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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