A firm that manufactures office desks has the following production function in t

Question

A firm that manufactures office desks has the following production function in the short run: Q = 400 L0.8 K0.5 where Q = the quantity of chairs produced in a month L = the amount of labor (hours of work) used in a month K = the amount of capital (building, machines, equipment) used. Assume that in the short run L = 1,000 and K = 100.

1. What is the quantity produced if L = 1,000 and K = 100? (5 points)

2. What is the quantity produced if L = 1,200 and K = 100? (5 points)

3. What is the quantity produced if L = 1,400 and K = 100? (5 points)

4. Does the law of diminishing marginal returns to labor apply to the production process? Why? Why not?

Explanation / Answer

1. Q = 400 L0.8.K0.5

Q = 400 (1000)0.8(100)0.5

Q = 400 X 251.18 X 10 = 1,004,720

2. Q = 400 L0.8.K0.5

Q = 400 (1200)0.8(100)0.5

Q = 400 X 290.63 X 10 = 1,162,520

3. Q = 400 L0.8.K0.5

Q = 400 (1400)0.8(100)0.5

Q = 400 X 328.78 X 10 = 1,315,120

4. Marginal output from L = 1000 to L = 1200 is (1,162,520 - 1,004,720) = 157800

Marginal output from L = 1400 to L = 1200 is (1,315,120 - 1,162,520) = 152600

Therefore, it follows law of diminishing marginal returns to labor because additional units of labor does not increase output in that proportion.

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