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Chapter 8: 6CCQ (page 316)

The accompanying diagram shows the demand, marginal revenue, and marginal cost of a monopolist.

a. Determine the profit-maximizing output and price.

b. What price and output would prevail if this firm’s product were sold by price-taking firms in a perfectly competitive market?

c. Calculate the deadweight loss of this monopoly

Short Answer

Expert verified

a. The profit-maximizing output is 3 units, and the price is $40.

b. The price and output in the competitive market are $60 and 5 units, respectively.

c. The deadweight loss is $180.

Step by step solution

01

Determining the profit-maximizing output

a.

The profit-maximizing output and price are attained by looking at the MR and MC curves. The profit-maximizing output is shown on the horizontal axis, which are 3 units. At a quantity of 3 units, the MC curve crosses the MR curve. The price is shown on a vertical axis. The price is the point where the MC curve crosses the MR curve. In this case, the price is $40.

02

Finding the price of a product

b.

The price of a product offered by price-taking firms in a completely competitive market would be $60, and the profit-maximizing output would be 5 units. The MC curve crosses the demand curve at this moment.

03

Calculating the deadweight loss

The deadweight loss is the triangle shown between the points where the MC curve crosses the MR curve. This is the point where the MC curve crosses the D curve and the point on the D curve where Pm (on the vertical axis) and Qm(on the horizontal axis) meet.

Qm*Pm-Qc*Pc=3×40-5×60=120-300=-180

Here, Qm= monopoly output, Pm= monopoly price,

Qc= competitive output, and Pc= competitive price.

Hence, the deadweight loss is $180.

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Most popular questions from this chapter

Apply the marginal principle to determine the profit-maximizing price and output. Try these problems: 2, 21

The owner of an Italian restaurant has just been notified by her landlord that the monthly lease on the building in which the restaurant operates will increase by 20 percent at the beginning of the year. Her current prices are competitive with nearby restaurants of similar quality. However, she is now considering raising her prices by 20 percent to offset the increase in her monthly rent. Would you recommend that she raise prices? Explain.

You are a manager at Spacely Sprockets—a small firm that manufactures Type A and Type B bolts. The accounting and marketing departments have provided you with the following information about the per-unit costs and demand for Type A bolts:

Materials and labor are obtained in a competitive market on an as-needed basis, and the reported costs per unit for materials and labor are constant over the relevant range of output. The reported unit overhead costs reflect the \(10 spent last month on machines, divided by the projected output of 2 units that was planned when the machines were purchased. In addition to the above information, you know that the firm’s assembly line can produce no more than five bolts. Since the firm also makes Type B bolts, this means that each Type A bolt produced reduces the number of Type B bolts that can be produced by one unit; the total number of Type A and B bolts produced cannot exceed 5 units. A call to a reputable source has revealed that unit costs for producing Type B bolts are identical to those for producing Type A bolts, and that Type B bolts can be sold at a constant price of \)4.75 per unit. Determine your relevant marginal cost of producing Type A bolts and your profit-maximizing production of Type A bolts.

Last month you assumed the position of manager for a large car dealership.The distinguishing feature of this dealership is its “no hassle” pricing strategy; prices (usually well below the sticker price) are posted on the windows, and your sales staff has a reputation for not negotiating with customers. Last year, your company spent\(2million on advertisements to inform customers about its “no hassle” policy, and had overall sales revenue of\)40million. A recent study from an agency on Madison Avenue indicates that, for each3percent increase in TV advertising expenditures, a car dealer can expect to sell12percent more cars—but that it would take a 4percent decrease in price to generate the same12percent increase in units sold. Assuming the information from Madison Avenue is correct, should you increase or decrease your firm’s level of advertising? Explain.

A monopolist's inverse demand function is P=150-3Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC1(Q1)=6Q1, and the marginal cost of producing at facility 2 is MC2(Q2)=2Q2.

a. Provide the equation for the monopolist's marginal revenue function. (Hint: Recall thatQ1+Q2=Q.)

b. Determine the profit-maximizing level of output for each facility.

c. Determine the profit-maximizing price.
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