econ's my b*tch
(1.13)A consumer has utility function µ = u(x,y) which assigns utility numbers µ to baskets of commodities (x,y) as follows: u(10,12) = 19 u(13,13) = 29 u(11,11) = 20 u(10,14) = 23 u(13,12) = 28 Calculate MUx(10,12) in approximate form. Please show your work.
(u(13,12) - u(10,12))/(△x)= (28-19)/3= 3
(1.9)What does the size of the coefficient of elasticity imply about a. the relationship between changes in price or quantity and changes in total revenue along the demand curve? b. the sign of marginal revenue along the demand curve? Please cover all 5 cases of elasticity in your answer.
- perfect e: TR↑, MR+ - elastic: TR↓, MR+ - unitarily elastic: TR doesnt change, MR=0 - inelastic: TR↑, MR- - perfectly inelastic: TR↑, MR-
(2.7)Describe the properties of consumer demand functions obtained in our model of consumer buying behavior.
1. D is always positive 2. marg rate of sub = price ratio at every pt on demand, so every pt is utility maximizing 3. if prices and income are scaled by the same constant --> no change in demand 4. consumers use all their income 5. substitution ratio is always negative
(4.5)Give the argument that shows why general equilibrium under perfect competition is Pareto optimal (in general). It is not necessary to give definitions of the concepts general equilibrium and Pareto optimality. Just use them in your argument.
1. consumers consume to max utility subject to budget constraint so marginal rate of substitution = 2. firms hire inputs and sell outputs to max profit so ratio of marginal products is = as they hire cost minimizing baskets 3. @ gen eq, supply = demand, as supply = MC curve, MC=price ratio
(3.3)List all of the assumptions made to construct our model of the perfectly competitive firm. Do not include the assumptions that define the perfectly competitive market.
1. firm has LR production function x=f(l,k) w/ given tech 2. LR production function has following properties - f is continuous and all MP can be calculated - zero input --> zero output\negative input --> negative output - if ridge lines exist, MP is positive and isoquants are striclty conves btwn ridge lines up until points of intersection(if pts exist) - if ridge lines DNE, MP is positive and isoquants are strictly convex everywhere and dont touch axes 3. LRTC + SRTC appear as drawn in class so AC + MC curves can be drawn 4. firms hire inputs and produce/sell output to max. profit
(4.10)Briefly describe the 4 kinds of market failure and in each case explain the cause of the failure.
1. imperfect comp: one rule of perf comp is violated(ex. few firms, unstandard product) --> firms face downward sloping demand curve --> P doesnt = MC 2. imperfect information: can't accurately maximize utility subject to budget constraint --> 3. public goods: no price or cost to consumers --> no demand curve 4. externalities: MC is not accurate reflection of MEB and MEC so MC doesnt equal P
(2.2)List all of the assumptions relating to the consumer that are made to construct our model of the consumer's buying behavior. (Do not include the properties required for a perfectly competitive market.)
1. preferences are complete (can identify) 2. preferences are transitive(A>B,B>C,-->A>C) 3. preferences are represented thru a utility function such that higher preferred basket --> higher utility value and equally preferred baskets have equal utility values 4. a) utility curves are continuous and all MU can be calculated b) larger baskets are always preferred c) all indiff curves strictly convex d) indiff curves dont touch coordinate axes 5. individuals consume in order to utility max. sub. to budget constraint
(S2.18)Describe two methods for correcting the inefficiencies caused by the presence of an externality in a market.
1. tax or subsidize production of good to increase or decrease output and accomodate the MEB or MEC imposed by the externality 2. regulate production directly by setting standards ex. set limit on quantity of pollutants a firm can release during production
(1.11)What is the relationship between preferences and the utility function?
Consumers preferences are represented as utility numbers such that a utility function will give a more preferred basket a higher utility value and equally preferred baskets have equal utility values
(3.15)Think of a decreasing cost, perfectly competitive industry and a representative firm in that industry at long-run equilibrium. Suppose the demand for that industry's output increases. Describe the steps by which the industry and representative firm adjust to a new long-run equilibrium. How does the new equilibrium compare with the old? Please include diagrams of the industry and representative firm in your answer.
D↑ --> P↑ --> firms enter market cuz profits --> market supply↑ --> LRAC and LRMC shift down
(1.8)Why is elasticity used as a measure of the responsiveness of quantity changes to price changes rather than (reciprocal) slope?
