Lecture 2 - Justin M. Rao

Lecture 2
Multiple Prices & Modeling Demand Curves
Econ 404
Jacob LaRiviere and Justin Rao
Bargaining with complete information
My value for a good: v = 20
Your cost of service for that good: 𝑐 = 10
We both know all this
P=0
Seller walks away
P=20
P=10
Bargaining region
Buyer walks away
Bargaining and outside options
My value for a good: v = 20
Your cost of service for that good: 𝑐 = 10
Competitor price for the same good is 15
P=0
Seller walks away
P=10
Bargaining region
P=20
Competitor gets sale
Buyer walks away
Bargaining and outside options
My value for a good: v = 20
Your cost of service for that good: 𝑐 = 10
Competitor has a good that I like less: vc = 15, 𝑝𝑐 = 12
P=0
Seller walks away
P=20
P=10
Bargaining region
Buyer walks away
Prefer to buy the
cheaper, less
preferred good from
the competitor
What price will be set?
Economic theory says  if both sides know each other’s values and costs,
some deal will be made. It does not say what price will be set.
Bargaining power: factors that determine how much of the surplus each side
gets from a transaction.
P=0
Seller walks away
P=20
P=10
Bargaining region
Buyer walks away
Threat points in bargaining
“threat points”: the outcomes if one party walks away
• If my threat point is bad, bargaining breakdown is very bad for me.
• What is my outside option if we don’t make a deal?
Ex. A factory negotiating with employees over wages.
• Each employee’s threat point is to quit, which may lead to financial troubles for them.
For the factory, having one less employee is probably not that big a deal. Bargaining
“alone”, the factory has most of the bargaining power.
• Unions allow workers to bargain together. Now the threat point is to strike, meaning
the factory is shut down, at least in the short-run.
Bargaining with uncertainty
My value for a good: v1 ~𝑈 10,20 (equal chance of any value 10 to 20)
You own the good and value it at: v2 ~𝑈 5,15
Myerson Satterthwaite Theorem:
there is no mechanism that
guarantees a transaction will be
made when 𝐯𝟏 >𝐯𝟐
Idea: the seller doesn’t know the
buyers valuation, wants to increase
price and may in advertently price
buyer out of market.
Buyer has no credible way of
conveying they have a low value
5
15
20
10
My value is probably above
yours, but maybe not
Why can’t we overcome Myerson-Satterthwaite?
Trusted intermediary: we both tell a third party our true values, if buyer’s value
exceeds sellers, then price is set as halfway between the two values.
• E.g. I say 15, you say 10  price = 12.5
• Problem: we both do not have an incentive to be fully truthful. You want to lie a bit to
increase price, I want to lie a bit to reduce price
Repeated play: we both agree to always be honest with each other and “split
20
the surplus” each “round” of play.
• Will only work if we know the distributions of each other’s values. Idea, if the buyer is
really uniformly U(10,20), then there should be an equal number of 20’s as 10’s, etc.
• Often we won’t know the distributions and have an incentive to like (“long con”)
Bargaining and elasticity
Low elasticity  minimal ability to switch to competing products/technologies
With low elasticity  margins are high. In other words, the firm captures a lot
of the “surplus” of the transaction.
With high elasticities (more competitive markets)  margins are low.
Consumer’s capture most of the surplus of transactions.
One price versus multiple prices
A firm charges a uniform price if it sets the same price for every unit of output
sold.
While the firm captures profits due to an optimal uniform pricing policy, it
does not receive the consumer surplus or dead-weight loss associated with
this policy.
The firm can overcome this by charging more than one price for its product.
A firm price discriminates if it charges more than one price for the same good
or service.
10
The inefficiency of a single price
• Customers “in the DWL triangle” could
have been profitably served, but are
“priced out” of the market
• To serve these customers with a single
price, the firm has to discount all units to
this price. Loses more money on the
intensive margin than it makes up by
serving more customers.
