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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

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?

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