Product Design and Pricing

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

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 _{Perfect (first-degree) price discrimination and its limits} 2 _{Tools and goals of product design}

3 _{Spence-Veiga-Weyl model and Leibnitz’s rule as framework} 4 _{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}

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?

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 _{Can’t make anyone pay more than worth to them} 2 _{So charge them exactly that, for each unit} 3 _{Anytime willing-to-pay above cost, profit available} 4 _{Thus monopoly sells efficiently}

Why does 1st degree discrimination do so well? 1 _{Selling more doesn’t require lowering price} 2 _{Seller can capture full value created} 3 _{Thus tries to maximize value created} However, seller captures all value

Consumers gain no surplus

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)}

Government auction, captures all profits for other things 2 _{Profit taxes}

Government taxes away profits, distributes as pleases 3 _{Labor unions}

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)

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

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

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

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

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

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!

Spence’s model of quality-choosing monopoly

Three basic effects I want to highlight:

1 _{Catering to maringal consumers (Spence)}

2 _{Intensity of consumption v. extraction (Mussa-Rosen)}

3 _{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

θis 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

N =R

θ:u(ρ;θ)≥Pf (θ) d θ

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 )≥0f (y , x )dx ; two effects?

1 _{Boundary: integral around boundary of d boundary*function} This is extensive margin, people entering/exiting market R

g=0f (y )gy(y , x )dx ; loose short-hand; see paper 2 _{Interior: integral on interior of dfunction}

This is intensive margin, people in market R

g≥0fy(y , x )dx

Let the set of marginal consumers ∂Θ ≡ {θ : u(ρ; θ) = 0} Let’s try applying this; ∂N_∂P =? −R

∂Θf (θ) d θ ≡ −M

Measure everything in fraction participating, cost C(N, ρ) Firm makes, and seeks to maximize, profits PN − C(N, ρ)

Solving the model

More interesting is level of ρ

First, what would be socially optimal? Value R

Θu (ρ; θ) f (θ) d θ − C(N, ρ)

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?

0 = dN_{d ρ} = ∂N_∂PdP_{d ρ}+∂N_∂ρ = −MdP_{d ρ} +R

∂Θu

0_{(ρ; θ)f (θ) d θ}

Define expectation operatorE [x |∂Θ]

Then becomes 0 = −MdP_{d ρ}+ME [u0|∂Θ] sodP

d ρ =E [u

0_|∂Θ]

Gives derivative of social welfare wrt ρ where N fixed? R

θ:u(ρ;θ)≥Pu

0_{(ρ; θ)f (θ) d θ − C}

ρ=NE [u0|Θ] − Cρ

Marginal and average consumers

Then we get simple formula for optimum:

N · Eu0|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)? eu0_{N − C}

ρ

Thus we obtain different expression?

N · Eu0_|∂Θ

| {z }

average marginal utility of marginals

= Cρ

|{z}

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

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 Think of it asR

Θc (ρ; u (ρ; θ)) d θ = 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

Solution of Mussa-Rosen model

Benefits side all the same; how does cost change?

∂R Θc(ρ;u(ρ;θ))d θ ∂P =ME [c|∂Θ] = Mc(ρ; P) ≡ MC ∂R Θc(ρ;u(ρ;θ))d θ ∂ρ =ME [u 0_{c|∂Θ] + NE [c} ρ+u0cu|Θ]

ME [u0c|∂Θ] = Mc(ρ, P)E [u0|∂Θ] so holding N fixed:

NE 

 cρ

|{z}

direct cost increase

+ u0cu

|{z}

extensive margin extraction

|Θ 



This replaces Cρabove, so cu <0

=⇒ Extract some of the surplus from more utility For example: more loyal, more products etc.

