Assume a firm’s production function is = K 1 2 1 2 where Q, L and K are defined. How much labor and capital would be purchased if it seeks to produce 100 units and labor costs $20 per unit and capital each cost $5 per unit?

200 labor

and 50 units of capital

Explanation:

The formula given is Q = K^(1/2)L^(1/2)

Now, considering we want Q = 100

and the cost formula 20K + 5L

we should look to minimize the cost using excel solver tool

        1        2          3         4

A       L20051000 (A2*A3)

B       K   50       201000  (B2*B3)

C      100         2000   (A4 + B4)

C2 =power(a2;1/2)*power(b2;1/2)

we want to minimize the cost formula (C4)

considering the restrain that output should be 100

and that quantity of labor and kapital should be integer.