MICROECONOMICS II.

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MICROECONOMICS II.

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ELTE Faculty of Social Sciences, Department of Economics

Microeconomics II.

week 7

MARKET THEORY AND MARKETING, PART 1 Author: Gergely K®hegyi

Supervised by Gergely K®hegyi

February 2011

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week 7 Gergely K®hegyi

Price discrimination

Prepared by: Gergely K®hegyi, using Jack Hirshleifer, Amihai Glazer és David Hirshleifer (2009) Mikroökonómia. Budapest:

Osiris Kiadó, ELTECON-könyvek (henceforth: HGH), and Kertesi Gábor (ed.) (2004) Mikroökonómia el®adásvázlatok.

http://econ.core.hu/ kertesi/kertesimikro/ (henceforth: KG).

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Market theory and marketing

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Market theory and marketing (cont.)

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Market theory and marketing (cont.)

Decision problems of the company in business (if it is considered as a separate decision-maker):

Examples for monopolistic behaviors

Pricing(should 12 straws of rose cost the same as 12*1 straw? What about occasions such as mothers' day?: Price discrimination

Choosing the product (Should menu be in the restaurant or only à la carte? Should one menu be? should meals cost always the same?): Quality, product range, tie-in sale, package-sale.

Examples for strategic behavior

Marketing, product support, advertising, etc. (Tisza shoes?):

It contains strategic elements.

Market stretching (OTP in Croatia?): It contains strategic elements.

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Price discrimination

1st example: How to determine the price of tickets? (Veszprém Zoo, 2010)

Single:

Child (age between 318) 1050 HUF Student (older than 18) 1370 HUF Adult 1560 HUF

Pensioner 1050 HUF Group:

Child (age between 318) 920 HUF Student (older than 18) 990 HUF Adult 1400 HUF

Pensioner 920 HUF

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Price discrimination (cont.)

2nd example: How to determine cell phone charges of a package?

(T-Mobile, 2010, Domino Active package) Within the T-mobile network:

Within peak periods 26 HUF Outside peak periods 16 HUF In domestic xed lines:

Within peak periods 26 HUF Outside peak periods 16 HUF In other mobile directions:

Within peak periods 36 HUF Outside peak periods 26 HUF

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Price discrimination (cont.)

Linear pricing (third degree price discrimination) Non-linear pricing (rst and second degree price discrimination)

Individual pricing Multiple pricing Block pricing Quantity discounts

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Price discrimination (cont.)

Conditions of price discrimination:

The company market has market power.

Information of the consumers' willingness to pay (of price sensitivity or demand function)

Denition of consumer-groups: Market segmentation Identication of consumers (or self-selection incentive contract menu), classication into consumer-groups

Prevention and restriction of reselling the product (arbitrage) In case of consumption the personality of the consumer can be identied: mostly in case of direct connection between buying and consuming.

Services

Non-storable goods (e.g. electricity, gas) Restrictions tied in contract

Abolition of guarantee

Prohibition of re-selling by contracts Product modication (e.g. drugstore alcohol)

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Price discrimination (cont.)

Increase of transactional costs: searching, travelling, transportation, etc. costs)

Market segmentation

Suppose the company divides the customers into two or more segments, oering dierent prices (quantities) to dierent classes of buyers.

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Linear pricing

Prices and quantities set in certain segments:

First segment: P1,Q1

Second segment: P2,Q2

Π =R1(Q1) +R2(Q2)−C(Q1+Q2)→max Π =P1(Q1)Q1+P2(Q2)Q2−C(Q1+Q2)→max Optimum condition:

∂Π

∂Q1 =0, ∂Π

∂Q2 =0 mr1=mr2=MC P1

1+ 1

η₁

=P2

1+ 1

η₂

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Linear pricing (cont.)

P₁ 1+ 1

η₁

=P₂ 1+ 1

η₂

Statement

Under market segmentation, the segment with more elastic demand will be charged a lower price.