Heterogeneity of value

Finally, suppose that customers diverse in value/cost c (ρ; θ); simplify double dependence

∂R

Θc(ρ;θ)d θ

∂ρ =ME [u

0_{c|∂Θ] + NE [c}0_|Θ]

To hold fixed N subtract ME [u0|∂Θ] E [c|∂Θ]

So first term is M (E [u0c|∂Θ] E [u0|∂Θ] E [c|∂Θ])

Recall that E [xy ] − E [x ]E [y ] = Cov (x , y ) =⇒ MCov (u0,c|∂Θ): sorting cost of ρ

To the extent ρ selectively attracts costly, avoid

Still NE [c0|Θ]; collapses Mussa-Rosen

This is Veiga-Weyl model; again, three effects we’ll track? 1 _{Cater to marginals (discrimination)}

2 _{Extract from infra-marginals (intensive, disciplines)} 3 _{Sort for most valuable 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 _{Senior, student and other discounts}

2 _{Library surcharges for journals} 3 _{Educator and public servant discounts} 4 _{Prescription drug pricing in developing world} 5 _{Home and office software licensing}

6 _{Unemployment insurance, height tax and other tagging} More on Thursday

7 _{Resident and tourist pricing in public services} 8 _{Discounting menus in foreign languages (Chinese)}

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

Pricing principles for explicit discrimination

Before discrimination, markets pooled; demand Q = Q1+Q2

Let’s derive the elasticity of pooled demand? Elasticity of total is d Q_{d p} p Q =  dQ1 d p + dQ2 d p  p Q1+Q2 = Q11+Q22 Q1+Q2

Thus  is quantity-weighted average elasticity Lerner Rule, price absent discrimination is p−MC_p = 1_

After discrimination, price in each market is pi−MC

pi =

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

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 _{Produces more and is more socially efficient} 2 _{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

Auctions and the monopoly problem

Common application of price discrimination is auction design Auctions very much like monopoly: set reserve price?

1 _{Higher price means less sales, but higher price} 2 _{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

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}

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}

More planned, more responsive it is to incentives 3 _{Temporary insanity defense}

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?

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

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

Swing voters and getting out the vote

What’s missing from the simple Median Voter model?

1 _{Voters in one dimension, usually in more}

2 _{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

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

Gentzkow-Shapiro data

FIGURE 4.—Newspaper slant and consumer ideology. The newspaper slant index against

Bush’s share of the two-party vote in 2004 in the newspaper’s market is shown.

a geographic market is exogenous to the political slant of the market’s daily newspaper.

TABLE III

DETERMINANTS OFNEWSPAPERSLANTa

OLS 2SLS OLS RE

Share Republican 0.1460 0.1605 0.1603 0.1717

in newspaper’s market (0.0148) (0.0612) (0.0191) (0.0157)

Ownership group fixed effects? X

State fixed effects? X

Standard deviation (SD) of 0.0062

ownership effect (0.0037)

Likelihood ratio test that SD of owner effect 0.1601 is zero (p value)

Number of observations 429 421 429 429

R2 _{0.1859 — 0.4445 —}

a_{The dependent variable is slant index ( ˆyn). Standard errors are given in parentheses. An excluded instrument in}

the 2SLS model is share attending church monthly or more in the newspaper’s market during 1972–1998, which is available for 421 of our 429 observations. The first-stage has coefficient 0.2309 and standard error 0.0450. The RE

model was estimated via maximum likelihood. See Section7.2for details.

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.} Application developers and system users

4 _{Transaction platforms: eBay, financial markets, etc.} Sellers, buyers, liquidity suppliers and consumers 5 _{Other examples: dating, yellow pages, shopping malls}

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 [u0|∂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 [u0|Θ] = 0; MC ≡ C0

Private value derivative P −N_M− MC + NE [u0_{|∂Θ] = 0} Label −N

M ≡ µ = P

0

N market power/Cournot distortion Formula exactly what you would think...

Platform pricing and the Spence distortion

Socially optimal is just Pigou?

P = MC − NEu0_|Θ

| {z }

externality to average users

Monopolists distorts in two ways?

P = MC + MS

|{z}

Cournot distortion (Friday)

− NEu0_|∂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

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?

