14.01SC Principles of Microeconomics Scholar, Midterm 2 Solution Set

14.01 Fall 2010: Midterm 2 Solution Set 1. True/False/Uncertain Questions (16 points) In this section, write whether each statement is True, False or Uncertain. You should fully explain your answer, including diagrams where appropriate, Points will be given based on your explanation. (a) (4 points) Two firms are producing similar goods, but one enjoys economies of scale and one has diseconomies of scale. Claim: both firms can have an identical long-run linear expansion path. True. A linear expansion path simply indicates that the optimal mix of labor and capital does not change, but there can be either economies or diseconomies of scale depending on the production function. These firms could have the same expansion path, but output using the same quantity of inputs will not be the same. (b) (4 points) A firm is currently earning negative profit on each good it produces. Claim: it is always optimal for this firm to shut down in the short run. False. A firm will not shut down in the short run as long as its revenue is greater than average variable cost. If revenue is less than average variable cost (i.c., the absolute value of negative profits is larger than the fixed costs), the firm will shut down. In the long run, of course, firm exit will occur and profits will go to zero. (c) (4 points) The market for drug production is characterized by both lengthy periods of patent protection and the need for FDA permission to market products. Claim: this market will be characterized by production at the minimum level of average cost in the long run. Uncertain. Both patent protection and government regulation constitute market bar- riers in this case. In a market with barriers to entry, the long-run supply curve will not necessarily be horizontal and average cost will not necessarily be minimized. To guarantee a horizontal supply curve, there must be be no barriers to entry, all firms must be identical, and there can be no variation in input costs. (d) (4 points) Cooperative behavior between two oligopolists is impossible if they know that they will be competing for a limited number of years. True. A cooperative equilibrium can be sustained only if the competition game will continue forever. If they know the period of competition is finite, both will chent. 2. Costs and profit maximization (22 points) A profit-maximizing, price-taking firm produces output Y using a single input X. The firm can produce 0, 8, 9, or 15 units of Y by using 0, 4, 7, or 9 units of X, respectively. 1 There are no other possible input-output combinations. The firm's production function is therefore given by: Y = f(X) = 0 HX-0 X=4 if X 7 if X=12 9 16 The price of input X is 1 dollar per unit. (a) (4 points) Write the firm's total cost as a function of output. 0 if Y=0 C(Y)= 4 if Y-8 7 if Y=9 12 if Y 16 (b) (6 points) Find the firm's supply function (p). Explain your answer 16 Hp≥1 If output increases from 0 to 8, costs per unit increase by $0.50/unit. Therefore the firm will supply O units if p < If the firm increases output from 8 to 9, the cost to produce the additional unit is $3. However, if the firm increases output from 8 to 16, the additional cost per unit of the additional units 8 is 81/unit. Therefore the firm will produce 8 units when the price is above $0.50 and below $1, and 16 units if the price is above $1. (c) (5 points) Suppose that there are 5 such price-taking firms in the market, and that there is no entry. Market demand is given by Q100-10p. What is the equilibrium price and quantity in this market? Total market supply with 5 firma 18: With this level of demand, the market clears at PM = 2 and Q80. (d) (7 points) Suppose now that instead of the 5 firms in part (c) there is actually a single monopolist that is five times as large as one of these individual firms. The monopolist's production function is therefore: 0 if Xat=0 Ум-5-(Хм) 2 40 if Xa - 20 45 if X=35 80 if Xx 60 Demand is given by Q 100-10p as before. Assume now that entry is once again impossible. What is the equilibrium price and quantity in this market? Compare this outcome with the equilibrium in (c) and explain why they are the same differ. The monopolist compares marginal revenue to marginal cost when deciding whether or not to increase production: QP-10-Q/10 TR TC MR MC Profit 0 10 40 6 45 5.5 0 0 240 20 240 247.5 95 7.5 20 15 212.5 0 220 80 25 100 160 60 -87.5 The monopolist will not increase production begond 40 because MR < MC for all quan- tities greater than 40. As a result, profits are maximized at Q40. The equilibrium price at this quantity is $6. This is a lower quantity and higher price than in (d) because the large monopoly firm has market power and the five smaller firms are assumed to be price takers. 