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 =
`√(L * K)`

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

Q =
`√(L * K)`

Q =
`√(L * 10)`

L =
`((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 * ((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 * ((Q)/(3.162) )^(2) ) + [ P_(k * 10)]`

MC =
`(TC)/(Q)` =
`(2Q)/(3)`

MC =
`(2*50)/(3)` = 33.33