Question 2 [16 marks] Consider a firm that uses labour and capital as inputs for production according to some production technology y = f(K, L). Let c(y, w, r) be the cost of producing y units of output if the wage rate is w and the cost of capital is r. Let L ∗ and K∗ be the optimal capital and labour demand for producing y units. Prove that ∂c(y, w, r) ∂w = L ∗ and ∂c(y, w, r) ∂r = K∗ .
