUMED IN THE STATED PROPORTIONS REGARDLESS OF PRICE/BUDGET. a) Pm = 1; Pc = variable; i = 10 --> Pm = 1 is constant for the BL; line just pivots/swivels for variable prices of Pc! --> For perfect complements, consumer consumes equal amounts of both goods regardless of BL so... --> Indifference curves are right angles in succession of each other --> *PCC goes straight through the indifference curves and cuts down the middle of the graph, into infinity!* b) Pm = 1; Pc = 0.5; i = variable --> Since Pm > Pc, budget line will have higher C intercept than for Pm --> For perfect complements, consumer consumes equal amounts of both goods regardless of BL so... --> Indifference curves are right angles in succession of each other --> *ICC goes straight through indifference curves and cuts down middle of graph, into infinity!* *PCC and ICC are identical for perfect complements!!! :D*

Why would the MRTS diminish as more and more labor is substituted by capital?

Remember that MRTS = MPl/MPk (or marginal x/y!)! Labor substituted FOR capital = labor substituted BY capital--> MPl will be decreasing = smaller MRTS!

What does MRTS = 3 mean?

Remember, MRTS = -change in y/change in x! so that output stays constant! (output being q; production version of utility) -3 rise; +1 run--> input on vertical axis(capital) decreased by 3 units; input on horizontal axis(labor) increased by 1 unit = output stays constant! Typically, K = y; L = x--> exchanging 3 capital for 1 labor

Suppose L = x-axis; K = y-axis 1) What does isoquant with flatter slope tell you? 2) What does isoquant with steeper slope tell you? 3) What industries do each type of isoquant represent?

Remember: y-axis = K or capital; x-axis = L or labor 1) With flatter slope--> -less K/more L = willing to give up lots of labor for capital! --> Capital more valued 2) With steeper slope--> -more K/less L = willing to give up lots of capital for labor! --> Labor more valued 3) Capital more valued/flatter slope = manufacturing industry Labor more valued/steeper slope = services industry

Returns to scale vs. economies of scale vs. economies of scope

Returns to scale = inputs double--> output doubles/more/less than doubles Economies of scale = output doubles--> cost LESS than doubles --> Constant returns to scale = cost LESS than doubles Diseconomies of scale = output doubles--> cost MORE than doubles Economies of scope = single firm producing 2 products > 2 firms producing 2 products

1) How do you find the price minimizing point that intersect between isocost line and isoquant? 2) How do you find the marginal product per dollar of input?

Same as the utility maximizing stuff! 1) MPl/MPk = w/r = change in K/change in L--> find L in terms of K or K in terms of L(variable function 1) into q function; plug back into variable function 1 to find the other value! 2) MPl/w = MPk/r--> to find whether or not labor or capital is more effective!

q = 10LK MPl = 10K MPk = 10L w = 8 r = 2 What is the cost minimizing solution?

Set MRTS = w/r to find cost minimizing solution! 10K/10L = 8/2 i. Set K = equation in terms of L! --> K = 4L ii. Plug K value into production function to find L in terms of q! (stop doubting yourself linda, you had it first the first time) --> q = 10L(4L)--> q = 40(L^2)--> *(q/40)^0.5 = L* iii. Now plug K value into isocost function! --> 8L + 2K = 8L + 2(4L) = 16L iv. Plug L value derived from production function into isocost function --> 16 x (q/40)^0.5) = ... PRETTY SURE THE COST MINIMIZING SOLUTION = 4 LABOR FOR 1 CAPITAL....

q = 5L + K; w = 8; r = 2 1) What are the marginal products? 2) What is the cost minimizing solution?

Since this production function is linear, will be a corner solution! (perfect substitutes) 1) MP = partial derivatives of function--> treat the OTHER variable as a constant--> derivative of constant = 0 --> MPl = 5 (K is constant; d/dx of constant = 0) --> MPk = 1 (L is constant; d/dx of constant = 0) 2) Cost minimizing solution = when MRTS = w/r --> 5/1 = 8/2--> 5 = 4--> this is a corner solution! --> Find out which input gives you more MP/$: --> MPl/w = MPk/r--> 5/8 vs. 1/2--> labor gives more MP/$! *Use more labor, less capital to minimize costs.*

What happens to substitution effect/income effect in relation to Qd when price of a normal good drops?

