Answer to Question #143885 in Finance for Mr. Dinesh Pal Singh

Question

52. The marginal product of labor function for Central Milling Inc. is given by the equation
MPL = 10 (K/L) 0. 5
Currently, the firm is using 100 units of capital and 121 units of labor. Given the very specialized nature of the capital equipment, it takes six to nine months to increase the capital stock, but the rate of labor input can be varied daily. If the price of labor is $10 per unit and the price of output is $2 per unit, is the firm operating efficiently in the short run? If not, explain why, and determine the optimal rate of labor input.

Answer 1

Profit maximization is possible only at such a level of employment, when the marginal income for the last employee accepted into the firm (MRL) is equal to the marginal cost of paying for their labor (MCL).

Thus, if MRL > MCL, you need to increase the number of employees. If MRL < MCL, you need to reduce the number of employees. If MRL = MCL, you do not need to change the number of employees, since the profit is maximized.

$MPL = 10 (\frac{K}{L})^{0. 5}=10(\frac{100}{121})^{0.5}=9.09$

$MRL = MRPL = MPL \times MR= MRPL = P\times MPL =2\times9.09=18.18$

$P \times MPL = W=MCL = W =10\times9.09=90.9$

MRL < MCL, you need to reduce the number of employees.

$MRL = MCL$

$18.18=P\times9.09$

P=2