Chapter 24 Monopoly. 2 Pure Monopoly A monopolized market has a single seller. The monopolist’s demand curve is the (downward sloping) market demand curve

Chapter 24Monopoly

2

Pure Monopoly

A monopolized market has a single seller.

The monopolist’s demand curve is the (downward sloping) market demand curve.

So the monopolist can alter the market price by adjusting its output level.

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3

Pure Monopoly

Output Level, y

$/output unit

p(y)Higher output y causes alower market price, p(y).

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Why Monopolies?

Some examples:a patent; e.g. a new drugsole ownership of a resource; e.g. a toll

highwayformation of a cartel; e.g. OPEC large economies of scale; e.g. local

utility companies.

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Pure Monopoly

Suppose that the monopolist seeks to maximize its economic profit,

What output level y* maximizes profit?

( ) ( ) ( ).y p y y c y

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Profit-Maximization( ) ( ) ( ).y p y y c y

At the profit-maximizing output level y*

d ydy

ddy

p y ydc ydy

( )( )

( ) 0

so, for y = y*,

ddy

p y ydc ydy

( )( ).

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Profit-Maximization

At the profit-maximizing output level the slopes of the revenue and total cost curves are equal:

MR(y*) = MC(y*).

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Marginal RevenueMarginal revenue is the rate-of-change of revenue as the output level y increases: MR y

ddy

p y y p y ydp ydy

( ) ( ) ( )( ).

dp(y)/dy is the slope of the market inverse demand function so dp(y)/dy < 0. ThereforeMR y p y y

dp ydy

p y( ) ( )( )

( )

for y > 0.

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Marginal RevenueE.g. if p(y) = a - by then R(y) = p(y)y = ay - by2

and therefore MR(y) = a - 2by < a - by = p(y) for y > 0.

p(y) = a - bya

ya/bMR(y) = a - 2by

a/2b9

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Marginal CostMarginal cost is the rate-of-change of total cost as the output level y increases;

MC ydc ydy

( )( ).

E.g. if c(y) = F + y +y2 then

MC y y( ) . 2

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Marginal Cost

Fy

y

c(y) = F + y + y2

$

MC(y) = + 2y

$/output unit

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Profit-Maximization: An ExampleAt the profit-maximizing output level y*,MR(y*) = MC(y*). So if p(y) = a - by and ifc(y) = F + y + y2 thenMR y a by y MC y( *) * * ( *) 2 2

and the profit-maximizing output level is y

ab

*( )

2

causing the market price to be

p y a by a bab

( *) *( )

. 2

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Profit-Maximization; An Example$/output unit

y

MC(y) = + 2y

p(y) = a - by

MR(y) = a - 2by

a

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y

MC(y) = + 2y

p(y) = a - by

MR(y) = a - 2by

y

ab

*

( )

2

a

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y

MC(y) = + 2y

p(y) = a - by

MR(y) = a - 2by

y

ab

*

( )

2

p y

a bab

( *)

( )

2

a

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Monopolistic Pricing & Own-Price Elasticity of Demand Suppose that market demand

becomes less sensitive to changes in price (i.e. the own-price elasticity of demand becomes less negative). Does the monopolist exploit this by causing the market price to rise?

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Monopolistic Pricing & Own-Price Elasticity of Demand

MR yddy

p y y p y ydp ydy

p yyp y

dp ydy

( ) ( ) ( )( )

( )( )

( ).

1

Own-price elasticity of demand is

p yy

dydp y

( )( )

so MR y p y( ) ( ) .

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MR y p y( ) ( ) .

11

Suppose the monopolist’s marginal cost ofproduction is constant, at $k/output unit. For a profit-maximum

MR y p y k( *) ( *)

1

1

which isp y

k( *) .

1 1 18

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p yk

( *) .1 1

E.g. if = -3 then p(y*) = 3k/2, and if = -2 then p(y*) = 2k. So as rises towards -1 the monopolist alters its output level to make the market price of its product to rise.

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Notice that, since

p y( *) 11

0 11

0

That is,1

1 1

.

So a profit-maximizing monopolist always selects an output level for which market demand is own-price elastic. 20

,1

1*)(*)( kypyMR

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Markup Pricing

Markup pricing: Output price is the marginal cost of production plus a “markup.”

How big is a monopolist’s markup and how does it change with the own-price elasticity of demand?

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Markup Pricingp y k p y

k k( *) ( *)1

1

11 1

is the monopolist’s price. The markup is

p y kk

kk

( *) .

1 1

E.g. if = -3 then the markup is k/2, and if = -2 then the markup is k. The markup rises as the own-price elasticity of demand rises towards -1. 22

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A Profits Tax Levied on a Monopoly A profits tax levied at rate t reduces

profit from (y*) to (1-t)(y*). Q: How is after-tax profit, (1-t)(y*),

maximized? A: By maximizing before-tax profit, (y*). So a profits tax has no effect on the

monopolist’s choices of output level, output price, or demands for inputs.

I.e. the profits tax is a neutral tax.23

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Quantity Tax Levied on a Monopolist A quantity tax of $t/output unit

raises the marginal cost of production by $t.

So the tax reduces the profit-maximizing output level, causes the market price to rise, and input demands to fall.

The quantity tax is distortionary.

