Question

Suppose in the short run a firm’s production function is given by Q = L 1 2 K 1 2 and that K is fixed at K = 10. If the price of Labor, w = $15 per unit of Labor, what is the firm’s marginal cost of production when the firm is producing 50 units of output?

Answer 1

The firm’s marginal cost of production when the firm is producing 50 units of output is 33.33

Solution:

The production function is Q = $\sqrt{L * K}$

The initial value is 10 units. The production value is 50 units The manufacturing cycle needs work as stated below.

Q = $\sqrt{L * K}$

Q = $\sqrt{L * 10}$

L = $(\frac{Q}{3.162} )^{2}$

The wage rate is $15 . The following is the expense of the manufacturing process.

TC = $P_{L} * L + P_{K} * K$

TC = $( 15 * (\frac{Q}{3.162} )^{2} ) + [ P_{k * 10}]$

The marginal production cost is really the increase in manufacturing costs as output increases by 1 point.

As listed below, the marginal cost:

TC = $( 15 * (\frac{Q}{3.162} )^{2} ) + [ P_{k * 10}]$

MC = $\frac{TC}{Q}$ = $\frac{2Q}{3}$

MC = $\frac{2*50}{3}$ = 33.33