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ECP 3703 Managerial Economics HW3 fall 2013.pdf
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?
ECP 3703 Managerial Economics HW4 fall 2013.pdf
ECP 3703 Managerial Economics
Homework #4
Fall 2013
Professor T. Levy
Due date: November 4th, 2013 in class
1. The Deering Manufacturing Company’s short- run average cost function in 2012 was
AC = 3 + 4Q, where AC is the firm’s average cost (in dollars per pound of the product), and Q is
its output level.
a. Obtain an equation for the firm’s short- run total cost function.
b. Does the firm have any fixed costs? Explain.
c. If the price of the Deering Manufacturing Company’s product (per pound) is $3, is the firm
making profit or loss? Explain.
d. Derive an equation for the firm’s marginal cost function.
2. The Dijon Company’s total variable cost function is TVC = 50Q – 10Q^2 + Q^3, where Q is
the number of units of output produced.
a. What is the output level where marginal cost is a minimum?
b. What is the output level where average variable cost is a minimum?
c. What is the value of average variable cost and marginal cost at the output specified in the
answer to part (b)?
3. The Jolson Corporation produces 1,000 wood cabinets and 500 wood desks per year, the total
cost being $30,000. If the firm produced 1,000 wood cabinets only, the cost would be $23,000. If
the firm produced 500 wood desks only, the cost would be $11,000. Calculate the degree of
economies of scope.
4. The Burr Corporation’s total cost function (where TC is the total cost in dollars and Q is
quantity) is TC = 200 + 4Q + 2Q^2
a. If the firm is perfectly competitive and the price of its product is $24, what is its optimal
output rate?
b. At this output rate, what is its profit?
c. Based on your answers above, should this firm shut down?
5. In a competitive market, there are 8 firms, each with total cost given by: TC = Q^2 +100
a. Derive the firm’s long-run supply equation and the market supply equation.
b. Market demand is given by Q = 120 - P. Determine the equilibrium price and total output in
the market. What is each firm’s output and economic profit?
c. In the long-run, is the number of firms likely to increase or to decrease?
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