Substitution effect raises Qd—cheaper good replaces more expensive good Income effect raises Qd—lower price of normal good = more purchasing power (lower price of inferior good would = more purchasing power but less Qd) --> Qd rises!

What are the 3 steps firms take to make production decisions? How do they relate to the theory of the firm? What is the theory of the firm?

TCI: 1) *Technology*- consider production technology 2) *Cost constraints*- account for cost constraints- take into account prices of inputs 3) *Input amount*- decide how much input should be used in production of output! They are the building blocks of the theory of the firm! Theory of the firm- economic theories that explain/predict the nature of the firm, including its existence/behavior/structure/relationship to the market

What is the relationship between marginal product and average product? What about between marginal product and total product?

They're very closely related! *When MP > AP, AP is increasing* --> This is pretty intuitive, when marginal output per 1 unit of input is MORE than average product, that must mean that average product will be increasing; as output is increasing at an extremely fast rate! *When MP < AP, AP is decreasing* --> This is also intuitive, as when marginal output per 1 unit of input is LESS than average product, average product will be decreasing; as output is decreasing at an extremely fast rate! Same with MP and TP! When MP is positive--> TP is increasing When MP is negative--> TP is decreasing --> MP = positive and increasing = TP is increasing at increasing rate --> MP = positive and decreasing = TP is increasing at decreasing rate --> MP = negative and decreasing = TP is decreasing

What is the link between productivity and standard of living?

To increase consumption/standard of living, consumers must increase total amount they produce --> Production and consumption are a cycle, after all, so we are both consumers AND workers! --> In any year, aggregate value of goods/services produced by economy = payments made for inputs/factors of production (wages, profit to firms, etc.)

What is total cost? What is variable cost? What is fixed costs?

Total cost = variable costs + fixed costs (total economic costs) Variable cost- costs that varies with amount of output --> Typically labor Fixed cost- cost that does NOT vary with amount of output --> Only way to eliminate = shut down --> Typically machinery

What is a production input that can be varied in both the short run and long run called? What is a production input that can ONLY be varied in the long run called?

Variable input- can be varied anytime! Fixed input- it is a constant during the short run!

Is it possible for consumer choice to violate the law of demand? If so, how would it happen?

Yes, it is possible. Supposing income increased/price decreased, and the good was so inferior as to decrease demand. Good example of this is giffen good- inferior good without many substitutes--> income effect dominates graph --> Price of giffen good increases = Qd increases --> Extremely rare, the unicorn of economics

Chapter 7 Paper HW 1) Units of output: 0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10 Total cost: 100; 125; 145; 157; 177; 202; 236; 270; 326; 398; 490 a) Create a table and find: FC, VC, MC, AFC, AVC, ATC b) Draw a graph that shows MC, AVC, and ATC—with cost on the vertical axis and quantity on the horizontal axis.

a) FC: 100; 100; 100; 100; 100; 100; 100; 100; 100; 100; 100 VC: 0; 25; 45; 57; 77; 102; 136; 170; 226; 298; 390 MC: —; 25; 20; 12; 20; 25; 34; 34; 56; 72; 92 AFC: —; 100; 50; 33.33; 25; 20; 16.67; 14.29; 12.5; 11.11; 10 AVC: 0; 25; 22.5; 19; 19.25; 20.4; 22.67; 24.29; 28.25; 33.11; 39 ATC: —; 125; 72.5; 52.33; 43.25; 40.4; 39.34; 38.58; 40.75; 44.22; 49 b) Cost = y-axis; Q output = x-axis

