(3). Given the following expressions to be used in the solution (the setup is similar to the problem in Chapter 8). (Not

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(3). Given the following expressions to beused in the solution (the setup is similar to the problemin Chapter 8). (Note: show all yoursteps and label your answers][maxim 1 page, 50points]
(nF/S)+ c = c + (1/bn)
n2 = (1/b)´ S/F
n = [(1/b)´ S/F] 1/2
Suppose that fixed costs for a firm in the automobile industry(start-up costs of factories, capital equipment, and so on) are $5billion and that variable costs are equal to $17,000 per finishedautomobile. Since more firms increase competition in the market,the market price falls as more firms enter an automobile market, orspecifically, P =$17,000 + (150/n),where n represents the number of firms in amarket. Assume that the initial size of the U.S. and the Europeanautomobile markets are 300 million and 533 million people,respectively.
Calculate the equilibrium number of firms (n)in the U.S. and European automobile markets without trade.
You are given the following information (with all dollarsamounts in thousands):
F =5,000,000,000
c = 17,000
SUS =300,000,000
SEU =533,000,000
P = c +(1/bn) = 17,000 + (150/n)
(a). The condition for n: n = [(1/b)´ S/F]. In the Price equation, we see that1/b = 150. Plug in the relevant parameters to solvefor the equilibrium number of firms in the United States and theEuropean Union:
nUS =
nEU =
(b). What is the equilibrium price of automobiles in the U.S.and Europe if the automobile industry is closed(autarky) to foreign trade?
Without trade, there will be different prices in Europe and theUnited States:
PUS =
PEU =
(c). Now suppose the U.S. decides on freetrade in automobiles with Europe. The trade agreementwith the Europeans adds 533 million consumers to the automobilemarket, in addition to the 300 million in the U.S. How manyautomobiles will there be in the U.S. and Europe combined?What will be the new equilibrium price of automobiles?
After trade, the new market sizeis S = 300,000,000 +533,000,000 = 833,000,000. Simply plugthis new market size into the equilibrium number of firm’sexpression:
n =
P =
(d). Why are prices in the U.S. different in (c) and (b)? Areconsumers better off with free trade? If so, in what ways?