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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 \$17,000.

Step by step solution

01

Find the Marginal Cost

Using the formula for price elasticity of demand \(P(1 + 1/\epsilon) = MC\), where \(P = $40\) is the price per unit and \(\epsilon = -2\) is the price elasticity of demand. Note that the elasticity is negative because of the law of demand which states that as price increases, quantity demanded decreases. Substitute these values into the formula to find the Marginal Cost (MC).
02

Calculate the Percentage Markup

The percentage markup is calculated as \((P - MC) / MC * 100%\), where \(P\) is the price and \(MC\) is the marginal cost found in the previous step. This formula comes from the definition of percentage markup which is the difference between the price and the marginal cost, divided by the marginal cost, all multiplied by 100.
03

Compute the Firm's Profit

The monopoly firm's profit is given by \((P - AC)Q - FC\), where \(P = $40\) is the price per unit, \(AC = $15\) is the average cost per unit, \(Q = 800\) is the quantity of output, and \(FC = $2000\) is the firm's fixed cost. Substitute these values into the formula to find the profit.

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Most popular questions from this chapter

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