Chapter 4 Paper HW: 3) For theater tickets, demand curve for students is Qds = 200-4P and for the general public is Qdgp = 600-4P. Suppose the current price of tickets is $50 for everyone. a) Graph demand for students, the general public, and the market. (Hint: don't forget the kink!) b) What is the equation(s) for market demand? c) At the current price, calculate the Qd for students, the general public, and the market. d) Calculate the elasticity(ies) of market demand. e) Can the theater owner increase revenue by lowering the price? Explain.

a) --> Graphing demand for students = Qd of students vs. price of tickets (use Qds equation!) --> Graphing demand for general public = Qdgp of general public vs. price of tickets (use Qdgp equation!) --> Graphing market demand = (Qdgp + Qds) vs. price of tickets- just construct the demand curve as usual! a) Find out what the minimum price is, and which demand ONLY responds to certain prices! --> 200-4P = 0; max price for students = 50 (only demands below $50) --> 600-4(50) = 400; only demand above $50 is GP line! --> So market demand only goes up to P = 50; anything above P = 50 is Qdgp; Qds doesn't demand anything above $50 --> Market function is continuous, so both equations exist for P = 50! b) Market demand = total sum of all demand within market--> (Qds + Qdgp) = (200-4P) + (600-4P)--> *Qdm = 800-8P* AND 600-4P* --> 800-8P only goes up to $50; 600-4P goes beyond $50! c) Current price = $50 Qds = 200-4(50) = 0 :o Qdgp = 600-4(50) = 400 Qdm = 800-8(50) = 400 d) PED of market demand--> [(New Qdm - old Qdm)/Old Qdm] x [Old P/(New P - old P)] Remember, old = OG! --> Old Qdm = 400; Old P = 50 --> Plug random number in for P to find "new" values--> suppose P' = 60; Q'dm = 320 --> [(320-400)/400] x [50/(60-50)] = *-1 for any price under $50* PED of market demand with price above $50 --> Old Qdm = 400; Old P = 50 --> Plug random number in for P to find "new" values--> suppose P' = 70; Q'dm = 320 --> [(320-400)/400]*[50/(70-50)] = *-0.5 for any price above $50* e) No, the theater owner canNOT increase revenue by lowering the price- this can be proven by plugging in lower prices and comparing the revenues with the higher prices' revenues. --> P = 50; Qdm = 400; R = 20,000 --> P = 30; Qdm = 560; R = 16,800 --> P = 10; Qdm = 720; R = 7,200 Can also be inferred from the PED for P < 50 which is -1—it is elastic but not elastic ENOUGH to radically increase demand enough that revenue increases

Chapter 6 HW: 1) Suppose a chair manufacturer is producing in the short run (with its existing plant and equipment). The manufacturer has observed the following levels of production corresponding to different numbers of workers: # workers: 1; 2; 3; 4; 5; 6; 7 # chairs: 10; 18; 24; 28; 30; 28; 25 a) Calculate the marginal and average product of labor for this production function. b) Does this production function exhibit diminishing returns to labor? Explain. c) Explain intuitively what might cause the marginal product of labor to become negative.

a) Calculate MP and AP for EACH increase of labor! (it changes throughout)--> very simple, don't overthink it MP = change in output/change in input AP = total output/total input MP = 10; 8; 6; 4; 2; -2; -3 AP = 10; 9; 8; 7; 6; 4.67; 3.57 b) Yes, it does exhibit diminishing returns to labor--> although adding workers DOES increase total output, MPl or returns to labor actually decrease with each new worker until it becomes negative! c) There are many factors that could come into play—there may not be enough specialized tasks for workers to take on as the firm hires more; workers might get in each other's way = inefficiency, etc.

