production
ECP 3703 Managerial Economics
Homework #3
Fall 2013
Professor T. Levy
Due date: October 28th, 2013 in class
1. In the Elwyn Company, the relationship between output (Q) and the number of hours of
skilled labor (S) and unskilled labor (U) is
Q = 300S + 200U – 0.2S^2 – 0.3U^2
The hourly wage of skilled labor is $10, and the hourly wage of unskilled labor is $5. The firm
can hire as much labor as it wants at these wage rates.
a. Elwyn’s chief engineer recommends that the firm hire 400 hours of skilled labor and 100
hours of unskilled labor. Evaluate this recommendation.
b. If the Elwyn Company decides to spend a total of $5,000 on skilled and unskilled labor, how
many hours of each type of labor should it hire?
2. Specialty Steel has carefully measured production in its new plant to determine whether it is
technically efficient in production. It has found that, for its two inputs K and L, it has the following
marginal products: MPK = 15 units and MPL = 22 units. The inputs are hired in perfectly competitive
markets, and the firm faces input costs of PK = $7.50 and PL = $10 per unit. You have been hired as a
consultant to assist Specialty in increasing profitability. What do you recommend about production
planning? Explain.
3. A firm uses two inputs to produce a final good. If the price of one of the inputs increases and
the price of the other remains the same, how will this affect the firm’s production isoquants? Its
isocost line? Its use of the two inputs?
4. Given the total cost equation: C = 32 + 2Q^2, derive equations for
a. Average total cost.
b. Average variable cost.
c. Marginal cost.
d. Average fixed cost
e. What level of Q yields the minimum level of total average cost of production?
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