Question

The production function of a product is given by q=100KL if the price of capital is ksh 150 per day and the price of labour is ksh 50 per day,calculate the cost of producing 1000 units of the product where K-capital and L-labour (10mks)

Answer 1

The optimal production is at

$MPK/k = MPL/w$

$MPK = Q'(K) = 100L,$

MPL = 100K,

$100L/150 = 100K/50,$

3K = L,

If 100KL = 1000, then:

100K×3K = 1000,

3K^2 = 10,

K = 1.83,

L = 5.48.

$TC = 1.83×150 + 5.48×50 = 548.5.$