1. 178.307, Markets, Firms and Consumers
Lecture 10- Pricing

2. Overview
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.
This topic considers the interaction with the firm and the consumer.
We will look at 2 issues:
Price bundling
Bait and Switch advertising.

3. Basic Definitions Commodity Bundling Consumer Surplus
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.

4. 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’.

5. 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…)

6. Yellen/Adams Model 1 Technology Indivisibility Independence
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.

7. 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 r2 A B
p2* C D
p1* r1

8. Pure Bundling Strategy
Offer the two commodities for sale only as a package.
Group A buys bundle
Group B does not r2
pB* A B
pB* r1

9. Mixed Bundling Strategy
Offer goods as either a package (pB*) or as pure components (p1* or p2*) W r2 C
pB* A
p2* X Z Y B D
pB*
p1* r1

10. 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).

11. Benchmark Complete Extraction Exclusion Inclusion
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

12. Dilemmas Pure Components Pure bundling Mixed Bundling
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.

13. 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

14. 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)

15. 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.

16. 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.

17. 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?

18. 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.

19. 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

20. 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.

21. Suppose Firm A advertises B
Conditions for sale:
N(W – PB - k) > R(W)
Consumer decides to shop
M(W - PA - k) > R(W - k)
Condition for buying after search is weaker than before.

22. Bait and Switch depictedM
C1=R(W)
C2=R(W-k)
N(.) is utility from B
M(.) is utility from A J c1 L c2
γM+
(1- γ)max{N,R(w-k)} = R(w) c2 c1 N

23. 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.

24. Summary Only occurs when
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.

25. References
Adams/Yellen (1976). Commodity Bundling & the Burden of Monopoly. Quarterly Journal of Economics 90(3):
Lazear, E. (1995). Bait and Switch. Journal of Political Economy 103(4):