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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
No, the price charged would not rise by 25%. Due to the inelastic demand, the monopolist can absorb part of the cost increase without losing all of its sales, so the price rise would be less than 25%.

Step by step solution

01

Understand the concept

A firm facing a demand elasticity of -2.0 signifies inelastic demand because the absolute value of elasticity is greater than 1. Marginal cost is $20. As the monopolist desires to maximize profit, it sets price where its marginal revenue equals marginal cost (MR=MC).
02

Analyze price change with increased marginal cost

Rearrange the formula MR=MC to derive the Lerner Index which is (P-MC)/P = -1/EL, where EL is the price elasticity of demand and P is price. When the marginal cost (MC) increases by 25%, the new MC is $25. But due to inelastic demand, the monopolist doesn't need to increase the price by the same percentage, so the price rise would be less than 25%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Demand Elasticity
Demand elasticity measures how sensitive the quantity demanded of a good is to its price change. It's a key concept for monopolists in price setting because it determines how much they can change their price without significantly losing customers. An elasticity of -2.0, as mentioned in our example, indicates an inelastic demand, where a given percentage increase in price leads to a smaller percentage decrease in quantity demanded. This gives a monopolist room to increase prices without facing a proportional decline in sales volume.
Marginal Cost
Marginal cost is the cost of producing one additional unit of a product. For a monopolist, knowing the marginal cost is crucial since it's used to determine the price level that maximizes profit. In our exercise, the marginal cost is set at $20. When a monopolist sets a price, they need to consider this cost to ensure each unit sold generates a profit. Changes in the marginal cost, like the 25% increase discussed, impact the pricing decision—a higher marginal cost might lead to higher prices to maintain profit margins.
Profit Maximization
Profit maximization is a fundamental objective for any monopolist. To achieve this, the firm finds the balance where marginal cost (MC) equals marginal revenue (MR), the extra income from selling one more unit of a good. This point ensures the firm is not overproducing, which would drive costs above revenue, or underproducing, which would mean missed profit opportunities. A monopolist leverages demand elasticity to find that sweet spot in price that maximizes the difference between total revenue and total costs.
Lerner Index
The Lerner Index is a measure of a firm's market power—the ability to set prices above marginal costs. It is calculated as \( (P - MC) / P \), where \( P \) represents price, and \( MC \) stands for marginal cost. The larger the value, the greater the firm's price-setting power, suggesting less competition. In the context of our exercise, it implies that with an inelastic demand, the firm does not have to raise prices proportionally to the increased marginal cost. This index helps understand the impact of cost changes on pricing and how much of that change can be passed on to consumers.

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Most popular questions from this chapter

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.

In some cities, Uber has a monopoly on ride-sharing services. In one town, the demand curve on weekdays is given by the following equation: \(P=50-Q\) However, during weekend nights, or surge hours, the demand for rides increases dramatically and the new demand curve is: \(P=100-Q\). Assume that marginal \(\operatorname{cost}\) is zero. a. Determine the profit-maximizing price during weekdays and during surge hours. b. Determine the profit-maximizing price during weekdays and during surge hours if \(\mathrm{MC}=10\) in stead of zero. c. Draw a graph showing the demand, marginal revenue, and marginal cost curves during surge hours from part (b), indicating the profit-maximizing price and quantity. Determine Uber's profit and the deadweight loss during surge hours, and show them on the graph.

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.

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 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.

There are 10 households in Lake Wobegon, Minnesota, each with a demand for electricity of \(Q=50-P\) Lake Wobegon Electric's (LWE) cost of producing electricity is \(\mathrm{TC}=500+\mathrm{Q}\) a. If the regulators of LWE want to make sure that there is no deadweight loss in this market, what price will they force LWE to charge? What will output be in that case? Calculate consumer surplus and LWE's profit with that price. b. If regulators want to ensure that LWE doesn't lose money, what is the lowest price they can impose? Calculate output, consumer surplus, and profit. Is there any deadweight loss? c. Kristina knows that deadweight loss is something that this small town can do without. She suggests that each household be required to pay a fixed amount just to receive any electricity at all, and then a per-unit charge for electricity. Then LWE can break even while charging the price calculated in part (a). What fixed amount would each household have to pay for Kristina's plan to work? Why can you be sure that no household will choose instead to refuse the payment and go without electricity?
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