Consider a duopoly with homogenous goods where Firm 1 has the following production function: Q 1 = F1(L, K) = L1/2 K1/2, Firm 2 uses labour and capital as well but has a different production function, given by Q2 = F2(L, K) = L 1/3 K 213 Wage rate is =40$ Capital rental rate = 10$ You may assume that the market for labour and capital is perfectly competitive. Both firms sell their products on the same market with inverse demand function P = 52 - (Q1 + Q2) a) Suppose Firm 1 wishes to produce 6 units. What is the cost minimising input mix for Firm 1? b) Suppose Firm 2 wishes to produce 4 units. What is the cost minimising input mix for Firm 2? Assume both firms now have the option to produce either 4 units or 6 units. We will consider the situation where both firms simultaneously, but independently, choose their strategies. Both firms are aiming to maximise their profits. c) For each player (firm), what are their strategies? Write the game in normal form. d) Find each player's dominant strategy (if they exists). e) Find all Nash equilibria