Elasticity is not affected by the units of price or quantity whereas price is
(S2.21)Describe two difficulties in obtaining individuals' willingnesses to pay for a public good with any degree of accuracy. In practice, how do we actually determine the amount of a public good to produce?
Free rider: free good --> no incentive to pay for good drop in the bucket problem: public goods costly --> ppl question if their contribution makes a difference --> don't want to pay elect representatives to make informed decisions
(S2.7)Assume constant returns to scale in the long run and that the long-run production function of the perfectly competitive firms does not change when combining them into a monopoly. Under these conditions, draw a diagram comparing the price and output under the two forms of competition and, in that diagram, indicate the social cost (deadweight loss) of the monopoly. Make your diagram large and label all curves, axes, and points.
MR, D, MC find pts for PF and monopoly deadweight loss= trapezoid under demand
(S2.2)Why, in the case of a monopolist, is marginal revenue at any output less than output price?
MR=px(1-E) and elasticity of D is always positive since monopoly faces downward sloping demand curve so, MR must always be less than price
(1.14)What are the relationships among marginal utilities, the marginal rate of substitution, and the slopes of indifference curves?
Marginal rate of substitution is the ratio between the MU w/ respect to one good and the MU w/ respect to another good. the slope of indifference curves = negative marginal rate of substitution
(3.14)In a perfectly competitive market, what is the difference between the way market price is determined in the short run and the long run?
SR: market price determined by intersection btwn S n D LR: market price = min pt of LRAC
(3.2)Why, under conditions of perfect competition, does the marginal revenue of the firm equal its output price?
TR=P * X take derivative with respect to x --> MR=P
(1.2)What is the difference between a model of real-world behavior and the real world behavior being modeled?
a simplified abstraction of a concept that allows one to takeaway some knowledge about the concept using the abstraction vs. complicated, includes every determining factor
(3.7)a. Give a step-by-step argument to show how the perfectly competitive firm's input demand and output supply functions are derived from the assumptions of our longrun model of that firm. (In your answer, start with the production function and include ridge lines, cost minimization, the expansion path, and cost and revenue functions.) b. How is this argument changed when focusing on the firm's short run input demand and output supply functions?
a) 1. if ridge lines exist, eliminate area beyond pts of intersection(if pts exist btwn ridge lines and isoquants, to obtain relevant region 2. use input prices of l,k to calculate expansion path--> minimizing baskets of inputs 3. use production function, EP, and input prices to calculate all cost functions and curves, expressing cost as a function output 4. using output price info, calculate all revenue functions and curves 5. using cost and revenue info, calculate profit functions and profit maximizing output 6. using profit maximizing output, find intersection of isoquant and EP and calculate profit maximizing quantities of l and k b)step 2: EP is simply using fixed capital info, not input prices--> horizontal, straight EP step 6: only calculate profit maximizing quantity of l
(3.8)Explain how a change in (a) the price of labor alone, or (b) the price of output alone, works its way through the long-run model of the perfectly competitive firm (i.e., through such elements as isocost curves, expansion paths, cost curves, and profit-maximizing isoquants) to affect input quantities demanded and output quantities supplied. How is your answer altered when focusing on the short run?
a) LR: if P(l) △ --> isocost slope △ --> isocost and isoquant intersection△--> LREP △ --> LRMC△ --> MR + MC intersection pt △ --> new profit maximizing output --> new isoquant --> new pt of intersection btwn isocost and isoquant --> profit max quantities of l and k △ SR: if P(l)△ --> SRTC△ --> SRMC△ --> MR + MC interesection pt △ --> profit max output△ --> new isoquant --> same EP(k constant) but isoquant, pt of intersection △ --> new profit max quantity of l b) LR: if Px△ --> MR△ --> MR + MC pt of interesction△ --> profit max output △ --> new isoquant --> new intersection pt btwn isoquant and EP --> new profit maximizing quantities of l and k SR: SRMC △ and only finding new quantity of l, since k constant
(3.5)Think of a firm in a perfectly competitive market without free entry or exit: a. Does profit maximization in the long- or short-run guarantee by itself that the firm produces an output at the minimum point of its long- or short-run average cost curves? Why or why not? b. Does profit maximization in the long- or short-run imply that the firm produces an output for which revenue is maximized? Why or why not? c. If the firm hires inputs so as to minimize the cost of producing each output, it is necessarily producing the profit-maximizing output? Why or why not?