Chapter 6 HW: 6) Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of labor as labor is increased and capital is held constant starting from input combo (20,20)? a) q = 3L + 8K b) q = 4(L^2)K c) q = 3(L^0.4)(K^0.3)

a) Constant returns to scale (no sq. roots or exponents, also a linear function); MPl constant Proof: *MPl = change in output/change in labor input --> q1 = 3(20) + 8(20) = 220 --> q2 = 3(21) + 8(20) = 223 MP1 = (223-220)/(21-20) = *3* --> q1 = 3(21) + 8(20) = 223 --> q2 = 3(22) + 8(20) = 226 MP2 = (226-223)/(22-21) = *3* b) Increasing returns to scale (exponent); MPl increases (exponent!) Proof: *MPl = change in output/change in labor input --> q1 = 4(20^2)20 = 32000 --> q2 = 4(21^2)20 = 35280 MP1 = (35280-32000)/(21-20) = *3280* --> q1 = 4(21^2)20 = 35280 --> q2 = 4(22^2)20 = 38720 MP2 = (38720-35280)/(22-21) = *3440* c) Decreasing returns to scale (sq. roots!); MPl decreases (sq. root!) Proof: *MPl = change in output/change in labor input --> q1 = 3(20^0.4)(20^0.3) = 24.43 --> q2 = 3(21^0.4)(20^0.3) = 24.91 MP1 = (24.91-24.43)/(21-20) = *0.48* --> q1 = 3(21^0.4)(20^0.3) = 24.91 --> q2 = 3(22^0.4)(20^0.3) = 25.37 MP2 = (25.37-24.91)/(22-21) = *0.46*

For which of the following goods would a 10 percent price increase lead to the largest income effect for most​ consumers? a) Housing b) Cell phone service c) Movie tickets d) Salt

a) Housing Housing takes up the most of your budget, so 10% increase in housing renders income less powerful--> less purchasing power = less relative income

Chapter 4 Paper HW: 5) Consider the utility function U = (10F^2)(C). The marginal utilities are MUf = 20FC and MUc = 10F^2. a) Derive the demand for food if income is $120 and the price of clothing is Pc = $5. Graph the demand curve. b) Derive the demand for food if income is $150 and price of clothing is Pc = $5. Graph the demand curve. How does it compare with the demand curve in (a)?

a) Keep Pf as a variable, and find the function as F = Pf relationship for the demand curve of food--> don't overthink it!!! --> find C in terms of Pf--> Plug into budget line to derive demand curve. i. Assemble budget line equation: 5C + PfF = 120 ii. Solve for C in terms of Pf by finding utility maximizing basket! --> Pf/5 = 20FC/10F^2--> Pf/5 = 2C/F--> C = PfF/10 iii. Plug C into budget line equation, find F! --> 5(PfF/10) + PfF =120--> 3PfF/2 = 120-->(120 x 2)/3Pf = F--> *F = 80/PfF*<-- This is the demand for food! :D b) Same shit as above! Keep Pf as a variable, and find the function as F = Pf relationship for the demand curve of food! i. Assemble budget line equation: 5C + PfF = 150 ii. Solve for C in terms of Pf by finding utility maximizing basket! --> Pf/5 = 20FC/10F^2--> Pf/5 = 2C/F--> C = PfF/10 iii. Plug C into budget line equation, find F! --> 5(PfF/10) + PfF =150--> 3PfF/2 = 150-->(150 x 2)/3Pf = F--> *F = 100/Pf*<-- This is the demand for food! :D --> Demand from a) is slightly steeper than demand from b)! Probably due to the lower income of a)! --> Slope of (a) = (4-1)/(20-80) = -0.05 --> Slope of (b) = (2-1)/(50-100) = -0.02

Chapter 6 HW: 4) Consider the production function q = (L^1.5) + 4K. a) Starting from the input combination (9,5), calculate the marginal product of adding 1 worker b) What is the marginal product of adding another worker after the 1 worker from (a)? c) Is the marginal product of labor increasing or decreasing?

a) MP of labor(adding 1 worker)= change in output/change in labor so... --> input 1 = (9,5) = (L,K) --> input 2 = (10,5) = (L+1,K) *Plug into q(production) function to find corresponding outputs of increasing labor! --> q1 = (9^1.5) + 4(5) = 47 --> q2 = (10^1.5) + 4(5) = 51.62 MP = (51.62-47)/(10-9) = *4.62 = MP of +1 labor* b) MPl of adding 1 worker, starting point = (10,5) of (a)! --> input 1 = (10,5) --> input 2 = (11,5) *Plug in q function to find corresponding outputs of increasing labor! --> q1 = (10^1.5) + 4(5) = 51.62 --> q2 = (11^1.5) + 4(5) = 56.48 MP = (56.48-51.62)/(11-10) = *4.86 = MP of +1 labor* c) MPl is increasing!

