Product Design
Extensive Margin
Intensive Margin
Product Design and Pricing
E. Glen Weyl
University of Chicago
Clase 6
Teoría Avanzada de Precios y Estructuras de Mercado
Escuela de Verano 2012
Departamento de Economía
Universidad de los Andes
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Introduction
Last lecture product and pricing details fixed
Today we’ll talk about these:
How to design, price and market a product (line)
Covers much of mechanism design, etc.
1
2
3
4
Perfect (first-degree) price discrimination and its limits
Tools and goals of product design
Spence-Veiga-Weyl model and Leibnitz’s rule as framework
Designing for the extensive margin
Logic and applications of explicit discrimination (3rd degree)
Qualitative product characteristics and the Hotelling model
Platforms and value generation by users
Empirical measurement of sorting
5
Designing for the intensive margin
Second-degree price discrimination and non-linear pricing
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Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
The idea of first-degree price discrimination
First-degree price discrimination is ideal?
1
Charge every person personalized price
2
Different price for each unit sold
3
Match everything exactly to willingness-to-pay
Capture full surplus consumers gain
Rarely observed in real world (theoretical benchmark), but
1
Bargaining institution with very competent bargainer
2
Personalized pricing systems on the internet
3
CVS coupon systems
Best possible thing for monopolist, gets everything
Therefore companies are always looking for better ways
But terrible for consumers, gain no surplus
But what about total social value?
Very attractive in many dimensions
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Efficiency of first-degree price discrimination
First-degree price discrimination is highly efficient
In fact, as efficient as perfect competition
Every consumer willing to pay above cost served
1
2
3
4
Can’t make anyone pay more than worth to them
So charge them exactly that, for each unit
Anytime willing-to-pay above cost, profit available
Thus monopoly sells efficiently
Why does 1st degree discrimination do so well?
1
2
3
Selling more doesn’t require lowering price
Seller can capture full value created
Thus tries to maximize value created
However, seller captures all value
Consumers gain no surplus
=⇒ Distributive issues important objection
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Distributive objections and (partial) solutions
Thus perfect price discrimination often unpopular
But more efficient...so should be possible to redistribute
Economists advocate pairing with redistributive method?
1
Bidding for right to monopoly (franchise)
2
Profit taxes
3
Labor unions
Government auction, captures all profits for other things
Government taxes away profits, distributes as pleases
Unions extract profits as higher wages
None of these solutions as perfect as it sounds
Redistributive authority, competitor needs to know profits
Also may be benefits not to redistributing
Allows firm to capture full value created (tomorrow more)
Lessons apply to broader price discrimination
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Information and barriers to perfect discrimination
Whatever its merits, first-degree discrimination difficult
This is why we rarely see it in practice
Barriers to implement include?
1
Administrative and “menu” costs
Requires quoting different price to consumers
Could they even process this? Predict? Plan?
2
Fairness constraints
Many people think that price discrimination is unfair
Can alienate consumers
3
Arbitrage and keeping track of consumers
Drug companies and publishers in developing countries
4
Information about willingness to pay
Most important, how to know what to charge each?
Fundamentally, distortion because monopolist uniformed
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Considerations in designing products
In considering product design, two crucial considerations:
1
Goals:
Keep costs low and price high
Attract as many consumers as possible
Attract most valuable (avoid most costly) customers
Either directly for the firm or for other customers
2
Tools or instruments:
Uniform price: not focus
Discriminatory/sophisticated pricing
Range of products offered
Product quality, ease of use, etc
Product niche, market segment, etc.
Advertising, marketing to consumers, placement, etc.