• Customers cannot credibly reveal their
value is below the set price, but above
costs, e.g. Myerson-Satterthwaite theorem
Economic Value to the Customer (EVC)
The maximum price a customer would be willing
to pay assuming she is fully informed about the
product’s benefits as compared to the closest
competitor’s product and price
Goal: Generate an accurate value proposition
Price discrimination as “value based pricing”
Goal: charge different prices based on differential value to the customer
For higher value customers, firm can charge a higher prices and still “share in
the surplus”
Allows firm to serve more of the demand curve by tailoring prices to the value
a customer gets from the good
Also, it sounds better than “discrimination”
Using EVC
• EVC = Reference Price + Differentiation value
• After Calculating EVC managers have to take strategic decisions about
how far below EVC they price.
• EVC Analysis can be used as
• To guide pricing
• As a diagnostic tool for underperforming products
Segmentation Basics
• Reference price will vary across customers, because “next best alternative” differs
• Differentiation value will vary across customers, because usage scenarios and
intrinsic valuations differ
• Segmentation tries to cluster customers into a smaller number of well-defined
“types”
• Pricing strategy targets these types with different products, features and offers
Strategic assessment of whether firm should
move from one-price to multiple price strategy
Does my product offering have differentiation value? i.e.
it is not totally “commodified”
Can I identify 2+ customer value profiles who
theoretically have different EVCs for my product?
Can I empirically identify these segments?
Can I actually implement a pricing strategy based on
these segments?
Hypothetical EVC profiles for radiology
EVC
6400
5800
Defense Systems
Radiology Imaging Labs
4400
Hospitals
3900
Ambulatory Facilities
3500
2800
Slide credit: Catherine Tucker
Doctors
Animal Hospitals
Millions of $ of market potential
We can reorganize value profiles to construct a
demand curve
EVC
6400
5800
4400
3900
3500
2800
Defense
Systems
Radiology
Labs
Ambulatory
Hospitals Facilities
Doctors
Millions of $ of market potential
Slide credit: Catherine Tucker
Animal Doctors
How can we effectively charge a different
price to these segments?
Three forms of price discrimination
• Direct (aka “3rd degree”)
• Different prices based on customer characteristics
• Has to be observable and legal
• Product-based or “indirect” (aka “2nd degree”)
• Offer multiple versions to all and allow consumers to “self select
• Examples: bundling, versioning (“good, better, best”), quantity discounts
• Perfect (aka “1st degree”)
• Charge each consumer her WTP.
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Slide credit: Preston McAfee
Direct Price Discrimination
• AKA customer value-based pricing
• Charge based on customer characteristics
• Student, elderly, enterprise
• Location, e.g. zone pricing
• Tied into other purchases
• Problem: Arbitrage
• Ex. How can you prevent doctors from buying as if they were a vet?
• Sometimes mechanisms exist to verifiably link customers to segment, like
a .edu email address, often you cannot
Implementation of customer-based
segmentation is challenging
Unambiguous indicator of group membership
Product must not be tradable across group members
Group membership must correlate with EVC
Must be legal
Must be acceptable
Indirect Price Discrimination
• Coupons/rebates
• Payment models (up-front, pay-as-you-go, etc.)
• Quantity discounts
• Timing
• Branding
• Multiple versions with different features offered to all
Solves arbitrage by “self-selection”
Coupons and Quantity Discounts
• Coupons and rebates are used by those with a low value of
time
• Value of time correlated with price sensitivity
• For a single product, quantity discounts work by correlation of
family size and price sensitivity
• Large families usually have tighter budgets than single people
• When selling multiple products, quantity discounts work in
different ways
• Customer may be unlikely you have a high valuation for many products
• “Additional products” get a low price that is not offered widely.
• Also works due to budget concerns---if I am near your budget (high quantity), you get more price sensitive
NY Times ad rates uses quantity discounts
Color
US ½ page: 133K
US Full page would be 266K, but is
actually 214K, or about 20% off.
Same 20% discount applies
internationally
B/W
½ page: 97K
Full page would be 196K, but is
actually 178K, or about 10% off
In other markets, discount is 20%
Do NY Times ad rates make sense?
• Lower per square inch price for large units
• Large ads are more disruptive to the newspaper, so arguably have “super linear costs” (e.g. a
whole page is a bigger disruption, harder to fit than 2 half page ads)
• Can always split a whole page into two half pages ads, so cost of half page ad is *at most*, ½
the cost of the whole, and maybe less
• How can we explain this:
• Values: 2 half pages more desirable than one whole page? Maybe, but maybe the opposite.
• Price sensitivity: Advertisers that can afford a whole page are *more* price sensitive?
