Chapter 25: Monopoly Behaviord.umn.edu/~watanabe/econ401su09/doc/mbho.pdf · Chapter 25: Monopoly...

Intro 1st Degree 3rd Degree Two-Part Tariffs Monopolistic Competition Σ

Econ 401 Price Theory

Chapter 25: Monopoly Behavior

Instructor: Hiroki Watanabe

Summer 2009

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1 Introduction2 First-degree Price Discrimination

Optimal PricingWelfare Property

3 Third-Degree Price DiscriminationOptimal Pricing: Equate Marginal RevenueHigher Price for Inelastic Market

4 Two-Part TariffsDefinitionOptimal Price Schedule: p1 = CS & p2 = MCImplication

5 Monopolistic CompetitionMonopolistically Competitive EnvironmentMonopolistic Competition Is Not Efficient

6 Summary

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So far a monopoly has been thought of as a firmwhich has to sell its product at the same price toevery customer.Uniform pricing.Q: Does a monopolist really charge the same pricefor anyone at anytime in anywhere?

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Figure:

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Three Types of Price Discrimination1 1st-degree: Each output unit is sold at a different

price. Prices may differ across buyers.2 2nd-degree: The price paid by a buyer can vary

with the quantity demanded by the buyer. But allcustomers face the same price schedule.

E.g., bulk-buying discounts.3 3rd-degree: Price paid by buyers in a given group is

the same for all units purchased. But price maydiffer across buyer groups.

E.g., senior citizen and student discounts vs. nodiscounts for middle-aged persons.

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group-wise PD no group-wise PDPD w/ quantity 1st degree PD 2nd degree PD

no PD w/ quantity 3rd degree PD Ch24

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6 Summary

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Optimal Pricing

Each output unit is sold at a different price. Pricemay differ across buyers.The monopolist should be able to discover

1 the buyer with the highest valuation of its product,2 the buyer with the next highest valuation,3 and so on

to engage in 1st-degree price discrimination.

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Optimal Pricing

Figure:

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Optimal Pricing

Figure:

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Optimal Pricing

Figure:

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Welfare Property

First-degree price discrimination gives a monopolistall of the possible gains-to-trade,leaves the buyers with zero surplus.Is the outcome efficient? (more on this in Ch16)It is. It just doesn’t seem fair (more on equity inCh31).

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6 Summary

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Optimal Pricing: Equate Marginal Revenue

Price paid by buyers in a given group is the samefor all units purchased.But price may differ across buyer groups.A monopolist manipulates market price by alteringthe quantity of product supplied to that market.

Note unlike 1st-degree price discrimination, firmcannot set the price respectively for each quantity.A monopolist can set the desired price by adjustinglocal quantity supplied for each group.

Assume marginal cost is constant for the following.

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Suppose there are two markets for Metrolink:students and adults.Let yS and yA denote the transaction volume ineach market.Aggregate transaction volume: Y = yS + yA.Metrolink’s profit maximization problem w/ 3rddegree price discrimination:

maxyS,yA

π(yS,yA) = MWTPS(yS)yS+MWTPA(yA)yA−TC(yS+yA).

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First order condition is the same as before:

MRS(yS) =∆TC(yS + yA)

∆yS

MRA(yA) =∆TC(yS + yA)

∆yA

Note additional cost of serving one more student issame as additional cost of serving one more adult.

MRS(yS) =∆TC(yS + yA)

∆yS= MRA(yA) =

∆TC(yS + yA)

∆yA.

In addition to first order condition, Metrolinkengaged in 3’ PD satisfies

MRS(yS) = MRA(yA).

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What if MRS(yS) >MRA(yA)?Metrolink transfer some yA to yS. The total cost isthe same (MC(yS) is cancelled by the equal amountof MC(yA)) but they will have larger revenue(MRS(yS) >MRA(yA)).(In effect, instead of segmenting the seats forstudents and adults, they charge different price inthe beginning. Metrolink slightly leans toward1st-degree price discrimination, but still they can’tcharge different price among students).

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Figure:

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Higher Price for Inelastic Market

Recall from Ch24:

MR(y∗) = p∗�

1−1

ε(y∗)

�

,

(called Ramsey rule).Since MRS and MRA are equated at the optimalamount,

p∗S

1−1

εS(y∗S )

!

= p∗A

1−1

εA(y∗A )

!

.

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Suppose that p∗S > p∗A , then

pA1− 1

εA

1− 1εS

> pA

⇒ 1− 1εA

> 1− 1εS

⇒ 1εA

< 1εS

⇒ εA > εS.

Metrolink charges higher price for a group withinelastic demand.

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Discussion: Ramsey Rule and Equity

While the theory implies that Ramsey rule maximizesmonopolistic profit, it is often criticized by politicians.Why?

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Example

Suppose Metrolink faces

MWTPS(yS) = −5yS + 12, MRS(yS) = −10yS + 12,MWTPA(yA) = −yA + 8, MRA(yA) = −2yA + 8,MC(y) = 2.

