Monopoly 4. Comparative statics: The effect of increasing costs. 5. - - PDF document

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Helsinki University of Technology Session 1 - Student presentation Seminar on Microeconomics - Fall 1998 / 1

Chapter 14:

Monopoly

Teemu Nyholm

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Helsinki University of Technology Session 2 - Student presentation Seminar on Microeconomics - Fall 1998 / 2

Outline of Presentation

• 1. Definition of monopoly.
• 2. Barriers to entry.
• 3. Theory of a single price monopoly.
• 4. Comparative statics: The effect of increasing costs.
• 5. Monopoly and Welfare.
• 6. Monopoly and Quality.
• 7. Price discrimination.
• 8. Why do natural monopolies exist?

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• 1. Definition of monopoly

Dictionary: Exclusive control by one group of the means of producing or selling a commodity or service. Economics: The amount of output a monopoly is selling responds continuously as a function of the price it charges.

• In a competitive markets a firm is a price-taker.
• In monopolistic market a firm is a price-maker.

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• 2. Barriers to Entry

Definition: Barriers to entry protect a firm from the competition. The existence

• f monopolies is always based on some kind of barriers to entry.

Legal barriers to entry: law, license, patent. => Legal Monopoly. Natural barriers to entry: unique source of supply, economies of scale, economies of scope. => Natural Monopoly. S ystems

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• 3. Theory of single price

monopoly

Monopoly’s maximization problem: Monopoly is choosing optimal output in order to maximize profit. ) ( ) ( max y c y y p

y

− First and second order conditions: ) ( ' ' ) ( ' ' ) ( ' 2 ) ( ' ) ( ' ) ( ≤ − + = − + y c y y p y p y c y y p y p S ystems

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) ( ) ( 1 1 ) ( y p y dy y dc       + = ε I Monopolist is producing such amount, that marginal cost equals to marginal revenue. II Monopolist is able to sell at a price level, that exceeds its marginal costs. Thus monopoly price exceeds competitive-market-price and the amount produced is less. III The difference between monopoly price and competitive-market-price depends on the commodity’s elasticity of demand. First order condition can be written using elasticity of demand

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y p D MR MC p* y* Linear example: S ystems

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• 4. Comparative statics

The effect of a cost change on price: ) ( ' ) ( ' ' 2 1 > + = = y p y yp dc dy dy dp dc dp Part of a monopoly’s cost increase is passed a long in the form of increased prices. S ystems

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• 5. Monopoly and Welfare

Social objective function: ) ( ) ( max ) ( x c x u x W

x

− = Let x* be the level of monopoly output. Then * *) ( ' ' *) ( ' > − = x x u x W => x* does not maximize welfare. IV Monopolist produces too little output relative to the social optimum. S ystems

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• 6. Monopoly and Quality

Let q be product quality and let’s suppose that costs and utility depend on quality. Social objective function: ) , ( ) , ( ) , ( q x c q x u q x W − = Let (x*, q*) be monopolist’s profit maximizing points. Then * *) *, ( * *) *, ( *) *, ( * *) *, ( *) *, ( x q q x p x q x u q q q x W x x q x p x q x W       ∂ ∂ −       ∂ ∂ = ∂ ∂ > ∂ ∂ − = ∂ ∂ S ystems

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V If the derivative of average willingness to pay exceeds the derivative of marginal willingness to pay for the quality change, so monopolist’s quality choice will not be optimal from the social viewpoint. S ystems

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• 7. Price discrimination

Definition: Price discrimination is the practice of charging some customers a higher price than others for an identical good or of charging an individual customer higher price on a small purchase than on a large one.

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7.1 First-degree price discrimination

In the perfect price discrimination the price charged for each unit is equal to the maximum willingness to pay for that unit. Monopolist’s maximizing problem, when perfectly price discriminating: . ) ( that such max

,

r x u cx r

x r

≥ − Let (r*,x*) be the optimal price and amount combination. Then from f.o.c: *) ( * *) ( ' x u r c x u = = S ystems

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VI If a firm is perfectly price discriminating, it will choose to produce a Pareto efficient level of output, that is the same level as a firm in the competitive markets would

• produce. A perfectly price discriminating firm gains all

the surplus from the trade. S ystems

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7.2 Second-degree price discrimination

Second-degree price discrimination occurs when prices differ

• nly depending on the number of commodities bought. It is

known as nonlinear pricing. Let’s suppose two consumers with utility functions u1(x) and u2(x) for product x such that ) ( ' ) ( ' and ) ( ) (

2 1 2 1

x u x u x u x u > > S ystems

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Self-selection constraints: Consumers choose ( x1, r1=p(x1) x1 ) and ( x2, r2=p(x2) x2 ). Because they want to consume amount xi and are willing to pay r1 ) ( and ) (

2 2 2 1 1 1

≥ − ≥ − r x u r x u And because they prefer their own consumption choice . ) ( ) ( ) ( ) (

1 1 2 2 2 2 2 2 1 1 1 1

r x u r x u r x u r x u − ≥ − − ≥ − Now monopolist’s optimization problem takes the form hold. s constraint selection

• self

that such, max

2 1 2 1

• cx

cx r r − + S ystems

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From the first order conditions c x u c x u x u c x u = > − + = ) ( ' ) ( ' ) ( ' ) ( '

2 2 1 1 1 2 1 1

VII If a firm is using nonlinear pricing, then the consumer with the highest demand pays marginal cost and others pays

• more. Thus only the consumer with the highest demand

consumes socially efficient amount. S ystems

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7.3 Third degree price discrimination

Third-degree price discrimination occurs when consumers are charged different prices, but each consumer faces a constant price for all units of output purchased. Let’s suppose that a firm is price discriminating among two groups with different demand curves p1(x1) and p2(x2). Now the profit maximization problem takes the form

2 1 2 2 2 1 1 1

) ( ) ( max cx cx x x p x x p − − +

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The first order conditions: c x x p x x p x p c x x p x x p x p =       − = + =       − = + ) ( 1 1 ) ( ) ( ' ) ( ) ( 1 1 ) ( ) ( ' ) (

2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1

ε ε which implies that

2 1 2 2 1 1

) ( ) ( ε ε < ⇔ > x p x p VIII If a firm is price discriminating among consumers, then the consumers with the more elastic demand are charged a lower price. S ystems

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• 8. Why do natural monopolies

exist?

A natural monopoly exists when a single firm can supply an entire market with lower costs than can any number of competitive firms. Definition: Strict economies of scale in the production of outputs in N are present if for any initial input -output vector (x1,…,xm;y1,…,yn) and for any w > 1, there is a feasible input output-vector (wx1,…,wxm;v1y1,…vnyn) where all vi>w. S ystems

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Definition: Strict and global subadditivity of costs. C(y) is strictly and globally subadditive in the set of N=1…n commodities, if for any m output vectors y1, … , ym we have C(y1 +…+ ym) < C(y1)+…+C(ym). IX Strict and global subadditivity is necessary and sufficient condition for natural monopoly of any output combination in the industry producing commodities in N. In the case of a single product firm, the existence of scale economies is sufficient but not necessary condition for natural

• monopoly. In the case of a multi-product firm, economies of

scale are neither sufficient condition for natural monopoly. S ystems

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