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Lecture # 16 Monopoly Lecturer: Martin Paredes

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Lecture # 16

Monopoly

Lecturer: Martin Paredes

Outline

- The Monopolist's Profit Maximization Problem
- The Profit Maximization Condition
- Equilibrium

- The Inverse Elasticity Pricing Rule
- The Welfare Economics of Monopoly

Monopoly Market

Definition: A monopoly market consists of a single seller facing many buyers.

Assumption: There are barriers to entry.

Profit Maximisation

- The monopolist's objective is to maximise profits:
Max (Q) = TR(Q) – TC(Q) = P(Q)· Q – C(Q)Q

where P(Q) is the (inverse) market demand curve.

Profit Maximisation

- Profit maximizing condition for a monopolist:
dTR(Q) = dTC(Q) …or… MR(Q) = MC(Q)dQdQ

- In other words, the monopolist sets output so that the marginal profit of additional production is just zero.

Profit Maximisation

- Recall that a perfect competitor sets P = MC, because MR = P.
- This is not true for the monopolist because the demand it faces is NOT flat.
- As a result, MR < P

Profit Maximisation

- Since TR(Q) = P(Q) · Q, then:
dTR(Q) = MR(Q) = P(Q) + dP(Q) · QdQ dQ

- In perfect competition, demand is flat, meaning dP(Q)/dQ = 0, so MR = P.
- For a monopoly, demand is downward-sloping, meaning dP(Q)/dQ < 0, so MR < P.

Example: Marginal Revenue

Price

Price

Competitive firm Monopolist

Demand facing firm

Demand facing firm

P0

P0

C

P1

B

A

B

A

q q+1

Firm output

Q0

Q0+1

Firm output

Price

Example: Marginal Revenue Curve and Demand

The MR curvelies below the demand curve.

P(Q0)

P(Q), the (inverse) demand curve

Quantity

Q0

Price

Example: Marginal Revenue Curve and Demand

The MR curvelies below the demand curve.

P(Q0)

P(Q), the (inverse) demand curve

MR(Q0)

MR(Q), the marginal revenue curve

Quantity

Q0

Example: Marginal revenue for linear demands

- Suppose demand is linear:P(Q) = a – bQ
- Total revenue isTR = Q*P(Q) = aQ – bQ2
- Marginal revenue is:MR = dTR = a – 2bQdQ
- So, for linear demands, marginal revenue has twice the slope of demand.

Market Power

Definition: An agent has market power if she can affect the price that prevails in the market through her own actions.

- Sometimes this is thought of as the degree to which a firm can raise price above marginal cost.

Shutdown Condition

- In the short run, the monopolist shuts down if the profit-maximising price does not cover AVC (or average non-sunk costs).
- In the long run, the monopolist shuts down if the profit-maximising price does not cover AC.

Example: Profit maximisation

- Suppose:P(Q) = 100 – Q
TC(Q) = 100 + 20Q + Q2

- Marginal revenue is:MR = dTR = 100 – 2QdQ
- Marginal cost is:MC = dTC = 20 + 2QdQ
- MR = MC ==> 100 – 2Q = 20 + 2Q ==>Q* = 20P* = 80

Example: Profit maximisation

- In equilibriumQ* = 20P* = 80
- Observe that: AVC = 20 + Q* = 40AC = 100 + 20 + Q* = 45Q*
- Hence, P* > AVC and P* > AC

Price

Example: Positive Profits for Monopolist

100

Demand curve

100

Quantity

Price

Example: Positive Profits for Monopolist

100

MR

Demand curve

50

100

Quantity

Price

Example: Positive Profits for Monopolist

MC

100

MR

20

Demand curve

50

100

Quantity

Price

Example: Positive Profits for Monopolist

MC

100

MR

20

Demand curve

20

50

100

Quantity

Price

Example: Positive Profits for Monopolist

MC

100

E

80

MR

20

Demand curve

20

50

100

Quantity

Price

Example: Positive Profits for Monopolist

MC

AVC

100

E

80

MR

20

Demand curve

20

50

100

Quantity

Price

Example: Positive Profits for Monopolist

MC

AVC

100

E

80

AC

MR

20

Demand curve

20

50

100

Quantity

Price

Example: Positive Profits for Monopolist

MC

AVC

100

E

80

: Profits

AC

MR

20

Demand curve

20

50

100

Quantity

Profit Maximisation

Notes:

A monopolist has less incentive to increase output than the perfect competitor: for the monopolist, an increase in output causes a reduction in its price.