a) No, profit max output occurs when MR=MC, which may or may not be min pt of AC curve, depends on cost minimization b) No, profit=revenue - cost, so the difference btwn revenue and cost is maximized, not revenue c) No, profit maximization has to do with revenue and cost. simply minimizing cost doesn't max profit. MR=MC
(3.6)a. Draw a pair of diagrams, one above the other, illustrating the short-run, profit-maximizing output for the perfectly competitive firm with abnormal profit. The top diagram should contain short-run total cost, total variable cost, total revenue, and profit curves; the bottom diagram should contain short-run average cost, average variable cost, short-run marginal cost, and marginal revenue curves. In the bottom diagram shade in the area that represents abnormal profit. Make your diagrams large and label all curves, axes, and points. b. How would your diagrams change if the firm were losing money, i.e., had negative profit?
a) a doosey b)MR, or price, would have to be below min pt of SRAC curve
(S1.6)Explain why cost minimization for each level of output implies that the firm hires that basket of inputs for which a. the marginal rate of technical substitution equals the input price ratio. b. the marginal products per dollar of the two inputs are equal. If you use a diagram in your answer, make the diagram large and label all curves, axes, and points.
a) cost minimization occurs at pt of intersection btwn isocost and isoquant; slopes of curves are price ratio and mrts respectively, so slopes equal at pts of intersection b) rearrange above equation isocost is straight line and isoquant tangent to line axes = l and k
(S1.7)a. Explain how, in a two-input world, the long-run total cost function is derived from the firm's production function or isoquant map. b. Explain how, in a two-input world, the short-run total cost function is derived from the firm's production function or isoquant map. c. Describe the relationship between the firm's long-run and short-run total cost curves and explain how the short-run curve can be tangent to the long-run curve. d. Describe the relationship between the firm's long-run and short-run average cost curves and between the firm's long-run and short-run marginal cost curves, and explain why that relationship occurs
a) cost minimizing basket found by pt of intersection btwn isoquant and isocost. as quantities of goods vary, LREP found along pts of intersection. from cost minimizing baskets found along EP, LRTC is found b) same as above w/ k constant c) LRTC and SRTC show the relationship between TC at diff levels of output and price when capital changes in LR or doesnt change in SR can be intersect where LREP and SREP intersect d) every pt on the firm's LRAC is associated w/ a dif SRAC curve determined by the level of capital used at that pt. MC is slope of TC and are be equal when LRTC and SRTC intersect
(3.10)a. In the short run, under what conditions relating to its output price and average variable cost should a perfectly competitive, profit-maximizing firm continue to produce and sell output when it is losing money (i.e., has negative profit)? Why? b. Why in the short run, can it not go out of business?
a) if Px is greater than or above minimum pt of AVC and firm has negative profit, firm shud continue selling, cuz all of variable costs can be covered and some of fixed costs b) k fixed so going out of business is a loss of k
(3.9)a. Explain how long-run profit maximization by a perfectly competitive firm leads to the selection of a particular plant (or firm) scale and the short-run profit maximization within that plant scale. b. Draw a diagram containing long-run average and marginal cost curves, the marginal revenue curve, and the short-run average and marginal cost curves for the plant size that a perfectly competitive, profit-maximizing firm uses to produce its profit maximizing output.
a) in order to profit max. in LR, firm must select cost minimizing quantities of l and k. the quantity of k that is cost minimizing and profit max selected in LR becomes the plant size of a firm in the SR as k becomes fixed in SR. this fixed k, determines the SREP, which then helps determine the profit max. values of l in the SR. b) everything @ min pt of LRAC
(1.5)a. Explain why, in our model of an isolated market, the intersection of demand and supply curves may be thought of as an equilibrium. b. Draw a diagram in which equilibrium arises without the intersection of demand and supply curves at a price of zero. Make your diagram large, label all curves and axes, and identify the equilibrium point.
a) intersection of SnD = equilibrium cuz pt of rest; neither consumers nor firms wanna change P or Q b) graph of SnD, both curves touch x axis; pt of equilibrium is at D x-intercept which is before S
(1.4)a. Explain how the market demand function for good x is derived from the demand functions of the individuals participating in the market. b. Explain how the market demand curve for good x is derived from the market demand function for good x. c. How, if at all, does a change in the price of good x affect the market demand curve for good x? d. How, if at all, does a change in the price of different consumer good or a change in market participants' income affect the market demand curve for good x?