Unlikely.
• Market power: there are more competitors for whole page ads, so the NY Times has lower
margins. Very unlikely.
• Market thickness: lots of demand for half page ads, limited, but some demand for whole
page ads (“too expensive”). Maybe.
• It’s a mistake. Maybe.
List prices versus realized prices
• ARPU: average revenue per unit, or average prices. If sales team has pricing
discretion, these will tend to differ
• A common sales scheme:
• List price: the starting point for negotiations
• Floor price: the absolute rock bottom price the salesperson cannot go below
• Incentive compensation = f(total sales, ARPU). Example:
• Commission = .1*(Q*ARPU - .9*Floor). Sales person gets 10% the revenue that is in excess of
selling at 90% of the floor price.
• Sales person has two incentives: close deals (want to offer lower price) and keep prices high
(increases commissions if sale will still be made)
Product based price discrimination
• The demand curve reminds of us of our missed pricing and
segmentation opportunities
• Product-based segmentation success rests on identifying key
differentiation value to distort and persuading customers of the
fairness of the segmentation.
Product based price discrimination
• Different versions in a product class
• Includes product attributes, included add-ons and bundling
Necessary conditions for product-based
customer segmentation
Correlation of attribute with EVC
Distortion (altering products)
Compensation
Ex. Capacity
(note: 16GB flash memory cost about $15
at the time, 3G chips cost much less than
$130)
Identifying the right kind of feature
Not Integral to the brand
Features that customer segments have
widely differing values
We’ll discuss how to use conjoint and
statistical methods
Payment models: two part tariff
Definition: A firm charges a two part tariff if it charges a per
unit fee, p, plus a lump sum fee (paid whether or not a
positive number of units is consumed), F.
This, effectively, charges demanders of a low quantity a
different average price than demanders of a high quantity.
Example: hook-up charge plus usage fee for a telephone,
club membership, etc.
This is a form of indirect price discrimination because it does
not rely on knowledge of customer valuations or group
membership.
36
Damaged goods: intentional reduction in the value of the
product in order to price discriminate
• Amazon “super saver” free shipping (7-10 days)
• Hold
thethis
itemreduction
in the warehouse
forcomes
a few days
Note:
in value
at a positive
• Copied
bythe
many
online
retailers, price
sensitive
consumers willing to wait,
cost to
firm.
Producing
a piece
of hardware
some people pay for “standard”
with fewer features is a different, but related,
• IBM LaserPrinter E
concept.
• Added
chips to slow processing
• Sony 74, 60 minute mini-discs
• differ by instructions on disc
• Throttling of internet speeds when there is no congestion
IBM LaserPrinter 5E
(4029-010)
IBM LaserPrinter
10L (4029-040)
38
Sharp DV740U Missing Button
39
Sharp DV740U Missing Button
40
Tracking shows that FedEx holds 2-day delivery
packages at distribution centers to reduce chance
they arrive in 1 day (intentional delays)
Due to increased routing complexity, it actually
costs FedEx to reduce the quality of the service…
why is this profitable?
Pushes high value of speed customers into one day
who would otherwise risk two-day
Differentiation to justify price differences
Note the arrow
43
Question: would this make sense if there were only
the following two types of customers?
1. Those that absolutely need overnight
2. Those that only require it arrives in 2-days
Answer, no. It only makes sense if there are three (or more) types,
those that:
1. Absolutely require overnight
2. Desire a good chance at overnight delivery
3. Just want delivery within 2-days.
The intentional delay strategy tries to drive group 2 to purchase costly
overnight shipping, which is paired with an “overnight guarantee”
Takeaway
The success of a damaged good strategy depends
critically on the types of consumers in the
marketplace and their relative frequency
Perfect Price Discrimination
• Theoretical standard: charge everyone their willingness
to pay, provided this exceeds costs
• In practice, impossible to achieve.
• View this as a benchmark
Example:
P
All customers are identical and have demand
• P = 100 – Q
100
• MC = AC = 10
• What type of payment scheme makes sense?
4050
10
48
90 100
Q
What is the optimal two-part tariff?
Two steps:
(1) maximize the benefits to the consumers by charging p = MC = 10.
(2) capture this benefit by setting F = consumer benefits = 4050.