3. Monopoly and oligopoly (27 points) A uniform pricing monopolist has the following cost function and faces the following demand curve for its product = 200 C(Q) P = 100-Q (a) (3 points) Find the monopolist quantity (Qm), price (Pm), and deadweight loss rel ative to the perfectly competitive outcome. Draw a diagram labeling the perfectly competitive outcome as A, and the monopolist outcome as B. Be sure to include the marginal cost and marginal revenue curves in your diagram. The monopolist sets MR MC100-2020 Q40, P60. DWL40-40-800. (b) (6 points) There are two possible scenarios for the monopolist: i. The government set a price ceiling of $ 40/unit in which case the monopolist does not invest in any R & D because it is wary of future government regulation. il. There is no government regulation, so then the monopolist invests in R & D which then changes the cost function so that MC = 0. Which scenario has higher welfare (ignore the cost of R & D for producer surplus)? Which scenario do the consumers prefer? Explain. i. At P40, Q60, we have CSBH 6060 1800. PSBH60(40-20)=1200 WCS+PS = 3000 ii. MC0, MR-MC100-200 Q50, P50 At Pm50, Qm50, we have: CSBH50*50=1250 PSBH50502500 WCS+PS=3750 3 Consumers would prefer scenario (i) since consumer surplus is higher because they pay a lower price. Welfare is higher under scenario (vi) because the cost saving R&D generates large producer surplus and also limits the loss to consumer surplus because output expands. (c) (6 points) For plan (i), the MR curve features a discontinuity at some Q. Explain intuitively why the MR curve has this discontinuity. Generally there are two effects for a monopolist when you mercase Q by one unst the "output effect" when you get to sell the additional wait you produce, and the "poisoning the well" effect when you receive a lower price on the inframarginal units (units you continue to sell). When QQ, the MR is constant at the price ceiling of 40 because the monopolist is a price taker. While the monopolist would like to charge more, it is constrained by the government regulation and only has the "output effect". When QQ, the MR suddenly drops because you are already selling a lot of inframarginal units, and now the government price ceiling no longer binds, which implies that the "poisoning the well" effect is very large, leading to this discontinuaty. (d) (6 points) In scenario (ii), when MC = 0, the monopolist chooses (Q, P) such that 1. Will an unregulated uniform pricing monopolist ever choose (Qm. Pm) such that e 1? Explain intuitively. On the inelastic portion of the demand curve, the marginal revenue is negative. If the monopolist is ever on this portion of the demand curve, you can increase profits unambiguously by decreasing quantity by one unst. It is able to save the marginal cost, and its revenues also increase since MR < 0. (e) (6 points) Go back to your solution in (a). Suppose now the government allows one other identical firm to enter this market and firms compete on quantity. Let the value of the MR at the monopolist output when there's only one firm. Claim: If the two firms each produce half the Monopoly quantity, then MR for both firms at current levels of output. Is this claim true, false, or uncertain? Please explain your reasoning. False. MR for each of the firms, because when the quantity is split between two firms, there are fewer inframarginal units so that the "poisoning the well" effect is smaller from the perspective of one firm. The "output effect" is the same for either the duopoly case or monopoly case, 4. Trade in sweat-trapping headbands (35 points) The U.S. demand for sweat-trapping headbands is summarized by the function ga 1200- p, where p is the market price of a headband. There are currently 49 identical, profit- maximizing domestic headband producers in the U.S., each with the cost function TC(q) = 72+0.542. U.S. consumers consider domestically produced headbands to be identical to foreign-produced headbands, and currently have access to a huge supply of foreign-made handbands at a constant price of $10 per band (that is, we can think of the worldwide supply of sweat-trapping headbands as a horizontal curve at p = 10). (a) (5 points) Write down an expression for the supply curve for an individual domestic headband producer. If there is perfectly free international trade in sweat-trapping headbands, what will be the market price of a headband in the U.S.? How many headbands will be purchased in the U.S.? How many of those will be imported from abroad?