Zowie! Surfboards has the following production function. If surfboards sell for $30 and the nominal wage rate is $200,how many workers should the firm employ?

Question

Zowie! Surfboards has the following production function.  If surfboards sell for $30 and the nominal wage rate is $200,how many workers should the firm employ?

Quizplus · Accepted Answer

To determine the optimal level of labor, we need to find the point where the marginal product of labor (MPL) equals the nominal wage rate divided by the price of output (w/P). Using the production function provided, we can calculate the MPL for each level of labor as follows:
MPL = ∆Q/∆L = 6L^(2/3)
To find the labor level that maximizes profits, we need to compare the MPL to the ratio of the nominal wage rate to the price of output, which is (200/30) = 6.67. 
For 2 workers, MPL = 9.66
For 3 workers, MPL = 11.08
For 4 workers, MPL = 11.87
For 5 workers, MPL = 12.45

Thus, the optimal level of labor is 4 workers, since that is the first point where MPL exceeds the ratio of the nominal wage rate to the price of output. Therefore, the firm should employ 4 workers for profit maximization.

Zowie! Surfboards Has the Following Production Function