PS04_Answers_ - EC 340 Spring 2011 Problem Set 4 1 Which theorem states that the capital‐abundant country will have a comparative advantage in

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Unformatted text preview: EC 340 Spring 2011 Problem Set 4 1. Which theorem states that the capital‐abundant country will have a comparative advantage in producing the capital‐intensive good? The Heckscher‐Ohlin Theorem. 2. Which theorem states that an increase in the price of the labor‐intensive good relative to the price of the capital‐intensive good will increase the real income of workers and reduce the real income of capital owners? The Stolper‐Sameulson Theorem. 3. Which two theorems combined imply that the introduction of trade benefits a country’s abundant factor and harms its scarce factor? The Heckscher‐Ohlin and Stolper‐Samuelson Theorems. 4. In the model of monopolistic competition, what happens to the PP curve when trade is permitted? Nothing happens to the PP curve. This curve shows the profit‐maximizing price charged by each firm as a function of the number of firms in the market. One of the underlying assumptions of the model is that this profit‐maximizing price does not depend on the size of the market. Since this does not depend on the size of the market, it does not depend on whether or not the firm has access to foreign markets via trade. 5. The following figure represents a monopolistically‐competitive industry that operates in two countries (A and B). Which country has the larger market? How would this figure be modified if A and B were permitted to trade with each other? 6. Nothing would happen to the PP curve (see answer to question 4), but there would be a new CC curve (applying to the integrated market of countries A and B together). Moreover, this new CC curve would lie lower and to the right of the CC curve for country B. Remember, this curve shows the average cost of production for each firm as a function of the number of firms in the market. Suppose, for example, that there are 5 firms in the market. The bigger the market, the lower the average cost of production (since each firm would have 1/5 of the market and there are increasing returns to scale in production). Market B must be bigger than market A (the CC curve for market B lies below the CC curve for market A). But the market for both A and B combined is clearly bigger than the market for either A or B alone. This is the reason for drawing the CC curve for the combined market below and to the right of the CC curve for market B. With trade, the price will be lower than it would be in either country in autarky, and the number of available varieties would be larger than the number of varieties available in either country in autarky. Suppose that Pfizer (an American pharmaceutical company) has a monopoly in the U.S. market for a vaccine that prevents the common cold. Further suppose that the demand curve for this vaccine in the U.S. market is represented in the diagram below. Draw the marginal revenue curve for Pfizer’s vaccine. MR With a linear demand curve, the marginal revenue curve is also linear. It has the same intercept as the demand curve, but is twice as steep. 7. Suppose that Pfizer’s marginal cost of production is $15 per dose of vaccine, regardless of how much vaccine is produced. Combined with the information in question 6, how many doses of vaccine will Pfizer sell in theU.S. market, and what price will they charge? MC MR Pfizer will produce more if its marginal revenue exceeds marginal cost, and will reduce production if marginal cost is larger than marginal revenue. Equilibrium occurs when marginal cost equals marginal revenue. In this case, that happens at 20 doses. The price charged is as much as the market will bear. Go up to the demand curve when quantity is 20 doses to find the price is 25. 8. 9. 10. Assuming that there are no fixed costs of production, how much profit will Pfizer earn? With no fixed costs, total cost will be the marginal cost ($15) multiplied by the number of units produced (20), for a total cost of $300. Total revenue is the price ($25) multiplied by the total number of units produced (20) for total revenue of $500. This gives a total profit of $500 ‐ $300 = $200. What is the value of consumer surplus when Pfizer sells its profit‐maximizing quantity of vaccine? At a price of $25, consumer surplus is represented by the area of a triangle that is ($35 ‐ $25) high and has a base of 20 units (the number sold). This has a value of ½ * $10 * 20 = $100. Suppose that Bayer (a German company) produces an identical vaccine. What (approximately) would Bayer’s marginal revenue be from selling just one dose of vaccine in the U.S. market? 11. Bayer’s marginal revenue from selling one dose in the U.S. market would be approximately $25. That is the price that Pfizer would charge if it were a monopolist. Bayer could charge the same price (perhaps a few cents less) to sell one dose of the vaccine. Assume that Pfizer and Bayer have identical costs and that there are no transportation costs. If Bayer is permitted to sell vaccine in the U.S. market, what will be the equilibrium value of Pfizer’s and Bayer’s marginal revenues? 12. This is an admittedly tricky question, but it has an extremely simple answer. In equilibrium, marginal revenue equals marginal cost. Since marginal cost is the same for both firms and independent of how much is produced, marginal revenue for each firm will be $15 in equilibrium. It can be shown that if trade between the two countries is permitted, total sales in the U.S. market will be 80/3 doses. This will also be the total sales in the German market. Of the 80/3 doses sold in the U.S. market, how many doses will be imported? How many doses will Pfizer export? 13. Since both firms are identical, they will each have a ½ share of each market. So, of the 80/3 doses sold in the U.S. market, half (40/3) will be imported (produced by Bayer). Likewise, of the 80/3 sold in the German market, half (40/3) will be imported (produced by Pfizer). Based on your answers to question 12, how much profit will Pfizer earn on the combination of its domestic sales and its exports? Pfizer will account for half of all vaccine sales in the world. World sales are 80/3 + 80/3, so Pfizer’s sales are 80/3. Their cost of production is $15 * 80/3. Their revenue equals the price at this equilibrium * 80/3. You can figure out the price explicitly by figuring out the equation for the demand curve (you know it’s intercept and slope, so you can write down an equation). The precise equation for this demand curve is P = 35 – Q/2. Therefore the price at Q = 80/3 is 35 – (80/3)/2 = 35 ‐40/3 = 105/3 – 40/3 = $65/3. Profit (rounded to the nearest cent) is $(65/3 ‐ 15)*(80/3) = $(20/3)*(80/3) = $(1600/3) = $533.33 14. 15. With trade, what is the value of consumer surplus in the U.S. market? From the answer to question 13, price is $65/3 and quantity is 80/3. So consumer surplus is ½*$(35 – 65/3)*(80/3) = ½*$(40/3)*(80/3) = $(1600/3). Rounded to the nearest cent, this is $533.33. How does the total of Pfizer profit plus U.S. consumer surplus with trade compare to the total under autarky? The sum of consumer surplus and producer profit increases relative to autarky. In this case (with no transportation costs), trade increases welfare. ...
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This note was uploaded on 11/11/2011 for the course EC 340 taught by Professor Ballie during the Spring '10 term at Michigan State University.

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