a) market D function = sum of individual D functions b) holding m and p of other goods constant, graph prices of x against Q demanded for x c) △ in P of x --> movement along demand curve △ in P of other goods and/or m --> demand curve shifts
(2.15)a. In our model explaining the consumer's supply of labor, what determines the slope of the consumer's budget line? the values at which the budget line meets the horizontal and vertical axes? the sign of the slope of the consumer's labor supply curve? b. Is it possible for the labor supply curve to be negatively sloped? Why or why not?
a) negative wage rate = slope intercepts are total time(x) and total possible income(t*wage)(y) sign of slope depends on consumer pref b) yes, if income effect(if wage↑ but consumer is already satisfied with m, so hours worked doesnt change) >sub effect(wage ↑ so cost of leisure↑ and consumer wants to work longer), labor supply curve can be neg. sloped
(S2.13)In the price-leadership-by-a-dominant-firm model: a. After the dominant firm sets the market price, what is the output-supply behavior of the remaining firms in the industry? b. In light of the supply behavior of the remaining firms, how is the demand curve facing the dominant firm calculated?
a) output supply = sum of mc for all remaining firms as they act as perf comp firms b)demand for dom firm = difference btwn demand at market price set by dom firm and output supplied by remaining firms
(1.7)a. Suppose the government sets the maximum legal price at which a good may be sold in a particular market and assume that this price is less than the free-market equilibrium price. Draw a diagram exhibiting the actual price and quantity that comes to exist in this market. Be sure to identify the latter quantity and price in your diagram and explain why this quantity and price become, respectively, the actual equilibrium (not the free-market equilibrium) quantity and price in the market. b. Draw the same kind of diagram for the case in which the government sets the minimum legal price at which a good may be sold and this price is more than the freemarket equilibrium price.
a) price ceiling graph(line below equilibrium) firms cannot sell at a price higher than this price so they pick a quantity along their supply curve --> new equilibrium b) price floor graph(line above equilibrium)
(4.3)What are the equations that characterize a. Pareto optimality in consumption? b. Pareto optimality in production? c. Pareto optimality (in general)? In cases (a) and (b) explain why the equation characterizes the concept in question.
a) ratio of MU of 1 consumer btwn goods no consumer can be better off w/out making other worse off b) ratio of MP for one good btwn inputs output of one good cant increase w/out decreasing output of other c) MC of one good equals price of good
(2.4)Explain why utility maximization subject to the budget constraint implies that the consumer purchases that basket of commodities for which a. all income is used up. b. the marginal rate of substitution equals the price ratio. c. the marginal utilities per dollar of the two goods are equal. If you use a diagram in your answer, make the diagram large and label all curves, axes, and points.
a) to utility max. must get basket w/ biggest utility value. larger baskets have larger utility values, to get large basket must spend all money. also point of intersection btwn budget constraint and indiff curve is utility max and every pt on budget constraint uses all income b) MU/p equal cuz slope of indiff curve is negative ratio of MU and slope of budget constraint is price ratio. pt of intersection btwn curves is where utility is max so slopes equal so ratio of MU = price ratio c)rearrange equation of ratio of MU and price ratio
(4.6)a. Explain how the utility possibility curve is obtained from the contract curve in the consumption Edgeworth box. If you use diagrams in your answer, make them large and label all curves, axes, and points. b. Explain how the grand utility possibility curve is obtained from the (ordinary) utility possibility curves as the output combination moves along the transformation curve. If you use diagrams in your answer, make them large and label all curves, axes, and points.
a) using pts along the ccc, plot the two consumer's utilty as distribution of goods changes b) the grand utility represents the outermost pt of every utility possibility curve, each one obtained from a dif ccc. Each ccc is obtained from a pt on the transformation curve, which represents a distribution of total goods graph: transformation curve(x,y), ccc box(x,,y2), utility (u1, u2)
(S1.2)a. Does the total-product-of-labor function TP(ℓ) = 3ℓ^2 exhibit decreasing (marginal) returns to the fixed factor k? Why or why not? b. Does the production function f (ℓ,k) = 5ℓk exhibit increasing returns to scale? Why or why not?
a)No, marginal product of labor is increasing. take derivative b) Yes, exhibits increasing returns because if you scale the amount of inputs by a positive constant, output increases by a greater constant( give ex)
(S2.17)Explain why, in a market with a a. negative externality, too much output (more than the efficient amount) is produced and sold. b. positive externality, too little output (less than the efficient amount) is produced and sold. If you use a diagram in your answer, make that diagram large and label all axes, curves, and points.
