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Unformatted text preview: PADP 8670 Fertig Homework 2 Solutions 1. Answer the following questions with reference to the diagram below and its labels. It shows the demand curve for a firms' product, the marginal revenue curve, and the constant marginal cost curve (which is equal to the average cost curve). Fall 2011 UGA P Demand MR A B C MC=AC D E F G Q Profit max quantity is found where MR=MC this occurs at quantity D. Profit max price is found where demand curve achieves quantity D price = A. The profit is maximized when MR=MC because any additional output would involve a higher cost than revenue and thus reduce profit; and any lower output would involve a higher revenue than cost meaning that increasing output would increase profit. 1 a. Identify the price and quantity at the profit maximum. Explain why it is the profit maximum. Revenue is at its maximum when MR=0, meaning any additional output would reduce revenue, and any less output would increase revenue. This occurs at quantity E and quantity E can be achieved with price B (from the demand curve). c. Identify the efficient quantity. Explain why it is the efficient quantity. The efficient quantity is F where the price is equal to MC. At this point, there is room for Pareto improvement. All consumers willing to pay above MC purchase the product at MC, creating a lot of consumer surplus, although the firm earns no profit. d. Explain which is more inefficient: the quantity in your answer to a or to b? The answer to b (the revenue maximum) is more efficient than the answer to a (the profit maximum) because it is closer to the efficient quantity (the answer to c). 2. Napster, the online file-swapping service, allowed people to use the Internet to download copies of their favorite songs from other people's computers without cost. In what sense did Napster enhance economic efficiency in the short-run? In what sense might Napster have reduced economic efficiency in the long-run? Why do you think the courts eventually shut Napster down? In the short-run, Napster increased consumer surplus by allowing anyone with positive utility from music to consume music for free (instead of just the consumers who valued the music above the retail price). However, in the long run, the incentive to musicians and recording companies to create music declines when they cannot ensure future profit, so the supply of music declines which reduces consumer and producer surplus. Napster was shut down because it infringed on the copyright of musicians and recording companies. 2 b. Identify the price and quantity where the revenue is at its maximum. Explain why it is the revenue maximum. 3. A monopolist's demand and marginal revenue is as follows below. The monopolist's marginal cost is $20 for every unit produced. Calculate the monopolist's output, price, profit, consumer surplus, and the deadweight loss to society. Also, draw the solution graphically. P = 160 - 2Q MR = 160 4Q MR=MC 160-4Q=20 140=4Q Q=35 P=160-2(35) P=90 Profit=(P-AC)Q Profit=(90-20)35 Profit=2450 Consumer Surplus = (max price P(profit max))*Q/2 CS=(160-90)35/2 CS=1225 DWL=(Q(efficient)-Q(profit max))*(P(profit max)-P(efficient))/2 To figure out Q(efficient), set P=MC(=20): 160-2Q=20 140=2Q Q=70 DWL=(70-35)*(90-20)/2 DWL=1225 3 4. Now assume that a new market emerges for the monopolist described in problem 3 to enter. Assume that the monopolist is able to separate the new market from the market described in problem 3, and thus price discriminate. The monopolist's demand and marginal revenue for the new market is as follows below. Calculate the output, price and profit derived from the new market. Also compute the additional consumer surplus generated from the monopolist entering the new market. Draw the solution graphically as well. Pnew = 80 (1/2)Qnew MRnew = 80 Qnew MR=MC 80-Q=20 Q=60 P=80-(1/2)60 P=50 Profit=(P-AC)Q Profit=(50-20)60 Profit=1800 Consumer Surplus = (max price P(profit max))*Q/2 CS=(80-50)60/2 CS=900 4 5. Finally, assume that the monopolist is not able to keep the markets separate due to Internet sales across the geographical areas. Thus, the firm can no longer price discriminate across the markets. The new demand curve that the firm faces is a combination of the two demands from the two markets, as shown below. Re-calculate the monopolists' output, price, profit if price discrimination is no longer possible. Draw this solution graphically as well. P = 160 - 2Q & MR = 160 4Q if P 80 P = 96 (2/5)Q & MR = 96 (4/5)Q if P 80 Looks like MR=MC intersects below P=80 so only need to use the second set of equations. MR=MC 96-(4/5)Q=20 76=(4/5)Q Q=95 P=96-(2/5)95 P=58 Profit=(P-AC)Q Profit=(58-20)95 Profit=3610 which is less than price discrimination combined profit=2450+1800=4250 5 6. Calculate the consumer surplus changes (in each market and combined) across the 3 different scenarios described in problems 3, 4, and 5. For each change, discuss whether this is what we expect given the general economic theory about price discrimination. Original Market Consumer Surplus Change: Problem 3: CS=1225 Problem 4: CS=1225 because nothing changed for the original market in problem 4. Problem 5: First, we need Q going to this market in this scenario. P=160 2Q Rearrange to Q=80-(1/2)P Q=80-(1/2)*58 Q=51 Consumer Surplus = (max price P(profit max))*Q/2 CS=(160-58)51/2 CS=2601 CS increased for original market from problems 3/4 to problem 5 (when the new market brought down the price for the original market). There was no change from problem 3 to 4 as economic theory suggests price discrimination does not affect the richer or original market. The increase from problem 3/4 to problem 5 is not explicitly discussed in price discrimination theory, but expected given that the price decreased for the original market. New Market Consumer Surplus Change: Problem 3: CS=0 because monopolist wasn't selling to this market in problem 3. Problem 4: CS=900 Problem 5: First, we need Q going to this market in this scenario. P=80 (1/2)Q Rearrange to Q=160-2P Q=160-2*58 Q=44 Consumer Surplus = (max price P(profit max))*Q/2 CS=(80-58)44/2 CS=484 CS increased from problem 3 to problem 4 (when the monopoly entered their market), as expected by economic theory, but decreased from problem 4 to problem 5 (when the monopoly could no longer price discriminate). As above, the general price discrimination theory does not explicitly detail what happens to each market, but it is expected given that the price increased for this market. Combined Market Consumer Surplus Change: Problem 3: CS=1225+0=1225 Problem 4: CS=1225+900=2125 Problem 5: CS=2601+484=3085 Overall CS increased when the monopolist entered the new market because new consumers were able to purchase the product, as price discrimination theory 6 predicts. However, overall CS fell when the monopolist was no longer able to price discriminate but still sold their product in both markets. The reason is that one price changed the allocation of consumers from those with lower utility (in the new market) to those with higher utility (in the original market), thus resulting in higher CS. Thus, price discrimination is beneficial to consumers when it brings consumers to the market, but detrimental to consumers if it serves to keep prices high in one market. 7. Read Simon and Gruber (2008) and write a one page summary. Crowdout = extent to which expansions in public programs reduce demand for private programs The authors find that expansions in public insurance (SCHIP) in the 1996-2002 period resulted in significant crowd-out, particularly with respect to family (not individual) eligibility. Anti-crowd-out measures include waiting periods and cost-sharing (copays and premiums). They do not find evidence that these measures reduce crowd-out, but they do reduce take-up among the uninsured. 7 ...
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- Fall '10