Consider a Cournot duopoly where there are 2 firms, and the inverse demand function is given by: P(Q)= = either CL (92) = 10 or CH (92) = 10 +592 60-Q if Q 60 otherwise Where, Q denotes total quantity produced by the two firms (Q = 91 +92), and P denotes the price in the market. The total cost function of firm 1 is: C(91) = 10. The total cost function of firm 2 is: While both firms know firm 1's cost, only firm 2 knows its own cost. Firm 1 believes that it is equally likely for firm 2 to have a cost function CL or CH. HINT 1: Use section 9.4 of the book for guidance HINT 2: There are two types of firm one with a low cost (CL) which produces the quantity qL, and one with a high cost (CH) which produces the quantity qH. (a) (1 point) Write out the profit function for firm 1 (assume Q 60). Here the profit for firm 1 will depend on the quantities that firm 1 chooses, as well as the quantity chosen by each type of firm 2 (91, 9L, and qH). (b) (2 points) Write out the profit function for each type of firm 2 (assume Q 60). (c) (3 points) Write out the best response function for firm 1 and for each type of firm 2(assume Q 60). (d) (3 points) Calculate q1 and qL and 9H in equilibrium. (e) (1.5 points) Suppose that firm 2 has a low cost (CL). Write out the Price in the market, and the Profit for each firm. (f) (1.5 points) Suppose that firm 2 has market, and the Profit for each firm. High a low cost (CH). Write out the Price in the