a)a neg externality --> MEC so MC should be lower b)a pos externality --> MEB so MC should be higher graph straight line at px curves: MC+MEC, MC, MC-MEB
(1.6) Suppose you observed that in the market for wheat, 20 million bushels were sold during the first week in September for $1.00 per bushel, and that during the second week in September 25 million bushels were sold at a price of $1.25 per bushel. a. Construct a model of the market (not of consumer or firm behavior) to explain what happened. Be sure to state all of the assumptions you make. If you draw a diagram in your answer, make it large and label all curves, axes, and points. b. Use your model to explain (i) how price and quantity were determined each week and (ii) why the price of wheat went up $.25 from one week to the next.
a)assume walrasian model and price are at equilibrium SnD graph; demand shifts out --> △ P b)(i) P and Q determined by point of equilibrium (ii) D↑ --> P↑ D possibly increased cuz m↑ and wheat is a normal good
(S2.12)a. In what sense does the firm in an oligopoly situation face uncertainty? b. How do the oligopoly models of price leadership by a dominant firm, a cartel, and the kinked demand curve get around this uncertainty?
a)firm's demand curve is dependent on price and quantities other firms sell at, so demand curve cannot be determined b)models make assumptions to diminish uncertainty the model of price leadership by dom firm assumes a dom firm sets the market price and allows remaining firms to sell at the is price and then sells the remaining demand cartel: assumes that firms sell at a p and q set by a central office who tries to max profit for the industry as a whole kinked demand curve: assumes a differentiated product, firms face two demand curves, one that assumes firms follow price changes and one that assumes firms don't follow other firms price changes, the two curves intersect at prevailing market price, and all firms follow price cuts but no firm follows price increases
(1.15)Explain how the assumption that "a larger basket of commodities is always preferred to a smaller one" implies (a) that indifference curves lying farther out from the origin are associated with higher utility values, (b) that marginal utilities are positive (c) that indifference curves are downward sloping.
a)indiff. curves farther from origin represent larger baskets than indiff curves closer to origin --> baskets along further out indiff curve are more preferred --> have higher utility values b) when moving from one basket to another, if △x is positive, than one basket is larger, so the diff between utility values is positive. since MU = (diff in utility)/△x, MU is positive as both num and den are positive. c) slope of indiff curve is negative marginal rate of substitution and marginal rate of sub is always positive since MU is always pos. so slope of indiff curve is always negative, making it downward sloping
(S2.4)a. Explain why a monopolist maximizes its long-run profit by producing that output for which marginal revenue equals long-run marginal cost. b. Can the profit-maximizing monopolist produce an output that lies in the inelastic portion of the demand curve it faces? Why or why not? c. Does long-run profit maximization by a monopolist imply that it must produce at the minimum point of its long-run average cost curve? Why or why not? d. Does long-run profit maximization by a monopolist imply that its revenue is maximized? Why or why not?
a)profit = TR-TC take derivatives and rearrange b)no, MR is negative, since inelastic, and profit max means MR=MC and since MC is always positive, MR can't be negative c) no profit max occurs where LRMC=MR which is not at min pt of LRAC since this pt means no profit. but since downward facing demand curve, mc<px in monopoly, so profit, so not at min of LRAC d) no, when revenue max, MR=0, but MC is positive so MR is positive, can't be zero
(4.9)Assume our model of the perfectly competitive economy is a good representation of the actual economy. Explain why, under this assumption, the following quotation is NOT generally true: "If left alone without government or other outside help, the actual economy will allocate resources and produce and distribute outputs so as to provide (a) an approximately equal distribution of goods among consumers and (b) maximize social welfare."
a)under perf comp, gen eq can fall anywhere along ccc since every pt pareto optimal. this means even pts where 1 individual gets no goods is pareto optimal, so distributions are unbiased in terms of equally distributing goods b) under perf comp, gen eq maximizes utility, meaning any pt along the grand utility curve, but welfare is not maximized at every pt on this curve, so equilibrium may or may not maximize social welfare.