Assuming that price of good x stays constant, how do you graph substitution and income effect for... a) Price increase of normal good b) Price decrease of normal good c) Price increase of inferior good d) Price decrease of inferior good

a) Normal good's price increases: -Original budget line before price increase = BL1 -Original IC before price increase = IC1 -Original optimal consumption bundle before price increase = OCB1 -New budget line after price increase = BL2 (swiveled inwards) -New IC after price increase = IC2 -New optimal consumption bundle after price increase = OCB2 -Dotted line tangent to OCB1 and parallel to new BL2 = what you would have to consume, with new prices, to be able to get old IC1!!! -Where dotted line tangent to OCB1 and parallel to new BL2 intersects with IC1 = B --> Substitution effect = movement from OCB1—B --> Income effect = movement from B—OCB2 (it is negative!) b) Normal good's price decreases: -Original budget line before price increase = BL1 -Original IC before price increase = IC1 -Original optimal consumption bundle before price increase = OCBa -New budget line after price increase = BL2 (swiveled outwards) -New IC after price increase = IC2 -New optimal consumption bundle after price increase = OCB2 -Dotted line tangent to OCB1 and parallel to new BL2 = what you would have to consume, with new prices, to be able to get old IC1!!! -Where dotted line tangent to OCB1 and parallel to new BL2 intersects with IC1 = B --> Substitution effect = movement from OCB1—B --> Income effect = movement from B—OCB2 (it is positive!) c) Inferior good's price decreases: -Original budget line before price increase = BL1 -Original IC before price increase = IC1 -Original optimal consumption bundle before price increase = OCB1 -New budget line after price increase = BL2 (swiveled outwards, but OCB2 is less than B) -New IC after price increase = IC2 -New optimal consumption bundle after price increase = OCB2 -Dotted line tangent to OCB1 and parallel to new BL2 = what you would have to consume, with new prices, to be able to get old IC1!!! -Where dotted line tangent to OCB1 and parallel to new BL2 intersects with IC1 = B --> Substitution effect = movement from OCB1—B --> Income effect = movement from B—OCB2 (it is negative!) d) Budget line swivels out for cheaper good Substitution effect = OCB1—B Income effect = B-OCB2; will be negative bc OCB2 will be placed behind B!

Chapter 4 Paper HW: 1) An individual sets aside a certain amount of her income per month to spend on her 2 hobbies, collecting wine and collecting books. Given the info below, illustrate both the (a) price consumption curve associated with changes in the price of wine AND (b) the demand curve for wine. Budget = $150 Pw = $10; 12; 15; 20 Pb = $10; 10; 10; 10 Qw = 7; 5; 4; 2 Qb = 8; 9; 9; 11

a) PCC: (only different in what is being held constant; Pb and budget held constant!) i. Remember that the Qs corresponding to the prices are not intercepts for the budget line, but the point where MRS = Px/Py and thus the point where the BL and IC intersects! (utility maximizing Qs) --> Q consumed of W = x; Q consumed of B = y ii. Find the intersects for the different prices--> construct budget lines for each price! ie- 10W + 10B = 150, and so on. iii. The PCC is just the line that traces all the different points of Qs that are utility maximizing through the different budget lines/ICs :D --> PCC would go through (7,8); (5,9); (4,9); (2,11) --> All these utility maximizing bundles would be on the BLs for the intercepts you found using PwW + PbB = 150! --> BL line A: w = 15; b = 15 --> BL line B: w = 12.5; b = 15 --> BL line c: w = 10; b = 15 --> BL line d: w = 7.5; b = 15 b) Demand is just price of wine vs. quantity demanded of wine --> (20,2); (15,4); (12,5); (10,7)

