A firm’s production function is given by Q = 80KL. Unit capital and labour costs are $2 and $1, respectively. The firm is contracted to provide 4000 units of output and wants to fulfil this contract at minimal cost.
(a) Explain briefly why the Lagrangian function is
g(K, L, λ) = 2K + L + λ[50 − KL]
(b) Write down expressions for
(c) Find values of K and L which fulfil the quota with minimal cost to the firm.