(S2.14)Describe the kinked-demand-curve oligopoly model. State your assumptions and draw the appropriate diagram. Make the diagram large and label all axes, curves, and points. Indicate how the model can explain long periods of price rigidity in an oligopolistic market.
assumes differentiated product, firms face two demand curves, (1) that assumes all firms follow price changes of other firms and (2) that assumes no firms follow price changes, prevailing market price occurs at pt of intersection btwn curves, all firms follow price decreases but not price increases (1) is steeper than (2)
(2.17)How is plant or firm size measured?
by fixed amount of capital in short run
(4.11)State the general case in terms of efficiency for government intervention in a market that fails.
can intervene to increase one person's utility w/out decreasing other's utility, can bring MC closer to accurately reflect MEB and MEC
(1.10)In what sense is an individual's demand function for a commodity observable? In what sense is an individual's preferences among baskets of commodities not observable?
can observe what ppl buy and how they spend income but not what they are thinking/preferences
(2.14)Describe how our model of the consumer's buying behavior is modified to explain the consumer's supply of labor.
consumers continue to have complete and transitive preferences, but in the labor market, the preferences are about baskets of income and leisure time. preferences are represented thru utility function w/ same properties as in consumer buying. consumer chooses basket of (leisure, income) to maximize utility subject to budget constraint
(1.12)In what sense is the utility function ordinal?
cuz actual values of utility function don't mean much on their own. Rather, what matters is utility values of different baskets relative cuz a higher utility value represents a more preferred basket
(S2.15)How does the presence of monopolistic competition or oligopoly create market failure and rule out Pareto optimality (efficiency)?
demand curve is not horizontal like w/ pf(downward facing or kinked) --> price is higher and output is lower than in pf so not pareto optimal
(3.18)Draw a diagram showing the perfectly competitive, profit-maximizing firm's long-run demand curve for labor in relation to its marginal revenue product (or value of marginal product) curves. Make your diagram large and label all curves, axes, and points. Explain why the long-run demand curve for labor is related to more than one marginal revenue product curve.
draw concave down two VMP curves with two diff quantites capitals w/ respect to L and downward demand axes are labor and P(l) to denote for diff values of k, as k changes, TP and MP of l changes so VMP changes
(2.8)Give a geometric construction of consumer demand curves based on preferences (indifference curves), prices, and the consumer's income. Make your diagrams large and label all curves, axes, and points. Explain your construction in words.
draw indiff curves and budget constraints where px changes(connecting line is steep) draw demand curve(downward sloping)
(4.7)Explain why, to each point on the grand utility possibility curve there corresponds a basket of outputs on the production possibility curve whose distribution between the two consumers is Pareto optimal (in general).
every pt along grand utility curve is outermost pt of a utility possibility curve. each utility possibility curve is associated w/ a ccc(-->MU=) that is derived from a pt on the ppc. Every pt on the ppc represents a basket of goods, i.e the total able to be sold within two consumers in the consumption edgeworth box. these baskets are derived from pcc(-->MP =) so pareto optimal
(S2.9)How do the demand curves facing the perfectly competitive firm, the monopolist, and the monopolistically competitive firm differ? Explain why these differences arise.
facing PF: horizontal - no market power facing monopolist: downward facing; market demand curve; complete market power facing monopolistically comp: downward facing; slope btwn that of demand curve of PF firm and slope of monopoly's demand curve <-- some market power
(S2.8)Explain how price regulation of a monopoly can reduce the social cost (deadweight loss) of monopoly.
gov can set price ceiling below profit max price set by monopoly --> forced to produce at a higher output and lower price, thus decreasing area of deadweight loss
(S1.8)Describe the relationship between the different kinds of returns to scale and the different kinds of economies of scale.
if the production function exhibits {increasing, constant, decreasing} returns to scale and expansion paths are straight lines from origin as input prices vary, then the LRAC curve exhibits {economies, constant economies, diseconomies} of scale
(3.17)Explain why the short-run labor demand curve of the perfectly competitive, profit-maximizing firm is that firm's marginal revenue product (or value of marginal product) curve.
in the SR, VMP=Px in order to profit max, and since every pt along demand is profit max --> VMP curve is labor demand curve
(3.12)Explain why abnormal profits earned and losses incurred by perfectly competitive, profit-maximizing firms cannot be present at long-run equilibrium.
in the long run, there is free entry and exit for firms. if positive profit --> firms enter the market --> supply ↑ --> P ↓ --> TR and MR↓ --> profit decreases till it reaches 0 if negative profit --> firms exit market --> supply ↓ --> P ↑ --> TR ↑ --> profit increases till it reaches 0
(2.12)How are upward sloping consumer demand curves explained in terms of income and substitution ratios?
income and sub ratios are negative
(2.3)Suppose you observe, on several occasions, Bob's buying behavior in a "supermarket" that sells only 2 goods x and y. Suppose that for each observed basket (x,y) that is purchased, you know the prices of the goods px and py, and the amount of money m Bob had to spend. In other words, you are able to observe Bob's demand functions x = hx (px,py,m) and y = hy (px,py,m). Construct a model to explain Bob's buying behavior. That is, state the assumptions you make and give an argument to show how the assumptions in your model of Bob's buying behavior are linked to, and therefore explain his demand functions. Do not discuss the properties of those demand functions - only the means by which the demand functions are obtained from preferences and how your model explains Bob's observed demand behavior.
indiff curve and budget constraint graph?
