This question asks you to think of how trade can result in gains due to increasing competition and variety. You do not need to do any algebra. Just draw the graphs needed. Suppose there two countries of equal size, i.e., both have the same number of people, S. There are n symmetric firms. Each individual has demand for the output of a representative firm denoted by q(p; P; n) where p is the firm's price, P is the overall average price in the market, and n is the number of firms. q(p; P; n) is decreasing in p, increasing in P and decreasing in n. With S individuals, the demand for a firm is thus Sq(p; P; n): Let c be marginal cost and F be the fixed cost of production. Firms behave monopolistically competitively and choose p to maximize profits taking P and n as given. Assume all firms are symmetric so that in equilibrium p = P and that firms enter till price equals average cost, i.e., profits are 0.
a: Depict the profit maximizing price charged by a representative firm for given P and n. You do not need to do any algebra. Just to draw demand and the profit maximizing price.
b: Show that the maximized profits of the firm are higher when its costs fall. (Hint: variable profits are also the sum of the difference in marginal cost and marginal revenue over units produced)
c: As n rises, what happens to the profit maximizing price? What is the intuition? Call this relation the P P curve.
d: Does an increase (or decrease) in S shift the P P curve? Why?
e: As n rises, what happens to output per firm in symmetric equilibrium and therefore to average cost? What is the economic intuition here? Call this curve CC:
f: Does an increase in S shift CC? Why? g: Depict the equilibrium n and p without and with trade where trade is just a doubling of S? h: Explain what the effects of trade are on prices, variety and welfare.