Consider a model with two countries called france and germany. france has one automaker, called citroen. germany has a competitor com­pany, called volkswagen. citroen can produce cars at a constant marginal cost of $1,000 each. vw can produce cars at a constant marginal cost of $2,000 each. within each country, the demand for cars is given by the same demand curve: q = (18 -p) x (10, 000),

where q is the number of cars demanded in that country per month and p is the price per car in that country, in thousands of dollars. assume that no one other than citroen or vw can transport cars between the two countries, so it is possible for the price of cars in the two econo­mies to be different.

(a) suppose initially that both economies are in autarky. what will be the price and the quantity sold in each country? (b) suppose that we now have free trade between the two economies. there is no cost to trans­ porting the cars across borders for either firm. suppose that the two corporations set their quantities in each market simultaneously. for any given quantity qfv that citroen expects vw to sell in the french market, find the profit-maximizing quantity qfc that citroen will sell in the french market. using your answer, draw citroen's reaction function for the french market.

(c) using logic parallel to (b), draw vw's reaction function for the french market on the same diagram.

(d) assume that each firm correctly guesses how much the other will produce in each market.
what will be the price charged and thequantity sold in each market?