BUS-111 MICROECONOMICS

PROBLEM SET 7 – Imperfect Competition

1. A publisher faces the following demand for the next novel of one of its authors:

The author is paid £2 million to write the book, and the marginal cost of publishing

the book is a constant £10 per book.

a. Compute the total revenue, total cost and profit at each quantity. What quantity

would a profit-maximising publisher choose? What price

would it charge?

b. Compute marginal revenue. How does marginal revenue

compare to the price? Explain why this is.

c. Graph the marginal revenue, marginal cost and demand curves.

At what quantity do the MC and MR curves cross? What does

this signify?

d. In your graph, label the deadweight loss. What does this

represent?

e. If the author were paid £3 million instead of £2 million, how

would this affect the publisher’s decision regarding the price to

charge? Explain.

f. Suppose the publisher was not profit-maximising but was

concerned with maximising economic efficiency. What price

would it then charge for the book? What profit would it make at this price?

The following table shows revenue, costs, and profits: Price

(£)

Quantity

(1,000s)

Total

Revenue

(£millions)

Marginal

Revenue

(£)

Total Cost

(£millions)

Profit

(£millions)

100 0 0 ---- 2 -2

90 100 9 90 3 6

80 200 16 70 4 12

70 300 21 50 5 16

60 400 24 30 6 18

50 500 25 10 7 18

40 600 24 -10 8 16

30 700 21 -30 9 12

20 800 16 -50 10 6

10 900 9 -70 11 -2

0 1,000 0 -90 12 -12

a. A profit-maximizing publisher would choose a quantity of 400,000 at a price of

£60 or a quantity of 500,000 at a price of £50; both combinations would lead to

profits of £18 million.

b. Marginal revenue is always equal to or less than price. Price falls when quantity

rises because the demand curve slopes

downward, but marginal revenue falls

even more than price because the firm

loses revenue on all the units of the

good sold when it lowers the price.

c. The diagram to the right shows the

marginal-revenue, marginal-cost, and

demand curves. The marginal-revenue

and marginal-cost curves cross

Price

(£)

Quantity

Demanded

100 0

90 100,000

80 200,000

70 300,000

60 400,000

50 500,000

40 600,000

30 700,000

20 800,000

10 900,000

0 1,000,000

between quantities of 400,000 and 500,000. This signifies that the firm

maximizes profits in that region.

d. The area of deadweight loss is marked “DWL” in the figure. Deadweight loss

means that the total surplus in the economy is less than it would be if the

market were competitive, because the monopolist produces less than the

socially efficient level of output.

e. If the author were paid £3 million instead of £2 million, the publisher would not

change the price, because there would be no change in marginal cost or

marginal revenue. The only thing that would be affected would be the firm’s

profit, which would fall. The author’s fee is a fixed cost – it does not vary as the

quantity of books sold varies.

f. To maximize economic efficiency, the publisher would set the price at £10 per

book, because that is the marginal cost of the book. At that price, the publisher

would have negative profits equal to the amount paid to the author.

2. a. Define marginal revenue.

b. Draw a diagram to explain how marginal revenue for the whole market is related to

the demand curve. Identify the level of output that maximises revenue in that market

and explain why revenue is maximised at that output.

c. Why does a profit maximising monopolist not produce the output that maximises its

revenue?

a. Marginal revenue is the change in total revenue arising from selling one more

unit of a good. More formally, marginal revenue is the derivative of total

revenue with respect to output: MR = dTR/dQ ≈ ∆TR/∆Q.

b. A monopolist's marginal revenue is less

than the price of its product because its

demand curve is the market demand

curve. Thus, to increase the amount

sold, the monopolist must lower the

price of its good for every unit it sells.

This cut in price reduces the revenue on

the units it was already selling.

A monopolist's marginal revenue can

be negative because to get purchasers to

buy an additional unit of the good, the

firm must reduce its price on all units

of the good. The fact that it sells a

greater quantity increases the firm’s

revenue, but the decline in price

decreases the firm’s revenue. The

overall effect depends on the price elasticity of demand. If demand is inelastic,

marginal revenue will be negative.

In the diagram above, the revenue maximising output is Q1 where MR=0.

Consider output Q0. Marginal revenue at this output, MR0, is greater than zero.

This means an increase in output will increase revenue. An increase in output of

one unit will increase revenue by MR0. Hence, total revenue cannot be

maximised when MR>0.

Consider output Q2. Marginal revenue at this output, MR2, is less than zero.

This means a decrease in output will increase revenue. Hence, total revenue

cannot be maximised when MR<0.

Total revenue can only be maximised when MR=0.

c. Marginal costs are positive for any level of output. A profit maximising firm

will always set MC=MR. Therefore, to maximise profit, the firm will always

choose an output where MR is positive, and so TR is not maximised.

3. Explain why a monopolist will always produce a quantity at which the demand

curve is elastic. (Hint: if demand is inelastic and the firm raises its price, what

happens to total revenue and to total costs?)

A monopolist always produces a quantity at which demand is elastic. If the firm

produced a quantity for which demand was inelastic, then if the firm raised its

price, quantity would fall by a smaller percentage than the rise in price, so

revenue would increase. Because costs would decrease at a lower quantity, the

firm would have higher revenue and lower costs, so profit would be higher.

Thus the firm should keep raising its price until profits are maximized, which

must happen on an elastic portion of the demand curve.

As the diagram below shows, another way to see this is to note that on an

inelastic portion of the demand curve, marginal revenue is negative. Increasing

quantity requires a greater percentage reduction in price, so revenue declines.

Because a firm maximizes profit where marginal cost equals marginal revenue,

and marginal cost is never negative, the profit-maximizing quantity can never

occur where marginal revenue is negative. Thus, it can never be on the inelastic

portion of the demand curve.

4. Define natural monopoly. What does the size of a market have to do with whether an

industry is a natural monopoly?

Natural monopoly exists when a single firm can produce the entire market

output at a lower cost than would be possible if there were several firms in the

market. As a market grows, it may become large enough that two or more firms

can survive in the industry. At that point it is no longer a natural monopoly.

5. Classify the following markets as perfectly competitive, monopolistic or

monopolistically competitive, and explain your answers.

a. wooden HB pencils

b. bottled water

c. cola

d. copper

e. local telephone service

f. strawberry jam

g. lipstick

There is no definite answer to this question. Perfectly competition, monopoly

and monopolistic competition are economic models rather than classifications

for real world industries, but the model that most closely resembles each of

these markets is as follows:

a. wooden HB pencils – perfect competition – many producers, no product

differentiation, free entry and exit.

b. bottled water – monopolistic competition – many producers, differentiation by

brand, free entry and exit.

c. cola – oligopoly – there are only a few firms that control a large portion of the

market.

d. copper – perfect competition – many producers, no product differentiation,

relatively free entry and exit.

e. mains sewerage – monopoly – one producer, high barriers to entry because of

massive fixed costs.

f. strawberry jam – monopolistic competition – many producers, differentiation

by brand, free entry and exit.

g. lipstick – monopolistic competition – many producers, differentiation by brand,

free entry and exit.