Consider a duopoly with homogenous goods where Firm 1 has the following production function: Q1 = 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. You may assume that the market for labour and capital is perfectly competitive and the current wage rate is $40 and the rental rate on capital is $10. Both firms sell their products on the same market with inverse demand function P = 52 - (Q1 + Q2), where P is measured in Dollars 1.Which production function(s) exhibit(s) decreasing returns to scale? 2.Suppose Firm 1 wishes to produce 6 units. What is the cost minimising input mix for Firm 1