Group of consumers for others to interact with: platforms
=⇒ Today we’ll learn how to use instruments for goals
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Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Vertical and horizontal characteristics
Common way of dividing up tools/instruments is:
1
Vertical
All consumers agree it is good (or bad)
Price is simplest example, but quality more generally
Speed of internet connection, level of insurance coverage
Consumers may differ in how much value they put on it
2
Horizontal
Some consumers view as good, some as bad
Often have “ideal points” that differ
We’ll see simple model of this below
Colors, flavors, designs, styles, political bias
3
But also, and most often, diagonal
Most, but not all, view it same way
But some feel differently, everyone differs in many ways
=⇒ Key to all of this is nature of consumer heterogeneity
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Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Classic and not so classic forms of discrimination
Economists often see price discrimination separate from design
By this, they usually mean two types:
1
3rd-degree or explicit discrimination
Different treatment of identifiably different individuals
2
2nd-degree or implicit discrimination
Different offerings into which individuals self-sort
Often pricing different packages of goods
Often, though, less “price” features serve similar purpose
Non-price product features bring in desired groups
Restaurant promotions or menus
Andres Carnes de Res layout and amenities
We’ll therefore consider these in unified way
But to highlight, briefly describe more exotic pricing
Shows continuum between price and non-price strategies
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Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Loyalty, sales and add-ons
Other forms of discrimination less perfect, efficient
1
Loyalty and personalized discounts
CVS and others track your purchasing
Offer targeted discounts based on purchasing behavior
Helps get closer to perfect, but incentives to manipulate
2
Inter-temporal (sales)
Department, outlet stores’ periodic sales/discounts
Those whose demand is time-sensitive willing to pay a lot
Thus discriminate by offering less to those willing to wait
Airline ticket and hotel room pricing similar
3
Add-ons and obfuscation
Hotels, printers, banks and others cheap to get into
But soak you for lots of extras once you are on board
=⇒ Discriminate against those who don’t read small print
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Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Miserable price discrimination
One of my favorite examples is from Les Miserables:
Inn keeper Thenardier describes his pricing policies
Reasonable charges
Plus some little extras on the side!
Charge ’em for the lice, extra for the mice
Two percent for looking in the mirror twice
Here a little slice, there a little cut
Three percent for sleeping with the window shut
When it comes to fixing prices
There are a lot of tricks he knows
How it all increases, all them bits and pieces
Jesus! It’s amazing how it grows!
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Spence’s model of quality-choosing monopoly
Three basic effects I want to highlight:
1
2
3
Catering to maringal consumers (Spence)
Intensity of consumption v. extraction (Mussa-Rosen)
Sorting for valuable customers (Veiga-Weyl)
Veiga and Weyl (2012) have unified model, but add pieces
Start with Spence, add Mussa-Rosen, then Veiga-Weyl
Suppose many consumers, each buys product or doesn’t
Each consumer gets utility u(ρ; θ) − P from consuming
θ is the consumer’s type, ρ is product characteristic
Types distributed (in some space) according to f (θ)
Anyone with u ≥ P, the price, purchases; sales are
R
N = θ:u(ρ;θ)≥P f (θ) dθ
Let Θ ≡ {θ : u (ρ; θ) ≥ P}
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Leibnitz’s rule and the mathematics of product design
Throughout we will be taking derivatives of integrals like this
=⇒ We need extension of Leibnitz’s Rule to many dimensions
R
x:g(y ,x)≥0 f (y , x)dx; two effects?
1
Boundary: integral around boundary of dboundary*function
RThis is extensive margin, people entering/exiting market
f (y )gy (y , x)dx; loose short-hand; see paper
g=0
2
Interior: integral on interior of dfunction
RThis is intensive margin, people in market
f (y , x)dx
g≥0 y
Let the set of marginal consumers ∂Θ ≡ {θ : u(ρ; θ) = 0}
R
Let’s try applying this; ∂N
∂P =? − ∂Θ f (θ) dθ ≡ −M
Measure everything in fraction participating, cost C(N, ρ)
Firm makes, and seeks to maximize, profits PN − C(N, ρ)
P
Optimal price still P − M
= P + P 0 N = MC = CN , same
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Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Solving the model
More interesting is level of ρ
First,
what would be socially optimal? Value
R
u
(ρ;
θ) f (θ) dθ − C(N, ρ)
Θ
We want to hold N fixed when we optimize
Separate cleanly from quantity distortion yesterday
Derivative by Leibnitz? How much does P for N fixed?
