(15 points) Consider a variant of Cournot model where a single good is produced by two firms, the firm 1 and the firm 2. 1hey compete in a market where all the output, Q= q, + 9, is sold at a single price(P) and inverse demand function is given by P=1-q-9. The firm 2 produces and sells only 9 in this market. The firm , however, is also a monopolist in the other market where inverse demand function is given by In =1-x, where In and are price and output produced in this monopoly market.

The costs to the firm and 2 are given by

C(4 ,t) =(9,+ x)/2 and C(4)=4/2 respectively. Find the Nash equilibria of this strategic game.