(2.6)Give a geometric example that illustrates how the character of the utility maximizing basket changes if one or more of the assumptions in answer (2-2) are weakened or discarded. Make your diagram large and label all curves, axes, and points.
indiff curve is not strictly convex draw indiff curve upside down with budget constraint tangent
(2.16)How, and in what time period, does a firm go out of business?
long run + when MR, or px, is less than AVC
(S2.16)How does the presence of an externality create market failure and rule out Pareto optimality (efficiency)?
market price doesn't accurately reflect cost to society or mc doesn't accurately reflect benefit to society, as MEB or MEC are not taken into account, so MC is not equal to p so not pareto optimal
(1.3)What is the Walrasian model a model of, and what are the Walrasian model's main characteristics?
model of how buyers and sellers act in a market in order to reach equilibrium - perfect competition - perfect information - fixed tastes and technology - acts in self interest and profit maximization - standardized product - free entry and exit - market forces equilibrate demand and supply
(S2.5)How does the presence of monopoly create market failure and rule out Pareto optimality (efficiency)?
monopoly faces downward sloping demand so mc<px, which means mc is not equal to mrs or mtrs so not pareto optimal
(4.4)Explain how the production possibility or transformation curve is obtained from the contract curve in the production Edgeworth box. If you use a diagram in your answer, make the diagram large and label all curves, axes, and points.
moving along pcc parallels moving along transformation curve as pts represent pareto optimal distributions. box is of l and k of x and y transformation axes is x and y
(S1.3)What are the relationships among marginal products, the marginal rate of technical substitution, and the slopes of isoquants?
mrts = ratio of mp between two goods; mrts is negative slops of isoquants
(S2.6)Why doesn't the abnormal profit of a monopolist, unlike that of the perfect competitor, reduce to zero in the long run?
no free entry or exit so supply can't change and thereby affect price so profits remain
(2.13)What must be true about the relative magnitudes of substitution and income ratios in order to have a normal good? an inferior good? a Giffen good?
normal: sub-, income+ inferior: sub-, income- giffen: sub-, income-(effect of income is greater)
(2.10)Show geometrically how it is possible in our model of consumer demand to generate an upward sloping consumer demand curve from constrained utility maximization. Make your diagram large and label all curves, axes, and points.
price consumption curve is downward sloping --> demand curve is upward sloping
(2.9)How is the price-consumption curve in our model of consumer buying behavior related to the consumer's demand curve?
price consumption curve traces utilty maximizing baskets when the price of one good changes. This relates to the demand curve, as every pt on the demand curve maximizes utility as price of a good changes (same drawings as 2.8)
(S2.11)In the long run, how do price and output compare for a perfectly competitive firm and a firm with the same cost curves in a monopolistically competitive environment?
price lower and output higher for perf comp firm price higher and output lower for monopolistically comp firm
(3.16)Explain why, in the short run, the perfectly competitive, profit-maximizing firm should hire labor up to the point at which its marginal revenue product (or value of marginal product) equals the price of labor (wage).
profit = TR - TC = pxTP - lP(l) - kP(k) take derivative w/ respect to l 0 = VMP(l) - P(l) rearrange derivative of profit = 0 cuz maximizing derivative of kP(k) = 0 cuz constant
(S1.5)Why does the assumption of profit maximization imply that the firm will produce each output with a basket of inputs that minimizes cost?
profit = TR - TC so basket with minimal cost maximizes profit
(3.4)Explain why in the long or short run, the perfectly competitive, profit maximizing firm always produces and supplies that output for which long- or, respectively, short-run marginal cost equals price. (Ignore the possibility that the maximum profit might be negative.)
profit = TR - TC, take derivative w/ respect to x --> 0 = MR - MC, d/dx(profit)=0 because to profit max, highest pt on profit curve, derivative=0 rearrange --> MR=MC since MR=P, as additional revenue of one unit would be price of unit, MC=P
(3.11)Explain why the short-run output supply curve of the perfectly competitive, profit-maximizing firm is the firm's short-run marginal cost curve above minimum average variable cost.