Chapter 4 Paper HW: 6) Suppose orange juice and apple juice are known to be PERFECT SUBSTITUTES, where the marginal utility of orange juice is 6 and the marginal utility of apple juice is also 2. a) Draw the price consumption curve for a variable price of orange juice. (Assume the price of apple juice is $1 per bottle and the income for the juice budget is $10.) b) Draw the income consumption curve. (Assume the price of apple juice is $1 per bottle and the price of orange juice is $0.75).

a) Price is kept constant at $1, so y coordinate stays constant. x also has intercept, but from there extends into infinity on the x axis, as price of OJ decreases (BC THEY'RE PERFECT SUBSTITUTES) \_______ (that's what the line looks like with OJ=x; AJ=y) b) *Find marginal utility per dollar for each one*--> consumer will spend all of their income on the higher MU/$ bc they're perfect substitutes --> MUo=6; Po=0.75 --> MUa=2; Pa=1 --> 6/0.75(OJ) vs. 2/1(AJ)= 8>2; consumer spends all income on OJ bc it has a higher MU/$ --> *ICC is just a line from origin to infinity on OJ's axis (x axis)!* --> Don't overthink it queen!

Chapter 6 HW: 2) For each of the following examples, draw a representative isoquant. What can you say about the MRTS in each case? a) Firm can hire only full time employees to produce its output, or it can hire some combo of full time and part time employees. For each full time worker let go, firm must hire an increasing # of temporary employees to maintain same level of output. b) Firm finds that it can always trade 2 units of labor for 1 unit of capital, while keeping output constant. c) Firm requires exactly 2 full time workers to operate each piece of machinery in the factory.

a) Put the input that will be given up MORE for 1 unit of the other input--> MANY temporary workers given up for 1 full time worker, as specified in problem--> temps = y; full time = x--> steep convex isoquant --> Alternatively, if you put temps = x; full time = y--> flat convex isoquant! --> Thus, MRTS = -change in y/change in x--> -change in temps/change in full time = constant output --> This is a typical isoquant, as these inputs are not perfect substitutes or proportional/perfect complements--> downward sloping convex curve, with a diminishing MRTS! b) Remember, MRTS = -change in y/change in x *1Firm can always give up 2 units of labor for 1 unit of capital--> can trade 1 unit of capital for 2 units of labor --> -change in y = -1 --> change in x = 2 MRTS = -1/2; the slope is constant and isoquant is linear! --> These are perfect substitutes. --> NO diminishing MPs; bc MRTS is constant and = MPl/MPk, both MPs are constant! c) Perfect complements! Requires exactly 2 full time workers to operate each unit of capital --> Labor = 2; capital = 1 --> Outwards pointing right angles, so x coordinate is always double the y coordinate! (2:1 ratio!) --> Vertical MRTS = undefined; horizontal MRTS = 0 :D --> (2,1); (4,2); (6,3), etc.

Chapter 7 Paper HW 4) In the short run, a firm's capital stock is fixed at K = 9. The firm's production function is q = 4(LK)^0.5. The marginal products are: MPl = 2(K/L)^0.5 MPk = 2(L/K)^0.5 Wage and rental rates are as follows: w = 1 r = 4 a) Derive the firm's short-run production function. b) Derive the firm's short-run total cost function and graph it. c) Derive the firm's short-run average total cost function and graph it. d) Derive the firm's short-run marginal cost function and graph it. e) Suppose the firm is producing q = 24 units of output. In the long run, how should it adjust labor and capital?

