The production function for laser eye surgery is given by Q = 20K0.5L0.5, where Q is the number of laser eye surgeries performed per day, K is the number of eye surgery machines (which is fixed at 2 in the short run), and L is the number of employees. The marginal product of labor for L = 3 is ____.

The marginal product of labor is 10.

Data and Calculations:

Production function = Q = 20K0.5L0.5 = 20 x K x 0.5 x L x 0.5

Where:

Q = number of surgeries per day

K = number of machines

L = number of employees

Assuming that:

K = 2

L = 2

Therefore, Q1 = 20 x 2 x 0.5 x 2 x 0.5

= 20 surgeries per day

Q2 = 20 x 2 x 0.5 x 3 x 0.5

= 30 surgeries per day

Change in productivity = 10 (30 - 20)

Change in labor = 1 (3 - 2)

Marginal product of labor = change in output / change in labor

= 10 (10/1)

Thus, the marginal product of labor for the production function is 10.

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