Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 18

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?

Short Answer

Expert verified
a) The monopolist's profit-maximizing price and quantity can only be determined algebraically. The resulting profit will also vary depending on these values. b) With the government imposed price ceiling of $4, the new quantity produced can be found by substitution into the demand curve equation, and the resulting profit can be calculated using the new price and quantity values. c) To induce the monopolist to produce the largest possible output, government should set the price equal to the AVC, after which the specific value can be found using algebraic methods.

Step by step solution

01

Profit-Maximizing Price and Quantity

To find the profit-maximizing price and quantity, we first need to equate Marginal Revenue (MR) to Marginal Cost (MC). The total revenue is given by the expression \(TR = P \cdot Q\) and the cost function includes the average variable cost and the fixed cost, \(TC = AVC \cdot Q + FC\). The profit is then defined by \(π = TR − TC\). By differentiating these equations and equating MR to MC, we can find the optimal price and quantity.
02

Effect of Government Regulation

Next, we need to account for the imposed price ceiling of $4. In this scenario, the monopolist will set its price to this maximum allowed, i.e., $4. We need to substitute this price into the demand curve equation which gives us the quantity this monopolist would produce. Once we know the price and quantity, we can calculate the overall profit.
03

Calculating the Optimal Ceiling Price

Finally, if the government wishes to set a ceiling price that induces the monopolist to produce maximum output, it would set the price equal to the AVC, at which the monopolist breaks even. If we substitute \(P = AVC\) in the given price equation, we get a quantity equation that instructs us to solve for the price or to calculate the highest ceiling price that the government would need to set in order to induce the monopolist to produce as much as possible.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

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.

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.

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 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 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 are \(\mathrm{MC}_{1}=20+2 Q_{1}\) and \(\mathrm{MC}_{2}=10+5 Q_{2}\). The firm's esti- 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?
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free