R
∂N dP
∂N
dP
0
0 = dN
dρ = ∂P dρ + ∂ρ = −M dρ + ∂Θ u (ρ; θ)f (θ) dθ
Define expectation operatorE [x|∂Θ]
dP
0
0
Then becomes 0 = −M dP
dρ + ME [u |∂Θ] so dρ = E [u |∂Θ]
Gives
derivative of social welfare wrt ρ where N fixed?
R
0
0
θ:u(ρ;θ)≥P u (ρ; θ) f (θ) dθ − Cρ = NE [u |Θ] − Cρ
Similarly defined expectation operator for interior
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Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Marginal and average consumers
Then we get simple formula for optimum:
N·
E u 0 |Θ
=
| {z }
average marginal utility of average
Cρ
|{z}
marginal cost of quality
Equates marginal cost and benefits to average purchaser
Derivative of profits PN − C(N, ρ)? ue0 N − Cρ
Thus we obtain different expression?
N·
E u 0 |∂Θ
=
Cρ
|{z}
| {z }
average marginal utility of marginals
marginal cost of quality
Cater to marginal not average; called the Spence distortion
Quality too high (low) if marginals value more (less)
May be offset by other influence of infra-marginals: voice
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Discussion of the Spence model
This is the basic logic lying behind much discrimination
Squeeze out of inframarginals w/o alienating marginals
Classic example is treating those locked-in differently
For example, cities, countries often obsequious to tourists
Famous Israeli joke about this
Then you were a tourist...
However, trade-off here is just losing people entirely
Sometime cost is that they use product less, downgrade
To capture this, change cost function
Rather than depending
on N, ρ directly
R
Think of it as Θ c (ρ; u (ρ; θ)) dθ = NE [c (ρ; u (ρ; θ)) |Θ]
Individuals with utility greater than 0 may increase cost
Same as reducing contribution to profits (payment)
Focus of the Mussa-Rosen model/models of moral hazard
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Solution of Mussa-Rosen model
Benefits side all the same; how does cost change?
R
c(ρ;u(ρ;θ))dθ
∂P
R
∂ Θ c(ρ;u(ρ;θ))dθ
∂ρ
ME [u 0 c|∂Θ] =
∂
Θ
= ME [c|∂Θ] = Mc(ρ; P) ≡ MC
= ME [u 0 c|∂Θ] + NE [cρ + u 0 cu |Θ]
Mc(ρ, P)E [u 0 |∂Θ] so holding N fixed:

NE 

cρ
|{z}
+
direct cost increase
u0c
|{z}u
|Θ
extensive margin extraction
This replaces Cρ above, so cu < 0
=⇒ Extract some of the surplus from more utility
For example: more loyal, more products etc.
We’ll return to this as 2nd-degree discrimination
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Why perfect discrimination fails
Tools and goals of product design
Leibnitz and the mathematics of product design
Heterogeneity of value
Finally, suppose that customers diverse in value/cost
c R(ρ; θ); simplify double dependence
∂
c(ρ;θ)dθ
∂ρ
= ME [u 0 c|∂Θ] + NE [c 0 |Θ]
To hold fixed N subtract ME [u 0 |∂Θ] E [c|∂Θ]
Θ
So first term is M (E [u 0 c|∂Θ] E [u 0 |∂Θ] E [c|∂Θ])
Recall that E[xy ] − E[x]E[y ] = Cov (x, y )
=⇒ MCov (u 0 , c|∂Θ): sorting cost of ρ
To the extent ρ selectively attracts costly, avoid
Still NE [c 0 |Θ]; collapses Mussa-Rosen
This is Veiga-Weyl model; again, three effects we’ll track?