How service do they provide for each (y∗S ,y∗A )? What is

the elasticity at y∗S and y∗A ?

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0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

9

10

11

12

Passenger (y)

Pric

e ($

)

Metrolink′s Supply

MWTPS(y)=−5y+12

MRS(y)=−10y+12

MWTPA(y)=−y+8

MRA(y)=−2y+8

MC(y)=2

Figure:

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Elasticity:

εS(yS) =

�

�

�

�

(−5yS + 12)/yS

−5

�

�

�

�

and εA(yA) =

�

�

�

�

(−yA + 8)/yA

−1

�

�

�

�

.

Metrolink charges students more while

εS(yS = 1) = 1.4 > εA(yA = 3) ≈ 1.66.

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6 Summary

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Definition

Recall how Sprint charge the for minutes exceedinganytime minute.Even if you do not make a single phone call, youhave to pay the monthly charge.Why does’t Sprint engage in 1st degree pricediscrimination?The way Sprint constructs its price schedule iscalled two-part tariffs.

Two-Part TariffsA two-part tariff is a lump-sum fee, p1, plus a price p2for each unit of product purchased.

Greg, in effect, has to pay p1 + p2y dollars toconsume y.

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Optimal Price Schedule: p1 = CS & p2 = MC

What is the optimal lump-sum fee p1 and unit pricep2?The maximum gains from trade greg can enjoy areCS.So if Sprint sets p1 = CS, then Greg becomesindifferent between making a contract and notmaking a contract.If Sprint charges more than CS, then Greg won’tmake a contract and Sprint gets nothing.Think of p1 as the market entrance fee.

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Where should Sprint set the unit price p2?MR(y∗) = MC(y∗) and p = MWTP(y∗)?

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Figure:

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Note Greg is indifferent between consuming y = y′

or y = 0.He will get no consumer’s surplus in either case.How about p = MC(y) instead?

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Figure:

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Figure:

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Implication

The optimal pricing strategy for two-part tariffs:1 Set lump-sum fee (or entrance fee) at p1 = CS(y∗).2 Set unit price at p2 = MC(y∗)

There is no consumer’s surplus and Sprint takes100% of total surplus.Compared to uniform pricing (Ch24), two-parttariffs make:

1 consumer’s surplus smaller (down to zero) /2 producer’s surplus larger ,3 total surplus larger (completely eliminates the

deadweight loss) ,

Two-part tariffs are efficient but probably not fair(more on this in Ch31).

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Implication

Example 2 (Increasing MC, cont’d from Ch24)

For Sprint MWTP(y) = −y+ 12, MR(y) = −2y+ 12 andMC(y) = 2y, compute producer’s surplus they introducetwo-part tariffs and compare it to PS when they chargetheir customers uniformly.

Steps:1 Find the target production level y∗ by

MWTP(y∗) = MC(y∗) and obtain p2 = MWTP(y∗).2 Compute CS(ish) above and set p∗1 = CS(ish).3 Compute regular PS and add it to CS(ish) to find

true PS.

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Implication

1 (y∗,p∗) = (4,8).2 CS(ish) = 8 so that p1 = 8 as well.3 True PS = 8+ 16 = 24 (w/ TS = 24).

PS = 18 when Sprint charges uniform price (w/TS = 22.5)

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Implication

0 1 2 3 4 5 6 7 8 9 10 11 120

1

2

3

4

5

6

7

8

9

10

11

12

Passenger (y)

Pric

e ($

)

Metrolink′s Supply

Demand MWTP(y)=−y+12MR(y)=−2y+12MC(y)=2y

Figure:

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6 Summary

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Monopolistically Competitive Environment

What do we really mean by monopoly?Metrolink the exclusive provider of publictransportation.But then cars are its substitutes.In many markets the commodities traded are veryclose, but not perfect, substitutes.Each individual supplier thus has some slightmonopoly power.What does an equilibrium look like for such amarket?

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Monopolistic Competition

In a monopolistically competitive market,1 Free entry.2 Monopolistic pricing (Ramsey condition).3 Less than perfect substitutes between

commodities.

Implications:1 Zero profit (like perfect competition in the long run).2 MR(y) = MC(y) (like monopoly).3 Elastic (slightly downward-sloping) demand.

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Figure:

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Monopolistic Competition Is Not Efficient

Is a monopolistically competitive market efficient?No, because p >MC(y).

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Figure:

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Also, a firm is not producing at the level where unitproduction cost is minimized.

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Figure:

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6 Summary

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4 types of price discriminations and their welfareproperties.Monopolistic competition.

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Chapter 25: Monopoly Behaviord.umn.edu/~watanabe/econ401su09/doc/mbho.pdf · Chapter 25: Monopoly...

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Transcript of Chapter 25: Monopoly Behaviord.umn.edu/~watanabe/econ401su09/doc/mbho.pdf · Chapter 25: Monopoly...