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Linear pricing (cont.)

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Linear pricing (cont.)

Paperbacks versus hardbacks

Hardbacks Paperbacks

$ % $ %

price 39,16 17,04

marginal cost 2,95 7,5 1,74 10,2

price-marginal cost (=margin) 36,21 92,5 15,30 89,8 Source: Hirshleifer et al, 2009, 314.

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Non-linear pricing

Whereas in market segmentation the seller charges dierent prices to dierent customers, in block pricing the seller charges dierent prices to a single customer. For example, a 1-pound package of detergent might sell for $1.00 while a 2-pound package sold for

$1.50. The seller is charging $1.00 for the rst pound bought and

$0.50 for the second pound.

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Non-linear pricing (cont.)

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Perfect Discrimination

Four-part pricing

In case of perfect price discrimination, the company charges a dierent price (which equals to the reservation prices of consumers) for each successive unit bought by each consumer (e.g. auction). In this case the company applies a four-part pricing schedule.

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Perfect discrimination

It can be applied in such cases when access to the good and dierent units of the good can be charged too (e.g. network services).

1st part: Lump-sum 'access fee' for the right to buy (T ) 2nd part: Unit-price paid for the bought units of product (p) Can be an instrument of price discrimination (rst and second degree price discrimination)

All consumer surplus can be skimmed if Consumers are the same

Consumers can be identied

In this case perfect (rst degree) price discrimination exists.

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Perfect discrimination (cont.)

1 E.g.: Disco

Dening prices of drinks (linear pricing)

Dening the entrance fee (access charge)+ drink prices (unit charge) (two-part pricing)

Entrance fee + coupons (amount that can be consumed) + dening drink prices (block pricing)

2 E.g.: Cell phone charges

Dening per-minute rate of calls (linear pricing)

Dening monthly fee + per-minute fee (two-part pricing) Dening monthly fee + amount of minutes can be applied + per-minute charges (block pricing)

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Perfect discrimination (cont.)

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Perfect discrimination (cont.)

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Perfect discrimination (cont.)

Two-part price (T,p)=(access fee, unit fee):

the old: T_i= (a−c)∗b∗0,5,p_i =c the young: T_f = (e−c)∗f ∗0,5, p_f =c Block price: (T,q,p)=(access fee, coupon, unit fee):

the old: T_i= (a−c)∗b∗0,5+c∗b,q_i =b,p_i ≥c the young: T_f = (e−c)∗f ∗0,5+c∗f,q_f =f,p_f ≥c

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Second degree price discrimination

Two consumers with dierent valuations (willingness to pay).

The company cannot identify the certain consumers.

Dierent packages (quality, quantity) should be combined for certain types and should be priced in such a way that every consumer chooses the one which is aimed at him (moreover it should be worth to him to buy that particular one) → Self-selection (incentive constraint).

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Second degree price discrimination (cont.)

The prices of packages are limited by the price oered to the other-type consumer (the other's willingness to pay)→Extra surplus (information benet) should be ensured for the good type consumer forcing him to choose the package aimed him (to reveal his type).

Possible solution: T1=A and T2=A+C (Namely the company is obliged to go without the surplus of area B in case of consumer 2.)

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Second degree price discrimination (cont.)

If the quantity of goods in the package of the worse type consumer is reduced (prot loss), then the consumer surplus (benet) of the good type consumer can decrease (extra prot).

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Second degree price discrimination (cont.)

Optimum: where the prot loss caused by the reduced bundle of low-demand consumer equals to the prot gained from the reduced information benet of high-demand consumer.

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Second degree price discrimination (cont.)

Condition: two types of consumers on the market: rstly, there are those who has a low (marginal) demand for the good: 'low-demand' consumers (ratio of them is p), secondly there are high-demand consumers (whose ratio is 1−p).

Condition: The company CANNOT dierentiate between the two types of consumers.

