Test 2 Questions

1. The Jenkins Tool Company has estimated the following demand equation for its product:

Q_D = 12,000 - 4,000 P

where

P = price per unit

Q_D = quantity demanded per year

The firm's total costs are $4,000 when nothing is being produced. These costs increase by 50 cents for each unit produced.

a. Write an equation for the total cost function.

b. Specify the marginal cost function.

c. Write an equation for total revenue in terms of Q.

d. Specify the marginal revenue function.

e. Write an equation for total profits in terms of Q. At what level of output are total profits maximizeed? What price will be charged? What will total profits be?

f. Check your answers in part e by equating marginal revenue and marginal cost.

2. A firm operating in a purely competitive environment is faced with a market price of $250. The firm's short-run total cost function is TC = 6,000 + 400Q -20Q² + Q³.

a. Should the firm produce at this price in the short run?

b. If the market price is $300, what will total profits (losses) be if the firm produces ten units of output? Should the firm produce at this price?

c. If the market price is greater than $300, should the firm produce in the short run?

3. The Poster Bed company believes that its industry can best be classified as monopolistically competitive. An analysis of the demand for its canopy bed has resulted in the following estimated demand function for the bed, P = 1,760 - 12Q. The cost analysis department has estimated the total cost function for the poster bed as

TC = 24,000 + 5Q - 15Q² + (1/3)Q³.

a. Calculate the level of output that should be produced to maximize short-run profits.

b. What price should be charged?

c. Compute total profits at theis price-output level.

d. Compute the price elasticity of demand at the profit-maximizing output level.

e. What is the impact of a $5,000 increase in the level of fixed costs on the price charged, output produced, and profit generated?

4. Suppose that the royalties received by an author for writing a college textbook are set at a rate of about 15 percent of the publisher's total revenue.

a. Demonstrate graphically that this creates an inherent conflict between the interests of a profit-maximizing publisher and a royalty-maximizing author.

b. As the student consumer, whose interests would you like to see prevail?

c. Does the magnitude of this conflict between author and publisher increase or diminish in the case of a highly inelastic demand curve? Explain and demonstrate graphically.

5. A monopolist faces the following demand function for its product, Q = 45 - 5P. The total cost function is TC = 12 + 5Q.

a. What is the profit-maximizing price and quantity? What are profits?

b. If the government inposes a franchise tax on the firm of $10, how do your answers in part (a) change?

c. If the government inposes an excise tax of 50 cents per unit of output sold, what is the impact on the profit-maximizing level of price, output, and profits?

d. If the government imposes a price ceiling of $6 on the price of the firm's product, what output will the firm produce and what will total profits be?