10.10: Exercises for Chapter 10

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EXERCISE 10.1

Consider a monopolist with demand curve defined by P=100–2Q. The MR curve is MR=100–4Q and the marginal cost is MC=10+Q. The demand intercepts are , the MR intercepts are .

Develop a diagram that illustrates this market, using either graph paper or an Excel spreadsheet, for values of output .
Identify visually the profit-maximizing price and output combination.
Optional: Compute the profit maximizing price and output combination.

EXERCISE 10.2

Consider a monopolist who wants to maximize revenue rather than profit. She has the demand curve P=72–Q, with marginal revenue MR=72–2Q, and MC=12. The demand intercepts are , the MR intercepts are .

Graph the three functions, using either graph paper or an Excel spreadsheet.
Calculate the price she should charge in order to maximize revenue. [Hint: Where the MR=0.]
Compute the total revenue she will obtain using this strategy.

EXERCISE 10.3

Suppose that the monopoly in Exercise 10.2 has a large number of plants. Consider what could happen if each of these plants became a separate firm, and acted competitively. In this perfectly competitive world you can assume that the MC curve of the monopolist becomes the industry supply curve.

Illustrate graphically the output that would be produced in the industry?
What price would be charged in the marketplace?
Optional: Compute the gain to the economy in dollar terms as a result of the DWL being eliminated [Hint: It resembles the area ABF in Figure 10.14].

EXERCISE 10.4

In the text example in Table 10.1, compute the profit that the monopolist would make if he were able to price discriminate, by selling each unit at the demand price in the market.

EXERCISE 10.5

A monopolist is able to discriminate perfectly among his consumers – by charging a different price to each one. The market demand curve facing him is given by P=72–Q. His marginal cost is given by MC=24 and marginal revenue is MR=72–2Q.

In a diagram, illustrate the profit-maximizing equilibrium, where discrimination is not practiced. The demand intercepts are , the MR intercepts are .
Illustrate the equilibrium output if he discriminates perfectly.
Optional: If he has no fixed cost beyond the marginal production cost of $24 per unit, calculate his profit in each pricing scenario.

EXERCISE 10.6

A monopolist faces two distinct markets A and B for her product, and she is able to insure that resale is not possible. The demand curves in these markets are given by P_A=20–(1/4)Q_A and P_B=14–(1/4)Q_B. The marginal cost is constant: MC=4. There are no fixed costs.

Graph these two markets and illustrate the profit maximizing price and quantity in each market. [You will need to insert the MR curves to determine the optimal output.] The demand intercepts in A are , and in B are .
In which market will the monopolist charge a higher price?

EXERCISE 10.7

A concert organizer is preparing for the arrival of the Grateful Living band in his small town. He knows he has two types of concert goers: One group of 40 people, each willing to spend $60 on the concert, and another group of 70 people, each willing to spend $40. His total costs are purely fixed at $3,500.

Draw the market demand curve faced by this monopolist.
Draw the MR and MC curves.
With two-price discrimination what will be the monopolist's profit?
If he must charge a single price for all tickets can he make a profit?

EXERCISE 10.8

Optional: A monopolist faces a demand curve P=64–2Q and MR=64–4Q. His marginal cost is MC=16.

Graph the three functions and compute the profit maximizing output and price.
Compute the efficient level of output (where MC=demand), and compute the DWL associated with producing the profit maximizing output rather than the efficient output.