onsider two countries that are freely trading in differentiated products. Each producer in the industry is subject to increasing returns to scale, derived from fixed costs of production. In particular, the cost function of a firm in the industry is linear with respect to output, with fixed costs of 100 and variable costs of 20 per unit of output. The demand function for each differentiated product is equal to
Q= s[1/n – 1/2 (p-P)]
where is size of the market, is the price charged by the producer and is the average price in the industry. There is free entry in the industry. Assume that the size of the market is 2,000 in the Home country and 3,000 in the Foreign country.
[HINT (in case you need it): If the demand function is: , then ]
a) Compute the equilibrium price that any producer will charge, as a function of the number of firms in the industry and the size of the market.
b) Write down the average costs faced by any firm, as a function of the number of firms in the industry and the size of the market.
c) Compute the number of firms (in the long run), the price charged for each product, and the quantity produced by each firm in the industry in the free trade equilibrium. Show it in a graph.
d) Assume now that entry in the market is not free: each firm has to pay a license fee 300 to its own government, to be renewed every year, in order to participate in the market. Compute the number of firms (in the long run) in the free trade equilibrium under this new situation.
e) Are consumers better off or worse off under the government licensing regime? EXPLAIN.
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