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.
Q = S [(1/n) - b x (p-P)]
The above equation shows the share of individual firm in total market share if the price offered by all firms is the same. Any change in price by a firm will have inverse impact on its market share. If the price is increased the market share of that particular firm will decline and vice versa. It means that there will be no new sales may be created for price reduction rather one firm will take the benefit of price reduction at the cost of other firm. The price reduction will increase the market share of one firm and at the same time the market share of another firm will decrease.
CT = F + c x Q
The total cost of a firm depends on the fixed cost which remains same at all level and the marginal cost which is represented by c then multiply by quantity being produced. As the large firms are more efficient therefore they can take advantage of internal economies of scales and thus can reduce its average total cost. In this way they can offer reduced price and can get more market share as compared to small firms.
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.