1
2
3
Cater to marginals (discrimination)
Extract from infra-marginals (intensive, disciplines)
Sort for most valuable consumers (sorting)
Not necessarily discrimination (discipline?); see below
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Product Design
Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Explicit price discrimination
Now to more specific problems
Common form of discrimination is 3rd degree
Use some objective characteristic
Charge different prices to people with these characteristics
=⇒ Charge higher prices to those with more elastic demand
Most commonly used in entertainment, transportation?
1
2
3
4
5
6
Senior, student and other discounts
Library surcharges for journals
Educator and public servant discounts
Prescription drug pricing in developing world
Home and office software licensing
Unemployment insurance, height tax and other tagging
More on Thursday
7
8
Resident and tourist pricing in public services
Discounting menus in foreign languages (Chinese)
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Product Design
Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
When are prices discriminatory?
Some of these practices can be explained by costs
1
Peak-load pricing leads to variation across time
Little marginal cost of movie tickets when not full
Very valuable during rush times
2
May be cheaper to sell goods in bundles
Most of cost of software is the CD; cheaper to put together
3
Some populations cheaper to serve than others
Different prices for different insurance risks
Senior citizens less disruptive to other movie watchers
Then what makes something price discrimination?
1
Different prices reflect demand not cost conditions
This would never happen in competitive market
Efficiency variation even more likely in competitive
2
Lack of variation when costs vary just as discriminatory
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Product Design
Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Pricing principles for explicit discrimination
Before discrimination, markets pooled; demand Q = Q1 + Q2
Let’s derive the elasticity of pooled demand?
p
p
dQ1
dQ2
Elasticity of total is dQ
+
=
Q1 +Q2 =
dp
dp
dp
Q
Q1 1 +Q2 2
Q1 +Q2
Thus is quantity-weighted average elasticity
Lerner Rule, price absent discrimination is p−MC
=
p
After discrimination, price in each market is
pi −MC
pi
1
=
1
i
=⇒ Discrimination useful to extent that elasticities are different
=⇒ Price rises in market with lower elasticity, falls in other
We call market where rises “high” or “strong” market
Market where price falls is “low” or “weak”
=⇒ Output and social welfare may rise or fall
Depends whether price rises more in high or falls more in low
Clear: profits rise (firm’s choice), high worse off, low better
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Product Design
Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Can effects be as unpredictable as they look?
That was a bit complicated, but can be solved
But results are a bit puzzling
Everything seems ambiguous, depends on details
But we know perfect price discrimination?
1
2
Produces more and is more socially efficient
Reduces consumer surplus
We can also get to perfect by many 3rd-degree
Slice up market once, then slice up submarkets, etc.
=⇒ Any given 3rd-degree ambiguous, eventually clear
Suggests that “typical” slicing of demand falls in right way
Simple example:
Segment for everyone willing-to-pay above/below x
If x < p don’t change in high, serve low, good for all
If x > p serve all in high, drop price in low
=⇒ Welfare increases every step, likely more accurate
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Product Design
Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Auctions and the monopoly problem
Common application of price discrimination is auction design
Auctions very much like monopoly: set reserve price?
1
2
Higher price means less sales, but higher price
Only difference is opportunity cost of sale
Determined by other buyers’ willingness-to-pay
Quantity is probability of sale, revenue is p [1 − F (p)]
F is cumulative distribution of values
If marginal revenue decreasing, award to highest value
Marginal revenue is opportunity cost
English auction a simple implementation of this
But this assumes everyone has same marginal revenue!
What if some sellers are more elastic?
This means they are expected to value less
Elasticity from distribution of values
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Product Design
Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Auctions, handicaps and 3rd-degree discrimination
Then you want to discriminate in favor of elastic buyers
You can give them a “handicap”
This forces others not just to beat them by a lot
This is beneficial intuitively because?
Forces bidders with higher value to admit this
If he only had to win by little, he would just pay low value
But if he has to win by a lot you can get more out of him
Without such discrimination, uniform reserve for everyone!