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Quantity Tax Levied on a Monopolist$/output unit

y

MC(y)

p(y)

MR(y)

y*

p(y*)

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y

MC(y)

p(y)

MR(y)

MC(y) + tt

y*

p(y*)

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y

MC(y)

p(y)

MR(y)

MC(y) + tt

y*

p(y*)

yt

p(yt)

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y

MC(y)

p(y)

MR(y)

MC(y) + tt

y*

p(y*)

yt

p(yt)

The quantity tax causes a dropin the output level, a rise in theoutput’s price and a decline indemand for inputs.

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Linear Demand

p=a-by, MR=a-2by With tax, MC=c+t Profit maximization: a-2by=c+t

y=(a-c-t)/2bp(y)=a-by=a-(a-c-t)/2

dp/dt=1/2 The monopolist passes on half of the

tax.29

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Linear Demand

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Constant Elasticity Demand

Can a monopolist “pass” all of a $t quantity tax to the consumers in the case of constant elasticity demand?

Suppose the marginal cost of production is constant at $k/output unit.

With no tax, the monopolist’s price isp yk

( *) .1

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The tax increases marginal cost to $(k+t)/output unit, changing the profit-maximizing price to

The amount of the tax paid by buyers is

p yk tt( )( )

.

1

p y p yt( ) ( *).

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p y p yk t k tt( ) ( *)( )

1 1 1

is the amount of the tax passed on to buyers. E.g. if = -2, the amount of the tax passed on is 2t.Because < -1, ) > 1 and so the monopolist passes on to consumers more than the tax!

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The Inefficiency of Monopoly

Social welfare=consumer surplus+ producer surplus

A market is Pareto efficient if it achieves the maximum possible total gains-to-trade (i.e. social welfare).

Otherwise a market is Pareto inefficient.

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The Inefficiency of Monopoly$/output unit

y

MC(y)

p(y)

ye

p(ye)

The efficient output levelye satisfies p(y) = MC(y).

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y

MC(y)

p(y)

ye

p(ye)


CS

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y

MC(y)

p(y)

ye

p(ye)


CS

PS

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y

MC(y)

p(y)

ye

p(ye)

The efficient output levelye satisfies p(y) = MC(y).Total gains-to-trade ismaximized.

CS

PS

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y

MC(y)

p(y)

MR(y)

y*

p(y*)

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y

MC(y)

p(y)

MR(y)

y*

p(y*)CS

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y

MC(y)

p(y)

MR(y)

y*

p(y*)CS

PS

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y

MC(y)

p(y)

MR(y)

y*

p(y*)CS

PS

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y

MC(y)

p(y)

MR(y)

y*

p(y*)CS

PS

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y

MC(y)

p(y)

MR(y)

y*

p(y*)CS

PS

MC(y*+1) < p(y*+1) so bothseller and buyer could gainif the (y*+1)th unit of outputwas produced. Hence the market is Pareto inefficient.

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y

MC(y)

p(y)

MR(y)

y*

p(y*)DWL

Deadweight loss measuresthe gains-to-trade notachieved by the market.

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y

MC(y)

p(y)

MR(y)

y*

p(y*)

ye

p(ye) DWL

The monopolist produces less than the efficient quantity, making the market price exceed the efficient market price.

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Natural Monopoly

A natural monopoly occurs when a firm cannot operate at an efficient level of output without losing money.

When there are large fixed costs and small marginal costs, you can easily get the kind of situation described above.

Many public utilities are natural monopolies of this sort.

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Natural Monopoly

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Inefficiency of a Natural Monopoly Like any profit-maximizing monopolist,

the natural monopolist causes a deadweight loss.

If allowing a natural monopolist to set the monopoly price is undesirable due to the Pareto inefficiency, and forcing the natural monopoly to produce at the competitive price is infeasible due to negative profits, what is left?

For the most part natural monopolies are regulated or operated by governments.

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Natural Monopoly: Solutions

Pricing policy: Set the prices that just allow the firm to break even – produce at a point where price equals average costs. But it is difficult to determine the true costs of the firm…

The other solution is to let the government operate it at price equals marginal cost and provide a lump-sum subsidy to keep the firm in operation.

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What Causes Monopolies?

1. Nature of technology. If the minimum efficient scale (MES) is

large relative to demand, then the market is likely to be monopolized. But if the MES is small relative to demand, there is room for many firms in the industry, and there is a hope for a competitive market structure.

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What Causes Monopolies? 2. Cartel. Several different firms in an industry

might be able to collude and restrict output in order to raise prices and thereby increase their profits. When firms collude in this way and attempt to reduce output and increase price, we say the industry is organized as a cartel.

Cartels are illegal.

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What Causes Monopolies? 3. Entry deterrence. An industry may have one dominant firm

purely by historical accident. If one firm is first to enter some market, it may have enough of a cost advantage to be able to discourage other firms from entering the industry. The incumbent may be able to convince potential entrants that it will cut its prices drastically if they attempt to enter the industry.

By preventing entry in this manner, a firm can eventually dominate a market.

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4. Patent. A patent offers inventors the

exclusive right to benefit from their inventions for a limited period of time.

Thus a patent offers a kind of limited monopoly.

Documents

Chapter 24 Monopoly. 2 Pure Monopoly A monopolized market has a single seller. The monopolist’s demand curve is the (downward sloping) market demand curve