International economics equilibrium price that any producer will charge,homework help

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Consider 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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