profit max occurs when MC=MR=Px and every pt on the supply curve is profit max. above min pt of AVC cuz if price falls below, this pt, firms no longer want to supply as earning negative profit and revenue is not enough to cover variable costs, so supply at pts below this pt is 0 as the firm shuts down and doesn't supply output
(4.8)Draw a diagram whose axes record individual utility values and which depicts (social) welfare maximization in a perfectly competitive economy. Make the diagram large and label all curves, axes, and points.
pt of intersection btwn grand utility and welfare function
(S2.3)a. Draw a pair of diagrams, one above the other, illustrating the profit maximizing output for the monopolist with abnormal profit. The top diagram should contain short-run total cost, total variable cost, total revenue, and profit curves; the bottom diagram should contain short-run average cost, average variable cost, short-run marginal cost, and marginal revenue curves. In the bottom diagram shade in the area that represents abnormal profit. Make your diagrams large and label all curves, axes, and points. b. How would your diagrams change if the firm were losing money, i.e., had negative profit?
pt where px and profit max output would fall under the min pt of srac and total revenue would be below srtc
(S2.19)How does the presence of a public good generally create market failure and rule out Pareto optimality (efficiency)?
public good nonrival and nonexclusive --> no incentive to pay for good -> no demand curve --> can't determine pareto optimal distribution
(S2.10)Draw a diagram containing the long-run average and marginal cost curves, the demand curve facing the firm, and the marginal revenue curve for a profit maximizing monopolistically competitive firm at long-run equilibrium. Make your diagram large and label all curves, axes, and points.
same as monopoly except side of LRAC touches demand curve at profit max pt
(S2.20)Assuming we know the willingnesses to pay of all individuals for a public good, explain how one could calculate the efficient amount of that good to produce. If you use a diagram in your answer, make that diagram large and label all axes, curves, and points.
sum of individual demand curves forms MARGINAL SOCIAL BENEFIT curve, essentially market demand curve for good graph MSB and MC curve --- pt of intersection is efficient
(S1.9)Draw a diagram with cost curves illustrating the relationship between long run and short-run total cost curves. Explain the tangencies between the long-run and short-run total cost curves in this diagram using another diagram containing isoquants and the expansion path. Make your diagrams large and label all curves, axes, and points.
tangent where LREP = SREP i.e. when capital equal srtc starts at Kpk; lrtc starts at origin isoquant and isocosts and lrep and srep intersect at isoquant
(2.11)Draw a diagram and use it to explain how to calculate income and substitution ratios. Make your diagram large and label all curves, axes, and points
three budget constraints: 2 are a price change, 3rd is parallel to farther out constraint substitution ratio = (x1-x2)/△px income ratio = (x3-x2)/△px
(3.13)Explain why the perfectly competitive firm at long-run equilibrium produces an output for which long-run average cost is minimized. Is this output profit maximizing? Why or why not?
to profit max, LRMC=MR, thus MR is tangent to LRAC at min pt, otherwise abnormal profits occur --> profits profit max cuz where MR=LRMC
(2.5)Explain why, if all prices and the consumer's income were multiplied by any positive number (for example, doubled), there would be no change in his/her utility maximizing basket.
utility max basket is at pt of intersection btwn indiff curve and budget constraint. since p and m changed by same constant budget constraint, does not change(px(x) + py(y) = m). indiff curves is not affected by(not dependent on) prices or income, so does not change. therefore pt of intersection doesn't change, so basket doesn't change
(S1.4)Without referring to costs or the expansion path, explain why a profit maximizing firm will always produce its output with a basket of inputs that lies between the ridge lines (assuming they are present) up to the point of intersection, if there is one.
where ridge lines intersect isoquants, MP is 0 or infinity and decreasing beyond pt of intersection. firms wanna produce when MP is positive and increasing
(4.2)In a two-person, two-good, consumption Edgeworth box diagram, consider a distribution that does not lie on the contract curve. If the two individuals are initially placed at that distribution, explain why they will begin to trade with each other, and continue to trade until they reach a distribution on the contract curve
will trade till pt on curve cuz both benefit from trading till pt on curve; every pt on curve is tangency pt btwn outermost pts on consumers utility indiff curves so trading past curve that increases 1 consumer's utilty, will decrease other's so at Pareto optimal distribution