Economics 5415 Professor Henderson
Managerial Economics Fall 1995
1. The Jenkins Tool Company has estimated the following demand function for its product:
The firm's total costs are $4,000 when output is zero and increase by 50 cents for each unit produced.
a. Write an equation for the firm's total cost function.
b. Specify the firm's marginal cost function.
c. Write an equation for the firm's total revenue function in terms of Q.
d. Write an equation for total profits, , in terms of Q.
e. At what level of output are total profits maximized? What
price will be charged? What will total profit be?
2. Summit Company produces television monitors (M) and home receivers
(R) using assembly time, chassis time,and inspection time.
| Input requirements and profit | ||
| Hours of assembly | 2 | 4 |
| Hours of chassis | 1 | 1 |
| Hours of inspection | 0.3 | 1 |
| Profit per cabinet | $10 | $15 |
The firm has 800 hours of assembly time, 300 hours of chassis time, and 180 hours of inspection time that it can use per day.
a. Set up this linear programming problem, clearly denoting your objective function and constraints.
b. How many hours of assembly time, chassis time, and inspection time should the firm allocate to each product?
c. How many of each product will be produced? What will Summit's profit be?
d. Set up the dual and solve for the shadow prices of the three
inputs.
3. A firm faces a demand function of the form P = 29 - 2Q and has a total cost function of TC = 20 + 7Q. In this case MC = AC = 7.
a. Calculate the profit-maximizing price, output, and profit levels for this firm.
b. If the government sets a maximum price to force the firm to produce the social optimum quantity, what price will it charge? What is the economic profit?
c. If the maximum price is instead the one that allows the normal rate of return, what is the allowable price? What is the economic profit?
d. Draw a diagram depicting your results.
e. What are the implications of the two regulated options in parts
(b) and (c)?
4. Backus Corporation makes two products, X and Y, jointly and in fixed proportions. For every unit of good X that the firm produces, it produces one unit of good Y. Backus' total cost function is TC = 500 + 4Q + 2Q2, where Q is the number of units of output (where each unit of output contains one unit of X and two units of Y). Marginal cost is MC = 4 + 4Q. The demand curves for the two goods are
PX = 400 - QX
PY = 300 - 3QY
where PX and PY are the prices of goods X and Y, and QX and QY are their respective outputs.
a. How much of each product should the Backus Corporation produce and sell per time period?
b. What price should it charge for each product?
5. The Pear Computer Company has just developed a totally revolutionary new personal computer. It estimates that it will take competitors at least two years to produce equivalent products. The demand function for the computer has been estimated to be P = 2,500 - 0.0005Q. The marginal cost of producing computers is constant at $900.
a. Compute the profit-maximizing price and output levels assuming that Pear acts like a monopolist.
b. Determine the total contribution to profits and fixed costs at these levels.
Pear Computer is considering an alternative pricing strategy of
sliding down the demand curve. It plans to set the following
schedule of prices over the coming two years.
c. Calculate the contribution to profit and overhead for each of the eight time periods.
d. Compare your results in part (c) with your answer in part (b).
e. How would you classify the "sliding down the demand curve"
pricing strategy? Explain its major advantages and disadvantages.