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 r ( y)  c( y)
y

F.O.C.: MR=MC
r c

y y
24.1 Maximizing profits

△r=p△y+y△p
r
p
 p
y
y
y

Marginal revenue in terms of elasticity
 p y 

1 
MR( y )  p( y ) 1 
 p( y ) 1 


 y p 
  ( y) 
24.1 Maximizing profits

The F.O.C. becomes

1 
p( y ) 1 
 MC ( y)

  ( y) 

1 
p( y) 1 
  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 market price is a markup over marginal cost.
MC ( y)
p( y ) 
1  1/ |  ( y) |

The amount of the markup depends on the elasticity
of demand.
1
1
1  1/ |  ( y) |
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.
