Question

The production function of a firm is given by Q=4L1/2K1/2 suppose the cost of labor is birr 40 per unit and the cost of using capital is Birr 10 per unit

A. Determine the amount of labor and capital that should be used in order to minimize the cost to produce 40 units of output? 

B. Calculate the minimum cost of producing 40 units?

Answer 1

a)

$Q=4K^{0.5} \times L^{0.5}$

$Q=4\times 40^{0.5} \times 10^{0.5}$

$Q=80$

the equation becomes $40=4K^{0.5} \times L^{0.5}$

if L =5 and k=20 we get

$Q=4\times5^{0.5} \times 20^{0.5}$

$Q=40$

amount of labor is 5 and capital is 20

b) minimum cost is

$mimimum cost = {20\times10} + {40 \times5}$

$mimimum cost = Birr 400$