178.307, Markets, Firms and Consumers Lecture 10- Pricing.

178.307, Markets, Firms and Consumers

Lecture 10- Pricing

Overview

This topic considers the interaction with the firm and the consumer.

We will look at 2 issues:

– Price bundling– Bait and Switch

advertising.

Readings:– See references at end of

lecture.

Administration– Makeup Test is Friday

(19th) at 12 noon, in QB7– It is only available to

students who got less than 60% in Test 1.

Basic Definitions

Commodity Bundling– Many goods are sold in

“packages”– Pure bundling- goods only

available as a package– Mixed bundling- goods

available separately (components) or as package

E.g. Fastfood “Special Meals”

Consumer Surplus– The difference between

what a consumer is willing to pay (reservation price) and what they actually pay (market price)

Price-discrimination– Selling identical units of

output at different prices.– Requires consumers to be

separated.

Forms of Price Discrimination

First Degree– Each consumer is identified

and charged their reservation price.

– All consumer surplus is extracted.

Third Degree– Separate markets are

identified and charged different prices (based on elasticities)

– Arbitrage must not be possible

Second Degree– Firm does not separate

market– Firm sets prices so that

consumers ‘separate’ themselves

– E.g. Two part Tariffs Entry fee to get into

amusement park Fee per ride

– Quantity ‘discounts’.

Commodity-Bundling

Why does a “special-meal” at McDonalds cost less than the components separately?

– Cost savings?– Complements in

consumption?

Adams/Yellen show it is a form of price-discrimination

– Firm does not need to know reservation price

– It’s not illegal (some forms of price discrimination are…)

Yellen/Adams Model 1

Technology– Marginal cost (c1,c2) of

supply is constant, cost of bundle (cB) = c1 + c2.

Indivisibility– Marginal utility of a second

unit of each good = 0.

Independence– Reservation price of bundle

(rB) equals sum of separate reservation price (r1,r2)

These assumptions exclude cost-savings and complementary consumption as explanations for bundling.

Pure Components Strategy

Set a single price on each commodity separately.

– Group A buys both components

– Group B buys only good 2

– Group C buys only good 1

– Group D buys none

r1

r2

p2*

p1*

AB

CD

Pure Bundling Strategy

Offer the two commodities for sale only as a package.

– Group A buys bundle

– Group B does not

A

B

pB*

pB*

r1

r2

Mixed Bundling Strategy

Offer goods as either a package (pB*) or as pure components (p1* or p2*)

pB*

pB*

r1

r2

p2*

p1*

W

0

X

Y Z

A

B

C

D

Consumption Behaviour

Group B- reservation price is below both components and bundled-price

Group A- only buy the bundle

Group C- only buy good 2 Group D- only buy good 1

Each strategy has advantages and disadvantages for the firm.

We establish a bench-mark (pure price discrimination).

Benchmark

Complete Extraction– No consumer realises

any consumer surplus on their purchases.

Exclusion– No consumer consumes

a good (i) if ci > ri.

Inclusion– Any individual whose

reservation price exceeds its cost, consumes the good.

Note: the symbol r or R is used to denote reservation prices

Dilemmas

Pure Components– Achieves exclusion– Cannot achieve both

inclusion and extraction.

Pure bundling– Problem is with

exclusion

Mixed Bundling– Is always more profitable

than pure bundling when Exclusion is violated

woth pure bundling

– Mixed bundling adds more sorting categories.

Illustration

Suppose we have but 4 consumers:

The reservation prices are:

– A- r1=$10, r2=$90

– B- r1=$45, r2=$55

– C- r1=$60, r2=$40

– D- r1=$90, r2=$10

Independence implies that the reservation price for the bundle is the same all consumers. This is for convenience.

Let C1 =20

Let C2 =30

Pure Components Strategy

Profit maximised with p1=$60 and p2=$90

– C and D buy good 1– A buys good 2.– Firm prevents A and D

buying good when r > c.

Profit– 2 units of good 1 ($60-

$20) = $80– 1 unit of good 2 ($90-

$30) = $60– Total = $140

Extraction violated (A) Inclusion violated (B,C)

Pure Bundling Strategy

Profit maximised with pB = $100

Each bundle costs $50. Net profit per unit sale is $50

All consumers buy 1 bundle Profit is $200

Pure bundling avoids excessive violation of inclusion and extraction.

– All consumer surplus extracted here.

Can violate exclusion if costs are relatively high.

– Eg. A consumes good 1 even though reservation price < supply cost.

Mixed Bundling

The rule is that mixed bundling is more profitable than pure bundling when exclusion is a problem.

Suppose the firm charges p1*=90, p2*=90 and pB*=100

Firm sells 2 bundles to B and C (net profit, $100)

Firm sells only good 1 to D (net profit $70)

Firm sells only good 2 to A (net profit $60).

Total profit is $230. All conditions for price

discrimination met.

Bait and Switch

Form of False-Advertising– Low-piced good is advertised– Replaced by different good in show-room

Surprising because false-advertising discourages appropriate buyers

Firms bait and switch to draw a greater number of shoppers

What are conditions that make it profitable?

Simplify the problem

There are two types of commodities (A,B) Consumers have wealth W, and face prices

PA and PB. Let search costs be k.

Utilities

If A consumed, M(W - PA - k)

If B consumed, N(W - PB - k) R(W) if neither A nor B is consumed; no

search occurs R(W-k) if neither A nor B is consumed;

search occurs

Firms

Let γ firms produce A and (1- γ) firms produce B. A potential customer gets a message from one (and

only one) seller The message identifies location of store and

commodity available for sale. After message, the consumer can decide to shop, or

not shop.

Suppose Firm A advertises B

Conditions for sale:

1. N(W – PB - k) > R(W)– Consumer decides to shop

2. M(W - PA - k) > R(W - k)– Condition for buying after search is weaker than

before.

Bait and Switch depicted

N

M

c2 c1

c1

c2

J

L

γM+

(1- γ)max{N,R(w-k)} = R(w)

C1=R(W)

C2=R(W-k)

N(.) is utility from B

M(.) is utility from A

Conclusions

Sellers of A will use bait-and-switch so long as individuals in Zone L exceeds individuals in Zone J.

Most likely when market is ‘dense’ at one end.

Bait and switch requires that A and B be close substitutes.

Search costs crucial– R(W-k) <– M(W-PA-k) <

– R(W)

Can only hold if k>0.

Summary

Bait and switch occurs because

– Sellers gain shoppers by lying

– Once search costs are paid, marginal cost of buying commodity falls

– Firm loses customers who would genuinely desire good.

Only occurs when– Many shoppers prefer a

good to the other– Hence false adverstising

increases number of shoppers

Must involve close substitutes or costly search

Less likely if there are costs of showing good.

References

Adams/Yellen (1976). Commodity Bundling & the Burden of Monopoly. Quarterly Journal of Economics 90(3): 475-498.

Lazear, E. (1995). Bait and Switch. Journal of Political Economy 103(4): 813-829.