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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 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.

A monopolist faces the following demand curve: \\[ Q=144 / P^{2} \\] where \(Q\) is the quantity demanded and \(P\) is price. Its average variable cost is \\[ \mathrm{AVC}=Q^{1 / 2} \\] and its fixed cost is 5 a. What are its profit-maximizing price and quantity? What is the resulting profit? b. Suppose the government regulates the price to be no greater than \(\$ 4\) per unit. How much will the monopolist produce? What will its profit be? c. Suppose the government wants to set a ceiling price that induces the monopolist to produce the largest possible output. What price will accomplish this goal?

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?

Caterpillar Tractor, one of the largest producers of farm machinery in the world, has hired you to advise it on pricing policy. One of the things the company would like to know is how much a 5 -percent increase in price is likely to reduce sales. What would you need to know to help the company with this problem? Explain why these facts are important.

Will an increase in the demand for a monopolist's product always result in a higher price? Explain. Will an increase in the supply facing a monopsonist buyer always result in a lower price? Explain.
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