Please solve the following :

- Question 2 (26 marks). Fill in the table under the question: The inverse market demand curve for cocoa beans is given by P =201 3Q and the total cost tunction for ANY firm in the industry is given by TC(q) = 6q where Q represents industry output and q 1s for the single firm level of output. a) b S c) d) e) What is the marginal cost function for a representative firm? What does that marginal cost function tell you? (2 marks) If the coffee-bean industry were perfectly competitive, compute the industry output and price. (3 marks) Suppose now that two Cournot firms operated in the market. Solve for each firm's best response function. Compute the market price, each firm quantity and each firm profit. (5 marks) If now two firms decided to collude, what would be the optimal colluding quantity for each firm? Compute the resulted market price and profit. (Hint when collude, treat them as a monopolist, which equally divides its production in two plants). (5 marks) Suppose now that we are in the Stackelberg environment where firm 1 is the leader and firm 2 1s the follower. Solve for each firm best response function, quantity and profit. What is the resulted market price? (5 marks) Table: Fill in and assume that there are only two firms. (6 marks) Model Quantity Quantity 1 firm 1 Firm Perfect Comp Monopoly (cartel) Stackleberg Now both firms decides to collude Q = 2, + 2 2 .: Profit : T( = PQ - 69 - 672 = (201 - 36 ) 2 - 6 ( 2 , + 92 ) = ( 201 - 36) 2 - 62 = 125 Q - 362 .: 27 JQ = 125 - 62) Profit maximizing condition 27 JQ 20 . :195 - 60 = 0 Q - 125 65 6 =(32. 5 2 . . P = 201 - Q = 201 - 65 2 337 2 168.5 . : TH= 168.5 x 65 - ( X 65 2 5 281 . 25 : TA = mlB=. Titot 2 640 . 625 2