Answer questions 17-19 below using the following information: A firm is producing in the short-run (with...
Answer questions 17-19 below using the following information: A firm is producing in the short-run (with K fixed at 10 units) according to the following production function: F(L) = Q =10L -0.25L^2 . You also know that w=$15, r=$20 and the firm can sell its product for P=$7.50.
17. To minimize costs how much labor should the firm hire in the short run? a. L=16 b. L=30 c. L=20 d. None is correct
18. How much output Q is produced? a. Q=525 b. Q=300 c. Q=96 d. None is correct
19. How much is the company’s profit? a. Profit=$3287.5 b. Profit=$280 c. Profit=$1750 d. None is correct
Homework Answers
Given
P=$7.50
w=$15
K=10
r=$20
17)
Q=10L-0.25L2
Marginal Product of labor=MPL=dQ/dL=10-0.50L
Marginal Revenue product=MRPL=P*(10-0.50L)=7.50*(10-0.50L)=75-3.75L
Set MRPL=wage rate for cost minimization
75-3.75L=15
3.75L=60
L=16
Correct option is
a. L=16
18)
Q=10L-0.25L2=10*16-0.25*16^2=96
Correct option is
c) Q=96
19)
Total Cost=rK+wL=20*10+15*16=$440
Total Revenue=P*Q=7.50*96=$720
Profit=Total Revenue-Total Cost=720-440=$280
Correct option is
b) $280
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