Download Economies of Scales

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The airplane sector is characterized by scale economies. The following equations represent an individual firm’s sales and its cost function, respectively: Q = S [(1/n) – b x (p-P)] and CT = F + c x Q where S is total sales of the industry, n is the number of firms in the industry, p is the price of the variety produced by the firm itself, P is the average price in the industry, F is the fixed cost of production and b and c are two positive constants.
a) Explain intuitively both functions.
b) Assume that the demand function for this industry is Q=A-B x P. Determine the long-term equilibrium price and average cost as a function of the number of firms in the industry, and represent it graphically.
c) Suppose now that there are two countries, Home and Foreign, and that the cost function are the same in both countries. Home has annual sales of 1,125 planes and Foreign has annual sales of 2,000 planes. Assume further that b=1/2,000,000 , F=$ 250,000,000 and c=$ 75,000,000.
i) Determine each country’s long-run equilibrium autarchy price and average cost as well as the number of firms.
ii) Determine the integrated market’s equilibrium price, average cost and number of firms. Conclude on the desirability of openness to trade in this case.
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