Calculate the profit-maximizing price and quantity of output/ Managerial Economics
Question :1 Perfect Competition
1. Royesford Knitting Mills manufactures and sells underwear in a perfectly competitive market. Currently, it sells 20,000 units at a price of $10 per unit. The fixed costs of production are $60,000 and total variable costs at this level of output are $120,000.
The in-house statistician has estimated various cost relationships and reports the following: a 10 percent increase in output will lower the variable costs by $0.40 per unit produced (but will have no effect on fixed costs).
At the same time, the marketing department of the firm advocates lowering the price by 5 percent in order to “increase sales, revenues and profits.” The arc-price elasticity of demand is known to be Ep = 2.
Evaluate the impact of a 5 percent price cut on the firm’s total revenue, total cost, and profit.
3. The Public Service Company of the Southwest is regulated by an elected state utility commission. The firm has total assets of $500,000. The demand function for its services has been estimated as
P = 250 – 0.15Q
The firm faces the following total cost function:
TC = 25,000+10Q
(a) In an unregulated environment, what price would this firm charge, what output would be produced, what would total profits be, and what rate of return would the firm earn on its asset base?
(b) The firm has proposed charging a price of $100 for each unit of output. If this price is charged, what will be the total profits and the rate of return earned on the firm’s asset base?
(c) The commission has ordered the firm to charge a price that will provide the firm with no more than a 10 percent return on its assets. What price should the firm charge, what output will be produced, and what dollar level of profits will be earned?
4. Suppose that econometricians at Hallmark Cards determine that the price elasticity of demand for greeting cards is -2.
(a) If Halmark’s marginal cost of producing cards is constant and equal to $1.00, use the optimal price formula to determine what price Hallmark should charge to maximize profit.
Managerial Economics STEPHEN F. AUSTIN STATE UNIVERSITY Fall 2015
(b) Suppose that Hallmark Cards wishes to know the price elasticity of demand faced by its archrival, American Greetings. Halmark hires you to estimate it. Hallmark provides you with an educated guess concerning the marginal cost of producing a greeting card, which they estimate to be constant and equal to $1.22. A quick trip to the store tells you that American Greetings is selling its cards for an average of $3.25. Using these numbers and assuming that American Greetings is maximizing profit, calculate the price elasticity of demand faced by American Greetings.
5. MicroChips Corp. has a patent on a new product, the Penultimate, a microprocessor for desktop computers. The market demand for this good is given by
P = $5,500 ? $0.005Q
Fixed costs are zero (costs of research and development have been fully amortized already over the previous years) and variable costs per unit are constant at $4,500.
(a) Calculate the profit-maximizing price and quantity of output and economics profits if MicroChip acts as a monopolist (because of patent protection).
(b) Calculate the price/output combination and total economic profits that would result if competitors offered clones of the Penultimate, making the market perfectly competitive.