Profits can remain positive in the long run because of the assumption that there are barriers to entry.

Profit Maximisation

Notes:

- A monopolist does not have a supply curve: because price is determined endogenously by the demand:
- The monopolist picks a preferred point on the demand curve.
- Alternative view: the monopolist chooses output to maximize profits subject to the constraint that price be determined by the demand curve.

Inverse Elasticity Pricing Rule

- We can rewrite the MR curve as follows:
MR = P + dP · Q dQ

= P + dP · Q · P dQ P

= P 1 + dP · Q dQ P

= P 1 + 1

( )

( )

Inverse Elasticity Pricing Rule

- Given that is the price elasticity of demand:
- When demand is elastic ( < -1), then the marginal revenue is positive (MR > 0).
- When demand is unit elastic ( = -1), then the marginal revenue is zero (MR= 0).
- When demand is inelastic ( > -1), then the marginal revenue is negative (MR < 0).

Price

Example: Elastic Region of Linear Demand Curve

a

Demand

a/b

Quantity

Price

Example: Elastic Region of Linear Demand Curve

a

MR

Demand

a/2b a/b

Quantity

Price

Example: Elastic Region of Linear Demand Curve

a

Elastic region ( < -1), MR > 0

MR

Demand

a/2b a/b

Quantity

Price

Example: Elastic Region of Linear Demand Curve

a

Elastic region ( < -1), MR > 0

Inelastic region (0>>-1), MR<0

MR

Demand

a/2b a/b

Quantity

Price

Example: Elastic Region of Linear Demand Curve

a

Elastic region ( < -1), MR > 0

Unit elastic (=-1), MR=0

Inelastic region (0>>-1), MR<0

MR

Demand

a/2b a/b

Quantity

Inverse Elasticity Pricing Rule

- A monopolist will only operate on the elastic region of the market demand curve
- Note: As demand becomes more elastic at each point, marginal revenue approaches price.

The Lerner Index of Market Power

- The monopolist will produce at MR = MC, but we also found that:
MR = P 1 + 1

- Then:P 1 + 1 = MC
or:P – MC = –1 P

( )

( )

The Lerner Index of Market Power

Definition: The Lerner Index of market power is the price-cost margin, (P*-MC)/P*.

- It measures the monopolist's ability to price above marginal cost, which in turn depends on the elasticity of demand.
- The Lerner index ranges between 0 (for the competitive firm) and 1 (for a monopolist facing a unit elastic demand).

The Welfare Economics of Monopoly

- A monopoly equilibrium entails a dead-weight loss.
- For the following analysis, suppose the supply curve in perfect competition is equal to the marginal cost curve of the monopolist.

Example: Welfare Effects of Perfect Competition

Supply

PC

Demand

QC

MR

Example: Welfare Effects of Perfect Competition

Supply

: Consumer Surplus

PC

: Producer Surplus

Demand

QC

MR

Example: Welfare Effects of Monopoly

MC

PC

Demand

QC

MR

Example: Welfare Effects of Monopoly

MC

PM

PC

Demand

QM

QC

MR

Example: Welfare Effects of Monopoly

MC

PM

: Consumer Surplus

PC

Demand

QM

QC

MR

Example: Welfare Effects of Monopoly

MC

PM

: Consumer Surplus

: Producer Surplus

PC

Demand

QM

QC

MR

Example: Welfare Effects of Monopoly

MC

PM

: Consumer Surplus

: Producer Surplus

PC

: Deadweight Loss

Demand

QM

QC

MR

Summary

A monopoly market consists of a single seller facing many buyers (utilities, postal services).

A monopolist's profit maximization condition is to set marginal revenue equal to marginal cost.

Marginal revenue generally is lower than price. How much less depends on the elasticity of demand.

Summary

A monopolist never produces on the inelastic portion of demand since, in the inelastic region, raising price and reducing quantity make total revenues rise and total costs fall!

The Lerner Index is a measure of market power, often used in antitrust analysis.

A monopoly equilibrium entails a dead-weight loss.