This sort of discrimination works exactly like standard
1
Compared to no discrimination, lower overall reserve
=⇒ Those thought to have low values win more often when high
2
High value bidders (inefficiently) win less often
But pay higher price, so profitable
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Product Design
Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Intentions, situation and criminal justice
One particularly interesting instance is criminal justice
Becker famously argued justice like monopoly problem?
Enforcement, jail time are costly, activity bad
Costly to police, uncompensated loss to punished
=⇒ Higher elasticity, more enforcement called for
Different circumstances imply different elasticities
=⇒ Punishments meted out should depend on these
Examples?
1
Age of offender
Young get off with lighter sentence as less planning
2
Degree of murder
3
Temporary insanity defense
More planned, more responsive it is to incentives
More general lesson about why motive, intention matters
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Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
The Hotelling line
So that is classic discrimination; what about product design?
Most famous model is by Hotelling
Product characteristic along line, like consumers
Classic example horizontal, single-peaked, other spatial
Location of store; consumers uniformly, travel to the store
Consumers always buy one of two competing products
Technically not monopoly, but logic similar
Each firm starts somewhere along the line
Question: where do they move from there?
Spence says: cater to the marginal consumer
Here she is half way between you and competitor
=⇒ Move towards your competitor
This holds at every point, so wind up in same spot!
Where does this spot have to be?
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Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Graphical depiction of Hotelling
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Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
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Hotelling’s Law
Hotelling’s Law
In this simple model, both firms end up at center.
Extremely famous result
Everyone better off if firms spread out to .25 and .75
But no firm does this on its own, monopoly would do better
Very widely applied and very relevant for geography...
But not necessarily right direction (even for geogrpahy)
Some consumers might buy nothing; these marginal too
Not everything horizontal like this
Are switchers or exiters more representative?
Depends if dimension main one of differentiation or not
If not, then opposite result typically true
=⇒ Interesting way of thinking about things, useful baseline
But Spence offers broader answer, check on reasoning
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Intensive Margin
Explicit price discrimination
Catering to marginal consumers
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The Median Voter Theorem
Perhaps most common application is electoral competition
Two political parties competing, voters left to right
Everyone votes, just a question of for whom
Direct extension of Hotelling’s logic is?
The Median Voter Theorem
Both political parties will adopt the positions of the median
voter, who has an equal number of voters to her left and right.
This is most basic result in all of political science
Also matches common sense/conventional wisdom:
In two-party, winner-take-all system, both run to “center”
Subsidiary: if more competition, more towards center
One dominant party may be able to favor its own view more
But this all is very simplified, more general principle behind
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Product Design
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Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Swing voters and getting out the vote
What’s missing from the simple Median Voter model?
1
2
Voters in one dimension, usually in more
Not everyone votes, need to make sure people turn out
Spence’s logic shows us how to extend:
1
Swing voters, not just “median voter”, are the targets?
Different groups of swing voters
Sensible centrist v. “radical middle”
Different policies try to target these groups
Core of political strategy
2
Parties also cater to base that may not turn out?
Get-out-the-vote efforts, but also policies targeting
This is constant debate within party: non-voters also pivotal
However, half as much weight as don’t benefit other side
=⇒ Much political science application of Spence
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Product Design
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Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Gentzkow and Shapiro (2010) on media slant
Gentzkow and Shapiro (2010) use to study media slant
Local, monopoly newspapers around US
Single dimension (left-right), but one firm; like Spence
Measure slant by language used by newspapers?
Phrases used by Republicans: “death tax”, “illegal aliens”
Democrats use “poor people”, “workers rights”, “tax breaks”
Calibrate based on Congressional record
Rate papers on whether they write like each party
Break local markets into districts with different politics
Measure which districts do and do not read; how?
Left-wing papers read less in right-wing zip codes
Shows how much value slant, what would maximize profit
Do papers max profits? Or do they serve owner’s goals?
