In: Economics
The production function of a firm is given by Q(K,L) =15K^(1/4) L^(1/4) . Wage is
$3 per unit of labor (L), and rent is $6 per unit of capital
(K).
(1) The firm’s objective is to produce Q units of output at minimum
cost. Write the Lagrangian and derive the FONC.
(2) Find the optimal levels of K, L, and λ given Q.
(3) Find the minimum cost given Q = 100. Find the firm’s minimum cost functiongiven any Q.
(4) Explain the meaning of the optimal λ obtained in part (2).
(5) Check the SOSC.
Could someone help me with this question step by step? Thanks!!