a) SR = K is constant; plug in--> 4(L(9))^0.5 = q--> (4 x 3)(L^0.5)--> *q = 12(L^0.5)* b) TC = FC + VC = rK + wL = (9 x 4) + (1)(L) --> To find L, set L in terms of q from the production function! --> q = 12(L^0.5)--> (q/12)^2 = (L^0.5)^2--> q^2/144 = L --> *TC = 36 + q^2/144* c) ATC = TC/q--> (36 + q^2/144)/q--> *ATC = 36/q + q/144* d) MC = derivative of TC!--> *MC = q/72* e) q = 24; LR = K is varied; find cost minimizing bundle! i. Set MRTS = w/r --> (2(K/L)^0.5)/(2(L/K)^0.5) = 1/4 --> Cross multiply: (L/K)^0.5 = 4((K/L)^0.5) --> Square both sides to get rid of square rts: L/K = 16K/L --> Cross multiply to get rid of fractions: L^2 = 16K^2 --> Square root both sides: L = 4K! ii. Plug L value (in terms of K) into production function --> q = 24 = 4(LK)^0.5 --> Plug in: 4((4K)K)^0.5 = 4(4K^2)^0.5 --> Simplify: 24 = 4(2K)--> 8K = 24 --> K = 3! iii. Plug K value into L equation to find L! --> L = 4K--> L = 4(3) = 12! *Cost minimizing input combo = (12,3)*

Chapter 6 HW: 3) Consider the production function q = 6(L^0.3)(K^0.6). MPl = 1.8(L^-0.7)(K^0.6) MPk = 3.6(L^0.3)(K^-0.4) a) Assume that capital is fixed/constant at K = 10 in the short run. Derive formulas for the short run Total Product (TP), Avg Product (AP), and Marginal Product (MP of L). Graph these 3 functions! b) Capital is not fixed/constant in the long run! Graph the isoquant for q = 6. Identify and label 3 points on the isoquant. (You'll need to do some math here) c) Calculate the MRTS. d) Use the MRTS formula to determine the slopes of the isoquant at the 3 points you identified. Label the slopes at these points.

a) TP for K = 10--> q = 6(L^0.3)(10^0.6)--> *TP or q = 23.89(L^0.3)* --> Graph: relationship between TP or q and L--> y=q; x=L AP = total output/total input--> plug in K = 10 into q to get L alone as a variable(total output), and then divide by L (total input) --> To find APl = TPl/L! --> Total output or q = 6(L^0.3)(10^0.6)--> 23.89(L^0.3) --> Total input = L --> [23.89(L^0.3)]/L--> *23.89/(L^0.7) = AP* --> Graph: relationship between AP and L--> y=q; x=L MPl for K = 10--> 1.8(L^-0.7)(10^0.6)--> *7.17(L^-0.7) = MPl* --> Graph: relationship between MP and L--> y=q; x=L b) q = 6--> plug in! --> 6 = 6(L^0.3)(K^0.6) --> Find (L,K) that fit into equation to = 6! :D (start with L, find K) *Plug random L value; divide 6 by that value to isolate K^0.6; then ^ each side by 10/6 to get rid of 0.6 exponent --> Point A: L = 1; then K = 1 --> Point B: L = 3; then K = 0.58 --> Point C: L = 5; then K = 0.45 c) MRTS = MPl/MPk = [1.8(L^-0.7)(K^0.6)]/[3.6(L^0.3)(K^-0.4)]--> *K/2L = MRTS* (or 0.5K/L) --> Remember that MRTS changes for any isoquant not perfect substitutes, but the formula is the same--> numbers are different. d) Use MRTS derived from (c) to find slopes of the 3 points (they're all negative, bc slope is negative!)! :D--> MRTS = -K/2L --> Point A: -1/2(1) = -0.5 --> Point B: -0.58/2(3) = -0.0967 --> Point C: -0.45/2(5) = -0.045

When there is a negative network externality for a​ good, the demand for that good... a) will be less elastic than it would have been without the negative network externality. b) will be more elastic than it would have been without the negative network externality. c) may have a degree of elasticity that is​ more, less or the same as it would have without the negative network externality. d) will be just as elastic as it would have been without the negative network externality.

a) will be less elastic than it would have been without the negative network externality. --> less elastic = price rises, Qd either remains the same or increases --> Negative network ext = price rises, Qd increases

Chapter 4 Paper HW: 4) Consider the demand curve Q = 150-3P. a) Graph the demand curve. b) Calculate the consumer surplus if the price is $20.