Mostly profit, perhaps because small, free rider
Important for policy on media ownership, diversity
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Explicit price discrimination
Catering to marginal consumers
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Gentzkow-Shapiro
data
WHAT
DRIVES MEDIA SLANT?
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Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
The idea and examples of platforms
In many situations, characteristics determined by consumers
Serve both as consumers and producers of characteristics
Thus we will refer to them by vaguer term “users”
When user-generation important, call monopoly “platform”
Also called “two-sided markets” or “networks”
Examples abound and increasingly important?
1
Media platforms: newspapers, television, websites
Primarily readers valuable to advertisers
2
Payment platforms: credit, debit, PayPal
Payment acceptance and payment use
3
Operating systems: smart phones, video games, etc.
4
Transaction platforms: eBay, financial markets, etc.
5
Other examples: dating, yellow pages, shopping malls
Application developers and system users
Sellers, buyers, liquidity suppliers and consumers
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Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
A simple model of platforms
To focus on Spence type effects, only number matters
Identity of consumers irrelevant
Other effects show up in natural way
Shows basic logic, generalizes, maybe for telecom network
Users, like Spence, have utility for joining u (N; θ)
N now serves both the role of N before and ρ!
=⇒
dP
dN
=? − M1 + E [u 0 |∂Θ], may rise or fall!
If cannot sell, might still avoid raising price (problem set)
Attracts in other customers (popular restaurants, theaters)
For everything else, just combine ρ and N: C(N)
Social value derivative P − MC + NE [u 0 |Θ] = 0; MC ≡ C 0
N
Private value derivative P − M
− MC + NE [u 0 |∂Θ] = 0
N
Label − M
≡ µ = P 0 N market power/Cournot distortion
Formula exactly what you would think...
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Intensive Margin
Explicit price discrimination
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Platform pricing and the Spence distortion
Socially optimal is just Pigou?
P = MC −
NE u 0 |Θ
| {z }
externality to average users
Monopolists distorts in two ways?
P = MC +
MS
|{z}
−
Cournot distortion (Friday)
NE u 0 |∂Θ
|
{z
}
Spence distortion (today)
Just as in Spence, may go either way
Newspapers v. credit cards (two-sided markets, next slide)
This effect may be bigger here...only one product
Interacts with market power: may be good or much worse
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Multi-sided platforms
In many (most?) cases different distinct groups
Usually called “sides of the market” I = A, B, . . .
Readers and advertisers, card-holders and accepters, etc.
A bit more more notation, math in deriving, but same idea
Social optimum is Pigou?
X
PI =
CI
−
N J E uIJ |∂ΘJ
|{z}
J
marginal cost
|
{z
}
externality to average users
Private optimum adds two distortion?:
P
P I = CI +
µI
− J N J E uIJ |∂ΘJ
|{z}
|
{z
}
Cournot distortion
Weyl Summer Course
Spence distortion
Product Design
Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Einav et al. (2011) on subprime lending
Now let’s turn to sorting
Left out of platforms, but often important there
Einav et al. (2011) have nice application
Subprime auto loans to diverse consumers
Product dimensions: down payment, interest rate, price
Observable credit scores, but also hidden risks
Changing required down payment affects in two ways?
