Question

A profit-maximizing entrepreneur rents an apple orchard for a day. He is a price taker in both the market for labor and the market for apples. Assume that a bushel of apples sells for $10. Laborers are hired by the day (the variable input) to pick apples (the product). The production function (the relationship between the number of laborers hired and the number of bushels of apples picked) looks like this:
Laborers hired per day Total product(bushels of apples per day)
4 52
5 60
6 66
7 70
8 72

Required:
How many laborers would the entrepreneur employ if the government raised the minimum wage to $75 per day?

a. 4
b. 8
c. 5
d. 7
e. 6

Answer 1

Answer:

c. 5

Explanation:

L       Q     MPL (ΔinQ/ΔinL)    VMPL

4      52  

5      60              8                       80

6      66              6                       60

7      70               4                       40

8 72               2                       20

Note: Labour hired per day = L, Total product = Q, Marginal Product of labor=MPL, VMPL =Price*MPL

A firm will maximize the profit by increasing the number of labor as long as VMPL is higher than or equal to the wage rate. In this case, we observe that VMPL ($80)>wage rate ($75) for L=5 but VMPL ($60)<wage rate ($75) for L=6. So, the optimal number of labor to be hired is 5.