Reference no: EM13219021
A country produces manufactured goods, whose industry is characterized by increasing returns to scale, monopolistic competition, and firms that differentiate their products. Firms are symmetric all firms have identical costs functions and demand functions given below: Q=S[(1/n)-b(P-P*)] TC=F+aQ where Q is the quantity demanded when total industry demand is S, the number of firms in the industry is n, the average price in the industry is P* and the price charged by the firm is P. TC is the total cost of producing Q units where F is the fixed cost of production and a is the marginal cost of production. Assume that S does not change with the price in the industry.
a) Derive an equation that relates average cost (AC) to n, F, S and a. That is, derive an equation with AC on the left-hand side and n,F,S, and a on the other. Hint: firm symmetry implies that each firm charges the same price.
b) Derive an equation that relates marginal revenue (MR) to P, n, and b. Hint: Use the demand function to get P as a function of Q. Then, multiply it by Q to get total revenue as a function of Q. Derive marginal revenue. Then use the demand function again, to substitute for Q.
c) To maximize profits, firms set marginal revenue equal to______
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