1
Reduces chance of default directly by reducing debt
2
Cash-strapped borrowers less likely to repay
Mussa-Rosen effect discussed above
=⇒ Down-payment requirements sort for good risks
Einav et al. measure looking at variation in requirement
Sticker price counter-productive, as it translates into debt
=⇒ Raises chance of default
Weyl Summer Course
Product Design
0.00
0
Product Design
Extensive Margin
500Intensive Margin
1,000
High Risk Applicants
1.00
-400
2,500
Minimum Down
Einav et al. results
1,200
Prob. of Default
0.80
800
0.60
400
0.40
Expected Profit
0
0.20
Expected Profit per Applicant
Probability of Sale / Default
Explicit price discrimination
Catering to marginal consumers
2,000
Sorting 1,500
Prob. of Sale
0.00
-400
0
500
1,000
1,500
Minimum Down
2,000
2,500
Notes: Based on model estimates for all applicants. The horizontal axis represents the required minimum down payment applied t
applicants in each risk category. The left-hand y-axis represents the probabability of sale (for applicants) and probability of default (fo
buyers). The right-hand y-axis represents expected profit per applicant, calculated as the probability of sale times net operating revenu
Weyl =Summer
Course+ PV ofProduct
Design+ PV of recovery - vehicle cost - unobserved cost. Th
per sale, where net operating revenue
down payment
loan payments
Product Design
Extensive Margin
Intensive Margin
Explicit price discrimination
Catering to marginal consumers
Sorting
Other applications of heterogeneous contributions
Basic logic applies in very wide range of contexts:
1
2
3
Optimal media slant also depends on politics of rich
Soap operas appeal to melodrama-loving women
Credit card “points” useful if frequent users may leave
We’ll see this formalized below
And travel benefits useful to attract
4
Insurers may hold down coverage to drive away sick
We’ll talk more about this on Wednesday
5
6
7
8
Colleges make facilities to attract right types of students
Goldman Sachs makes like hell to scare off wimps
Intellectual property more valuable to good products
Industrial policy valuable if it targets high AU
P
Basic logic applies very broadly!
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Multiple products and quality of service
Non-linear pricing and two-part tariffs
Combining the extensive and intensive margins
Non-linear pricing and quantity discounts (surcharges)
Now let’s turn to intensive margin: per-customer profits
Standard lever to affect this is non-linear tariffs
Different prices for different numbers of units
Often choice of different discrete bundles
Examples of this (typically discount) abound?
1
2
3
4
5
Bulk discounts in commercial goods
Punch cards for loyal customers
New York Times: free for 20 articles, charge after that
Pricing of cloud file-sharing services
Income taxes: rates vary depending on income level
Goal: consumers self-select into right price
Lower price if they don’t mind storing, keeping track of card
Lower price to those who don’t value enough to use often
=⇒ Not as effective, as must incentivize limited cheating
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Multiple products and quality of service
Non-linear pricing and two-part tariffs
Combining the extensive and intensive margins
Qualities of service and multiple products
Can offer not just different quantities but also qualities
This is very common strategy?
1
2
3
4
Classes of service in airlines
Qualities of rooms at a hotel
Different levels of American Express card
Tiers of cable and internet service
Common observation: low-quality deliberately degraded
Not that the airline can’t offer better service
Deliberately makes Coach experience bad
This forces those who can to pay for business, first
Thus monopolist distorts quality as well as quantity
Particularly large for low-end customers
Less reason to make first-class worse
We’ll model this in one moment
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Multiple products and quality of service
Non-linear pricing and two-part tariffs
Combining the extensive and intensive margins
Graphical illustration of quality-based discrimination
6
Marginal WTP
5
High quality demand
4
3
2
1
0
0.0
Low quality demand
0.5
1.0
Weyl Summer Course
1.5
2.0
Product Design
2.5
Quality 3.0
Product Design
Extensive Margin
Intensive Margin
Multiple products and quality of service
Non-linear pricing and two-part tariffs
Combining the extensive and intensive margins
Bundling, two-part tariffs and efficiency
Price discrimination takes related (more specific) forms
Some of these achieve efficiency just like perfect
Also transfer all value to the monopolist
1
Bundling: two products cheaper together than apart
Two pieces of software free to produce: Excel and Word
Some people like Excel better, some Word
Values for the package much more homogeneous
Then monopolist can capture much more value in package
=⇒ Packaging/bundling clarifies information
2
Extreme form is “two-part tariff” (Oi 1971)
Extreme form of bundling; charge for right to buy
Low pricing for various services, near (or below) cost
Rides at Disneyland, Costco, Rhapsody, etc.