PI = CI |{z} marginal cost −X J NJEuJ I|∂Θ J | {z }

externality to average users

Private optimum adds two distortion?:

PI =CI+ µI |{z} Cournot distortion −P JNJ Eu J I|∂Θ J | {z } Spence distortion

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}

Mussa-Rosen effect discussed above 2 _{Cash-strapped borrowers less likely to repay}

=⇒ 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

Product Design

Extensive Margin

Intensive Margin

Explicit price discrimination Catering to marginal consumers Sorting

Einav et al. results

-400 0 400 800 1,200 0.00 0.20 0.40 0.60 0.80 1.00 0 500 1,000 1,500 2,000 2,500 Ex pec ted Pr of it per Applic ant Pr obabilit y of Sale / Def ault Minimum Down

Low Risk Applicants

Prob. of Sale

Expected Profit

Prob. of Default

1,200 1.00 High Risk Applicants

-400 0 400 800 0.00 0.20 0.40 0.60 0.80 0 500 1,000 1,500 2,000 2,500 Ex pec ted Pr of it per Applic ant Pr obabilit y of Sale / Def ault Minimum Down

Notes: Based on model estimates for all applicants. The horizontal axis represents the required minimum down payment applied to applicants in each risk category. The left-hand y-axis represents the probabability of sale (for applicants) and probability of default (for buyers). The right-hand y-axis represents expected profit per applicant, calculated as the probability of sale times net operating revenue per sale, where net operating revenue = down payment + PV of loan payments + PV of recovery - vehicle cost - unobserved cost. The unobserved cost is estimated as described in Section 5. White diamonds show observed average minimum down payments for each credit category. Black diamonds show optimal minimum down payments based on model estimates.

Prob. of Sale

Prob. of Default

Expected Profit

Other applications of heterogeneous contributions

Basic logic applies in very wide range of contexts:

1 _{Optimal media slant also depends on politics of rich}

2 _{Soap operas appeal to melodrama-loving women}

3 _{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 _{Colleges make facilities to attract right types of students}

6 _{Goldman Sachs makes like hell to scare off wimps}

7 _{Intellectual property more valuable to good products}

8 _{Industrial policy valuable if it targets high} AU

P

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 _{Bulk discounts in commercial goods}

2 _{Punch cards for loyal customers}

3 _{New York Times: free for 20 articles, charge after that} 4 _{Pricing of cloud file-sharing services}

5 _{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

Qualities of service and multiple products

Can offer not just different quantities but also qualities This is very common strategy?

1 _{Classes of service in airlines} 2 _{Qualities of rooms at a hotel}

3 _{Different levels of American Express card} 4 _{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

Graphical illustration of quality-based discrimination

High quality demand

Low quality demand Marginal WTP

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

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 P0(q) marginal price at ˆq Benefit and cost of increasing?

Gain $1 from everyone with q > ˆq; 1 − F (ˆq) Lose [P0(ˆq) − C0(ˆq)] f (ˆq) g (ˆq)

Optimal non-linear pricing

Let’s define (q) ≡ P0(ˆ_{1−F (ˆ}q)f (ˆq)g(ˆ_q)q)

Elasticity of purchase of marginal unit with respect to P0

FOC is 1 − F (ˆq) = [P0(ˆq) − C0(ˆq)] f (ˆq) g (ˆq) =⇒

P0_−C0

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

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}

Value from purchases is S (p; θ) =R_{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) | {z } mark-up     MCov(S0_,q|∂Θ) | {z } Veiga-Weyl +NE [qp|∂Θ] | {z } Mussa-Rosen     =N(E [q|Θ]−E [S0_|∂Θ]) | {z } Spence

Sp= −q by envelope so Cov (S0,q|∂Θ) = −Var (q|∂Θ)

Connect with concepts above: rearrange, define elasticities

1 _

X ≡ E [q|∂Θ]MpQ , avg q-weighted extensive elasticity

2 _

Optimal two-part tariff

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 formulap−c_p =1