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Chapter 10: Problem 3

A monopolist firm faces a demand with constant elasticity of \(-2.0 .\) It has a constant marginal cost of \(\$ 20\) per unit and sets a price to maximize profit. If marginal cost should increase by 25 percent, would the price charged also rise by 25 percent?

Short Answer

Expert verified
Yes, the price charged would also rise by 25 percent.

Step by step solution

01

Initial Price Calculation

Starting with the formula for optimal price for a monopolist firm, we can insert our values. Since the elasticity is negative, we can turn it to positive. So the initial price P1 = Marginal Cost / (1 - 1/2.0) = $20 / 0.5 = $40.
02

Price Calculation After Cost Increase

Next, we consider the 25% increase in marginal cost: Marginal Cost = $20 * 1.25 = $25. Now, we calculate the new price, P2 with the same formula: P2 = New Marginal Cost / (1 - 1/2.0) = $25 / 0.5 = $50.
03

Percentage Change in Prices

Finally, we have to calculate the percentage change in prices: ((P2 - P1) / P1) * 100% = (($50 - $40) / $40) * 100% = 25%

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Most popular questions from this chapter

1: } C_{1}\left(Q_{1}\right)=10 Q_{1}^{2} \\\ \text { Factory #2: } C_{2}\lef鈥� # A firm has two factories, for which costs are given by: \\[ \begin{array}{l} \text { Factory #1: } C_{1}\left(Q_{1}\right)=10 Q_{1}^{2} \\ \text { Factory #2: } C_{2}\left(Q_{2}\right)=20 Q_{2}^{2} \end{array} \\] The firm faces the following demand curve: \\[ p=700-5 Q \\] where \(Q\) is total output-i.e., \(Q=Q_{1}+Q_{2}\) a. \(\mathrm{On}\) a diagram, draw the marginal cost curves for the two factories, the average and marginal revenue curves, and the total marginal cost curve (i.e., the marginal cost of producing \(Q=Q_{1}+Q_{2}\) ). Indicate the profit-maximizing output for each factory, total output, and price. b. Calculate the values of \(Q_{1^{\prime}} Q_{2^{\prime}} Q,\) and \(P\) that maximize profit c. Suppose that labor costs increase in Factory 1 but not in Factory \(2 .\) How should the firm adjust (i.e. raise, lower, or leave unchanged) the following: Output in Factory \(1 ?\) Output in Factory \(2 ?\) Total output? Price?

A certain town in the Midwest obtains all of its electricity from one company, Northstar Electric. Although the company is a monopoly, it is owned by the citizens of the town, all of whom split the profits equally at the end of each year. The CEO of the company claims that because all of the profits will be given back to the citizens, it makes economic sense to charge a monopoly price for electricity. True or false? Explain.

One of the more important antitrust cases of the 20 th century involved the Aluminum Company of America (Alcoa) in \(1945 .\) At that time, Alcoa controlled about 90 percent of primary aluminum production in the United States, and the company had been accused of monopolizing the aluminum market. In its defense, Alcoa argued that although it indeed controlled a large fraction of the primary market, secondary aluminum (i.e., aluminum produced from the recycling of scrap) accounted for roughly 30 percent of the total supply of aluminum and that many competitive firms were engaged in recycling. Therefore, Alcoa argued, it did not have much monopoly power. a. Provide a clear argument in favor of Alcoa's position. b. Provide a clear argument against Alcoa's position. c. The 1945 decision by Judge Leamed Hand has been called "one of the most celebrated judicial opinions of our time." Do you know what Judge Hand's ruling was?

A monopolist faces the demand curve \(P=11-Q\) where \(P\) is measured in dollars per unit and \(Q\) in thousands of units. The monopolist has a constant average \(\operatorname{cost}\) of \(\$ 6\) per unit. a. Draw the average and marginal revenue curves and the average and marginal cost curves. What are the monopolist's profit-maximizing price and quantity? What is the resulting profit? Calculate the firm's degree of monopoly power using the Lerner index b. A government regulatory agency sets a price ceiling of \(\$ 7\) per unit. What quantity will be produced, and what will the firm's profit be? What happens to the degree of monopoly power? c. What price ceiling yields the largest level of output? What is that level of output? What is the firm's degree of monopoly power at this price?

A firm faces the following average revenue (demand) curve: \\[ P=120-0.02 Q \\] where \(Q\) is weekly production and \(P\) is price, measured in cents per unit. The firm's cost function is given by \(C=\) \(60 Q+25,000 .\) Assume that the firm maximizes profits. a. What is the level of production, price, and total profit per week? b. If the government decides to levy a tax of 14 cents per unit on this product, what will be the new level of production, price, and profit?
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