Achieves efficiency, but takes all from consumers
=⇒ Just like perfect price discrimination (information perfect)
Depends on certain type of homogeneity, as we’ll see
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Multiple products and quality of service
Non-linear pricing and two-part tariffs
Combining the extensive and intensive margins
The Mussa-Rosen-Wilson model
Let’s try to formalize some of these ideas
Use Wilson (1993)’s version of Mussa-Rosen
Individuals choose how much, q, to buy
Could be quality or quantity; equilibrium distribution F (q)
Cost per individual C(q); pay price P(q): smooth, P(0) = 0
Individuals never “jump” around as prices change
Can restrict utilities or P schedule to ensure
Jumps introduce things we’ll consider in minute
Fraction g(q) of individuals buying q would switch down a
unit if price of q rose by =⇒ Only people who stop consuming already 0
How to optimally price? Call P 0 (q) marginal price at q̂
Benefit and cost of increasing?
Gain $1 from everyone with q > q̂; 1 − F (q̂)
Lose [P 0 (q̂) − C 0 (q̂)] f (q̂) g (q̂)
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Multiple products and quality of service
Non-linear pricing and two-part tariffs
Combining the extensive and intensive margins
Optimal non-linear pricing
Let’s define (q) ≡
P 0 (q̂)f (q̂)g(q̂)
1−F (q̂)
Elasticity of purchase of marginal unit with respect to P 0
FOC is 1 − F (q̂) = [P 0 (q̂) − C 0 (q̂)] f (q̂) g (q̂) =⇒
P 0 −C 0
P0
=
1
Standard monopoly trade-off at each point
Quality distorted down just as quantity; people above key
This type of analysis used elsewhere (e.g. tax); nice but...
Who uses and do you really need whole schedule?
Need sophisticated to the extent elasticity varies
Wilson investigated data
Found few piecewise linear parts usually close to optimal
We’ll focus particularly on fixed and linear component
Allows adding richness (particularly discrete exit)
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Multiple products and quality of service
Non-linear pricing and two-part tariffs
Combining the extensive and intensive margins
Model of two-part tariff with exit
Now suppose individuals buy q, but price now P + pq, cost cq
Let q ? (p; θ) be optimal purchase R
∞
Value from purchases is S (p; θ) = x=p q ? (x; θ) dx
Come to store at all if S (p; θ) ≥ P
Profit maximizing P, social optimum boring
Let’s derive optimal p from the logic of the earlier model




(p−c)
MCov(S 0 ,q|∂Θ) + NE[qp |∂Θ]
=N(E[q|Θ]−E[S 0 |∂Θ])

| {z } |
{z
} | {z } |
{z
}
mark-up
Veiga-Weyl
Mussa-Rosen
Spence
Sp = −q by envelope so Cov (S 0 , q|∂Θ) = −Var (q|∂Θ)
Connect with concepts above: rearrange, define elasticities
1
2
X ≡ E[q|∂Θ]Mp
, avg q-weighted extensive elasticity
Q
p
I ≡ − E[q|Θ]
,
avg
q-weighted intensive ≡ dq
E[q|Θ]
dp q
Weyl Summer Course
Product Design
Product Design
Extensive Margin
Intensive Margin
Multiple products and quality of service
Non-linear pricing and two-part tariffs
Combining the extensive and intensive margins
Optimal two-part tariff
Spence
}|
{
E [q|∂Θ]
1−
p−c
E [q|Θ]
=
Var (q|∂Θ)
p
X
+
I
| {z }
|{z}
E [q|∂Θ]
Lerner’s mark-up
{z
} Mussa-Rosen-Wilson
|
z
sorting discipline
We can see from this many intuitions from above
1
If exiters average (E [q|∂Θ] = E [q|Θ]) no distortion?
This is exactly Oi’s efficient two-part tariff
Key point is similarity between marginals and inframarginals
2
If E [q|∂Θ] = Var (q|∂Θ) = 0?
Mussa-Rosen; Wilson formula
p−c
p
=
1
But also sorting effect from variance; both discipline
Weyl Summer Course
Product Design