b) Remember consumer surplus is the AREA below the demand curve, above a certain price! (the tip of the triangle must be at the y intercept, remember that demand curve should be starting at a y intercept when calculating this) --> Calculate area of triangle above P = $20 --> 1/2bh, lmao --> Base or Qd = 90; Height above $20 = 30--> 1/2(90)(30) = 1350

Decreasing returns to scale typically occur because... a) It costs more to operate a larger organization than it does to run a smaller organization b) Larger scale equipment is less efficient than smaller scale equipment c) Difficulty of coordinating tasks and maintaining communication between management and workers d) It is difficult to find good workers, so as an organization gets larger each additional worker produces less and less

c) Difficulty of coordinating tasks and maintaining communication between management and workers --> As input of labor doubles, this is what would cause the output to be LESS than doubled = inefficiency between management and workers --> a) would be irrelevant, by this logic larger organizations have less profit so it's complete nonsensical --> b) not even talking about larger scale equipment in this case, has nothing to do with doubling of inputs --> d) this relates to decreasing MPl, wherein each additional worker is making the MPl decrease; this is asking about output NOT doubling

When the price of good X increases and all goods​ (including X) are normal​ goods, the income effect leads consumers to buy... a) more of good X and less of other goods b) less of good X and more of other goods c) more of all goods d) less of all goods

d) less of all goods --> Increase in price of a good = decrease in overall purchasing power = less of all purchases. NOT <b) less of good X and more of other goods> bc this would be substitution effect--> income effect ONLY deals with how much you buy of the target good, doesn't deal with how you SUBSTITUTE other goods for a more expensive good

Explain intuitively what might cause the marginal product of labor to become negative: a) decreasing returns to scale b) constant returns to scale c) specialization among workers d) workers getting in each other's way e) fixed quantities of other inputs

d) workers getting in each other's way --> Decreasing returns to scale just means that doubling the input = LESS than double the output, has nothing to do to marginal product!

Suppose average house household in state consumes 600 gallons of gas per year. A 50 cent gas tax is introduced, coupled with a $300 annual tax rebate per household. Will the household be better or worse off under the new program? Why? a) will be worse off b) will be better off c) could be equally well off or worse off d) will be equally well off e) could be equally well of or better off

e) could be equally well of or better off ASSUMING A RATIONAL CONSUMER AND ASSUMING THE LAW OF DEMAND APPLIES (WHEN PRICE GOES UP, QD GOES DOWN) --> 50 cent gas tax in introduced = $300 extra expenditure on gas, if consumption of gas stays the same --> $300 rebate per household = balances out the $300 extra expenditure on gas --> Applying the Law of Demand, and since gas = normal good, demand for gas would go down with this new 50 cent tax--> average household would consume less gas = $300 rebate would allow them to profit! --> ie- household consumes 500 gallons of gas due to new tax --> (rebate - extra expenditure due to tax)--> $300 - $250 = $50 earned! :-D *ASSUMING A RATIONAL AND SMART CONSUMER*

Chapter 7 Paper HW 2) Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm's expansion path.

x axis = L; y axis = K --> Isocost line would become flatter, with x intercept swiveling outward due to lower labor costs! --> As a result, isoquants move with the isocost line, *resulting in expansion path moving TOWARDS cheaper input's axis!* *EXPANSION PATH ALWAYS MOVES TOWARDS AXIS OF THE CHEAPER GOOD!*

What does isoquant mean?

Equal quantity/same quantity (think isoceles!)

Demand for apples in US is Q = 800-20P, and foreign demand for apples is Q = 1200-40P. What is the world demand? What is the maximum price that allows world demand equation to remain legitimate?

(800-20P)+(1200-40P) =*2000-60P* --> Max price would be the price that results in one of the demand functions = 0; because world demand has to be both foreign AND domestic demand, otherwise not world demand lol --> 800-20P = 0--> P = 40 --> 1200-40P = 0--> P = 30 So *maximum price = $30* for the world demand function!