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Chapter 10: Problem 7

Suppose a profit-maximizing monopolist is producing 800 units of output and is charging a price of \(\$ 40\) per unit. a. If the elasticity of demand for the product is -2 find the marginal cost of the last unit produced. b. What is the firm's percentage markup of price over marginal cost? c. Suppose that the average cost of the last unit produced is \(\$ 15\) and the firm's fixed cost is \(\$ 2000\). Find the firm's profit.

Short Answer

Expert verified
a. The marginal cost of the last unit produced is \$20. b. The firm's percentage markup of price over marginal cost is 100%. c. The firm's profit is \$18000.

Step by step solution

01

Calculate the Marginal Cost

According to the formula for the markup of price over marginal cost for a monopolist, the markup is equal to -1 divided by the price elasticity of demand. Rearranging this formula in terms of marginal cost, we get \(MC = P / (1 + 1/Ed)\), where MC is marginal cost, P is price, and Ed is the elasticity of demand. Plugging in the given values, we get \(MC = $40 / (1 + 1/-2)\), giving us a marginal cost of \($20\).
02

Calculate the Percentage Markup

The markup of price over marginal cost is calculated by subtracting the marginal cost from the price, dividing by the marginal cost, and multiplying by 100. Using the calculated marginal cost from step 1, the calculation is \((\$40 - \$20) / \$20 * 100\), which gives a percentage markup of 100%.
03

Calculate the Total Cost and Profit

The total cost can be calculated by multiplying the average cost per unit by the quantity produced and adding the fixed cost. Here, the total cost is \(\$15 * 800 + \$2000 = \$14000\). The profit is then calculated by subtracting this total cost from the firm's total revenue, which is the price times the quantity, or \$40 * 800 = \$32000. Therefore, the profit is \$32000 - \$14000 = \$18000.

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Most popular questions from this chapter

A drug company has a monopoly on a new patented medicine. The product can be made in either of two plants. The costs of production for the two plants \(\operatorname{arc} \mathrm{MC}_{1}=20+2 \mathrm{Q}_{1}\) and \(\mathrm{MC}_{2}=10+5 \mathrm{Q}_{2}\). The firm'sesti mate of demand for the product is \(P=20-3\left(Q_{1}+Q_{2}\right)\) How much should the firm plan to produce in each plant? At what price should it plan to sell the product?

The employment of teaching assistants (TAs) by major universities can be characterized as a monopsony. Suppose the demand for TAs is \(W=30,000-125 n\) where \(W\) is the wage (as an annual salary) and \(n\) is the number of TAs hired. The supply of TAs is given by \(W\) \(=1000+75 n\) a. If the university takes advantage of its monopsonist position, how many TAs will it hire? What wage will it pay? b. If, instead, the university faced an infinite supply of TAs at the annual wage level of \(\$ 10,000,\) how many TAs would it hire?

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?

Dayna's Doorstops, Inc. (DD) is a monopolist in the doorstop industry. Its cost is \(C=100-5 Q+Q^{2}\), and demand is \(P=55-2 Q\) a. What price should DD set to maximize profit? What output does the firm produce? How much profit and consumer surplus does DD generate? b. What would output be if \(D D\) acted like a perfect competitor and set \(\mathrm{MC}=P ?\) What profit and consumer surplus would then be generated? c. What is the deadweight loss from monopoly power in part (a)? d. Suppose the government, concerned about the high price of doorstops, sets a maximum price at \(\$ 27\) How does this affect price, quantity, consumer surplus, and DD's profit? What is the resulting deadweight loss? e. Now suppose the government sets the maximum price at \(\$ 23 .\) How does this decision affect price, quantity, consumer surplus, DD's profit, and deadweight loss? f. Finally, consider a maximum price of \(\$ 12 .\) What will this do to quantity, consumer surplus, profit, and deadweight loss?

Michelle's Monopoly Mutant Turtles (MMMT) has the exclusive right to sell Mutant Turtle t-shirts in the United States. The demand for these t-shirts is \(Q=10,000 / P^{2} .\) The firm's short-run cost is \(\mathrm{SRTC}=\) \(2000+5 Q,\) and its long-run cost is \(\mathrm{LRTC}=6 Q\) a. What price should MMMT charge to maximize profit in the short run? What quantity does it sell, and how much profit does it make? Would it be better off shutting down in the short run? b. What price should MMMT charge in the long run? What quantity does it sell and how much profit does it make? Would it be better off shutting down in the long run? c. Can we expect MMMT to have lower marginal cost in the short run than in the long run? Explain why.
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