Answer to Question #180637 in Microeconomics for MURIITHI MUCHEMI

Question

Catalina Films produces video shorts using digital editing equipment (K) and editors (L).

 The firm has the production function where Q=K^1/5L^4/5 where Q is the hours of edited footage. The wage is $160, and the rental rate of capital is $40. The firm wants to produce 3,000 units of output at the lowest possible cost. Find the least costly combination of labor and capital to produce 3000 units 

Answer 1

The least costly combination of labor and capital to produce 3000 units is possible if MPL/MPK = w/r.

$MPL = Q'(L) = 4/5(K/L)^{1/5},$

$MPK = Q'(K) = 1/5(L/K)^{4/5},$

4K/L = 160/40,

K = L.

$Q=K^{1/5} K^{4/5} = 3,000,$

K = L = 3,000.