Chapter 24 MONOPOLY

24.1 Maximizing profits

The monopolist will always set p=p(y). r(y)=p(y)y The monopolist’s profit-maximization

problem then takes the form

max ( ) ( )y

r y c y

r c

y y

F.O.C.: MR=MC

24.1 Maximizing profits

△r=p△y+y△p

r pp y

y y

1( ) ( ) 1 ( ) 1

( )

p yMR y p y p y

y p y

Marginal revenue in terms of elasticity

24.1 Maximizing profits The F.O.C. becomes

1( ) 1 ( )

( )p y MC y

y

1( ) 1 ( )

( )p y MC y

y

Maximum can only occur where ||≥1.

24.2 Linear Demand Curve and Monopoly

Linear demand: p(y)=a-by Revenue: r(y)=p(y)y=ay-by2

Marginal revenue: MR(y)=a-2by The marginal revenue curve is steeper than the

demand curve. The optimal output is given by the intersection of the

marginal revenue curve and the marginal cost curve. The price is determined by the output and the demand

curve.

24.2 Linear Demand Curve and Monopoly Monopoly with

a linear demand curve

24.3 Markup Pricing

The amount of the markup depends on the elasticity of demand.

( )( )

1 1/ | ( ) |

MC yp y

y

11

1 1/ | ( ) |y

The market price is a markup over marginal cost.

EXAMPLE: The Impact of Taxes on a Monopolist Linear demand and

taxation The price will rise by

half the amount of the tax.

Price will increase by more or less than the amount of the tax for other demand functions.

24.4 Inefficiency of Monopoly

The monopolist charges a price higher than marginal cost.

The monopolistic output is lower than the competitive output.

The monopolistic market is Pareto inefficient. The monopolist is better off than in the

competitive market.

24.4 Inefficiency of Monopoly

Loss in consumer’s surplus: A+B

Increase in producer’s surplus: A-C

Loss in welfare: B+C

24.6 Natural Monopoly

Large fixed costs but small marginal cost. Competitive price is lower than the average

cost. A competitive firm will make losses. The firm need to charge the average cost to

break even. Output is lower than the efficient level. Cost measuring is critical.

24.6 Natural Monopoly

24.6 What Causes Monopolies? Minimum efficient scale (MES): the level of output

that minimizes average cost. A small market size is prone to monopoly.

24.6 What Causes Monopolies?

Cartel: Several firms in an industry collude and restrict output in order to maximize total profits.

OPEC, De Beers.