# Obtain an equation for the firm’s short- run total cost function. Does the firm have any fixed costs? Explain.

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**Obtain an equation for the firm’s short- run total cost function. Does the firm have any fixed costs? Explain.**

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?

**Obtain an equation for the firm’s short- run total cost function. Does the firm have any fixed costs? Explain.**