The monopoly oers dierent menus: orders a price t to every quantity q. If the consumer chooses menu (qi,ti), then his utility is the following:

Ui =θ_iV(qi)−ti(V⁰(qi)>0,V⁰⁰(qi)≤0).

Type of consumer: θ, cond.: θ₁< θ₂. Marginal cost of production: c, no x cost.

Participation constraints:

IR₁: θV(q₁)−t₁≥0 IR2: θV(q2)−t2≥0

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Second degree price discrimination (cont.)

Incentive constraints:

IC1: θV(q1)−t1≥θV(q2)−t2

IC2: θV(q2)−t2≥θV(q1)−t1

Expected prot of the company if both consumers chooses the bundle aimed at him:

Π(q1,q2,t1,t2) =p(t1−cq1) + (1−p)(t2−cq2)

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Second degree price discrimination (cont.)

Review of constraints:

IC1−IC2

(θ₂−θ₁) [V(q2)−V(q1)]≥0 Monotony assumption: the company should supply

high-demand consumers with an amount at least as much as low-demand consumers are supplied with. Ifθ₁< θ₂, then q1≤q2.

If IC2 and IR1 is fullled, then

θ₂V(q2)−t2≥θ₂V(q1)−t1≥θ₁V(q1)−t1≥0. Thus IR2 is always true, therefore can be omitted.

We expect that it is favorable for the high-demand consumer to choose the menu aimed at the other consumer but not vice versa, hence constraint IC1should be temporarily ignored and will be checked later whether it is binding in optimum or not.

Because the expected prot function is an increasing function in both two prices therefore IR1equals IC2:

θ₁V(q1)−t1=0 θ₂V(q2)−t2=θ₂V(q1)−t1>0

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Second degree price discrimination (cont.)

Optimal prices:

t1=θ₁V(q1)

t2=θ₂V(q2)−(θ₂−θ₁)V(q1)

Thus surplus of low-demand consumers is zero, while the high-demand consumers realize(θ₂−θ₁)V(q1)information surplus.

This surplus is the function of amount sold to low-demand consumers, therefore in order to make changing types less 'attractive' for high-demand consumers the amount supplied to the low-demand type must be reduced.

Using the abovementioned (substituting constraints into target function) the task is:

Π(q₁,q₂) =p[θ₁V(q₁)−cq₁] +

+(1−p) [θ₂V(q2)−(θ₂−θ₁)V(q1)−cq2]→max

q1,q2

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Second degree price discrimination (cont.)

First order conditions (optimum):

θ₁−1−p

p (θ₂−θ₁)

V⁰(q₁) =c θ₂V⁰(q₂) =c

Note

If the ratio of low-demand consumers (p)is substantially low or the dierence between parameters(θ₂−θ₁)is signicantly high, then the rst order condition may not be fullled to positive q₁, thus it is not worth for the company to supply low-demand consumers within the market because the surplus gained from them doesn't compensate for the information surplus paid for high-demand consumers. In this case only high-demand consumers are supplied with a menu at t₂=θ₂V(q₂)price.

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Second degree price discrimination (cont.)

Other methods of self-selection:

Well- and badly-informed consumers

Dierence of consumers' time-preference (opportunity cost) 'Impatient' early buyers vs. consumers waiting for

price-reductions

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Welfare eects of price discrimination

First degree price discrimination:

Ecient output but income rearrangement

Higher level of welfare in contrast to non-discriminating monopolistic pricing

Third degree price discrimination:

Ambiguous welfare eects

P>MC (allocation eciency-loss)

Results in higher welfare if discrimination-output is greater than non-discrimination-output

Second degree price discrimination:

Ambiguous welfare eects

Results in higher welfare if discrimination-output is greater than non-discrimination-output

It is common because the company supplies at Pareto ecient level (rst best) for consumers with high

willingness-to-pay and supplies below Pareto ecient level (but frequently above non-discriminating quantity) for consumers with low willingness-to-pay.

BUT! Price discrimination might turn such markets protable which wouldn't have supply without it.