Q4 (26 MARKS) Suppose that two firms want to enter a market to produce IDENTICAL goods. Firms are trying to determine the SIZE of their plants, Ki and K2. The size of their plants determines their capacity to produce output. Once firms have installed a certain production capacity, we assume that firms PRODUCE AT CAPACITY, that is, that qi = K, for i = 1,2. The profit functions of two firms are: m1(K1, K2) = K1 30 - K1 K2 INI 12 (K1, K2) = K2 30 - K2 - 7 K1 10 (a) Suppose that initially that the two firms compete in capacities in a SIMULTANEOUS-MOVE GAME, so that firms enter the market at the same time. (i) Is this a Cournot or Bertrand model? EXPLAIN. (ii) Are the firms identical? EXPLAIN. (iii) FIND the Nash equilibrium of the game. Show all of your calculations leading to the Nash equilibrium. Calculate the profits of the two firms in the simultaneous Nash equilibrium of the game 5 (b) In a LARGE diagram (marks deducted for small diagrams) DRAW the best-response function and identify the Nash equilibrium point. Using the corresponding numbers. CLEARLY label everything in the diagram. 5 (b) PROVE (DERIVE) that the general equation (at any given profit level 71) for the ISOPROFIT curve for Firm 1 for combinations of (X1, K2) is given by. K1 = 15 - -K2+ (15 K2 - 71 6 (c) IN THE DIAGRAM OF PART (b) SKETCH (using three points) the isoprofit function for F1 at the Cournot level of profits. SHOW your calculations for these three points