Chapter 4 4. [Question 3 on page 62] Consider a model with two countries called France and Germany. France has one automaker, called Citroen. Germany has a competitor, called Volkswagen. Citroen can produce cars at a constant marginal cost of $1,000 each. VW can produce cars at a constant marginal cost of $2000 each. Within each country, the demand for cars is given by the same demand curve: Q = (18 P) x 10000 Where (1 is the number of cars demanded in that country per month and P is the price per car in that country, in thousands ofdollars. Assume that no one other than Citroen or VW can transport cars between the two countries, so it is possible for the price of cars in the two economies to be different. (a) Suppose initially that both economies are in autarky. What will be the price and the quantity sold in each country? (b) Suppose that we now have free trade between the two economies. There is no cost to transporting the cars across borders for either firm. Suppose that the two corporations set their quantities in each market simultaneously. For any given quantity qK that Citroen expects VW to sell in the French market, find the profit-maximizing quantity org that Citroen will sell in the French market. Using your answer, draw Citroen's reaction function for the French market. (c) Using logic parallel to (b), draw VW's reaction function for the French market on the same diagram. (d) Assume that each firm correctly guessed how much the other will produce in each market. What will be the price charged and the quantity sold in each market? (e) Analyze diagrammatically the effect of trade on the profits of the two rms, on consumer welfare in the two countries, and on overall social welfare. Do the two countries benefit from trade? Does anyone lose from it? Answer: (a) To find prices and quantities in autarky, where both firms are monopolists in their own country, we set their marginal revenue equal to their marginal cost. In France, 18- 2CITROEN = 1 , so CITROEN = 85000 and P = 9.5. 5000 In Germany, 18- =2, so eww= 80000 and P = 10. (b) The residual marginal revenue for Citroen in the French market is 18- 2CITROEN _ Q vw 5000 10000 . To find Citroen's reaction function, we set the residual marginal revenue equal to Citroen's marginal cost, 1, and rearrange to find com CITROEN = 85000-2VW 2 . The following graph shows Citroen's reaction function (in red). QCITROEN his study resource shared via CourseHero" 050DO GRAPH 4-1 170000 QVW (c) Volkswagen's reaction function is 18- 2CITROEN _ 2 vw 10000 5000 . Setting this equal to VW's marginal cost, 2, we find 2ww= 80000- CITROEN 2 . This is shown in the graph above (in blue). (d) To answer this we must solve the system given by both reaction functions. This isequivalent to finding the intercept between them in the graph. This yields CITROEN = 60000 and 2ww= 50000 The price, P = 7, is found from the demand equation. (e) Under autarky, consumer surplus in Frances is CSFRANCEAUT =0.5 . (18-9.5) .85000=361250 and in Germany, CSGERMANY AUT =0.5 .(18-10) . 80000=320000 . Profits for Citroen are IIACT CITROEN =(9.5-1) . 85000=722500 and profits for VW are AUT =(10-2) .80000=640000. eHero.com Social welfare is 1083750 in France and 960000 in Germany. Under free trade, consumer surplus in Frances is CSFRANCETRADE =0.5 . (18-7).110000-605000 and in Germany, CSGERMANY TRADE =0.5 . (18-7) .110000=605000 . ua Profits for Citroen are CITROEN (7-1) . 60000=360000 in each market and 720000 in total. Profits for VW are (ITMADE = (7-2)50000 = 250000 in each market and 500000 in total. are Social welfare is 1,325,000 in France and 1,205,000 in Germany. Social welfare increased in both countries as a result of trade. Consumers were better off, and producers were worse off. This is shown in the following graphs. The first two graphs show the consumer surplus (in blue) and producer surplus (in red) in each country under autarky. The last graph shows consumer surplus (in red) and the profits of Citroen (in blue) and ofVolkswagen (in green) under free trade in France. The situation under free trade in Germany is the same as in France. P FRANCE 9.5 1 GRAPH 4-2 85000 P via CourseHero.com rest This stad 2 GRAPH 4-3 shared 80000FRANCE N QCITROEN QVW = GRAPH 4 = 60000 50000 Q W com 5. [not to submit] Review the graphic analysis of the lecture notes on oligopolistic competition and trade. Also review the model with equilibrium calculation. [See lecture note] via Coursel is study resou