(3) Goal is to extract maximum revenue from each customer
In essence, the firm maximizes the size of the "pie", then sets the lump sum fee so
as to capture the entire "pie" for itself.
The total surplus captured!
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Two-part tariffs with multiple types
Often better to charge the surplus of the
lower type consumer (A) and set a higher
price, 𝑝𝑚
In general, prices will be shaded up from
marginal cost because the entry fee will not
equal “high types” surplus (I can now raise
price on them a bit)
Figure source: Wikipedia
Examples of two-part tariffs
Phone contracts
• Monthly fee + usage charges (some included usage for “free” as well)
Cover charges
• Fee to get in + prices to drink/eat
Clubs
• Membership fee + usage fee (e.g. per visit, to play golf, etc.), also used for rentals, e.g. Zipcar
• May allow options with no membership, e.g. daily use, to appeal to travelers or causal users
Other methods of price discrimination
• Budget constraints
• Pay-as-you-go model can overcome budget constraints. Ex. “go phone”
• Can also help with the “sticker shock” of a big upfront price and expand market
• Sales force negotiated prices
• Salesperson has a range of “approved” prices and have incentives to sort out buyer valuations.
• Guarantees/warrantees & branding
• Appeal to certain sets of consumers, can be thought of as “added value” for these customers
• Timing
Timing
Price sensitive
customers wait for
a good deal
Timing
Not all products
show this much
variation.
Timing
Flash sales
Why timing can work
• Two sets of consumers, “shoppers” (price comparers) and “loyals” (show up and
buy)
• if firm knows rivals’ price, wants to undercut it slightly
• at low prices, would rather have high price sold only to loyal customers
• leads to randomization and price cycles
• Price sensitive customers will wait, die-hards want it now
• Hardbacks vs. paperbacks
• Video on demand prices start at high “purchase only” price and drop to low rental price over time
• The distribution of customers into “shoppers” vs. “loyals” or patient vs.
impatient can vary by product or over time
• For laptops/tv’s vs. headphones, we should see less price variation for the higher priced goods
• Supermarkets run sales on goods valued by price sensitive shoppers (milk, paper towels, cola, diapers) or when people are
likely to be “looking around” (Thanksgiving turkeys, Super Bowl chips, etc.)
• Price competition is highest during peak holiday shopping period
Branding
Branding
Branding
• Especially common in consumer packaged goods
• Premium brands vs. “low end”
• Often the products are very similar
• Legal issues
• Selling exact same product with different claims can be illegal
• E.g. selling same contact lens, but different recommended usage times,
was deemed fraudulent
• Can create a perception of competition and differentiation when
there in reality it is quite limited
Intro to modeling a
demand curve
Goal: measure “slope and shifters”
• Slope/elasticity: what is the response in terms of quantity sold to
price changes (this may be different at various price levels)
• Shifters: factors that shift the demand curve. E.g. seasonal
components, promotional activity, etc.
• It’s possible that external factors will change the slope as well. For
instance, for holiday shopping, people buy more consumer goods
overall, but are also more price sensitive due to holiday shopping
budget and when buying stuff for other people one cares more
about price than the “perfect fit” (relatively speaking)
Using logs
• Recall:
𝑦 = 𝑎𝑥
ln 𝑦 = ln 𝑎 + ln 𝑏
𝑦 = 𝑎𝑥 𝑟
ln 𝑦 = ln 𝑎 + r ∗ ln 𝑥
𝑦 = 𝑒𝑥
ln 𝑦 = 𝑥 ∗ ln 𝑒 = 𝑥 ∗ 1 = 𝑥
Find elasticity two ways
𝑦 = 𝑎𝑥 𝑟
𝑦 = 𝑎𝑥 𝑟
𝑑𝑦
= 𝑟𝑎𝑥 𝑟−1
𝑑𝑥
ln 𝑦 = ln 𝑎 + 𝑟 ∗ ln(𝑥)
𝑑𝑦 𝑥 𝑟𝑎𝑥 𝑟
∗ =
=𝑟
𝑟
𝑑𝑥 𝑦
𝑎𝑥
Elasticity
𝑑𝑙𝑛(𝑦)
=𝑟
𝑑𝑙𝑛(𝑥)
For small changes,
gives the elasticity too
More generally
𝑑𝑦
𝑑𝑙𝑛(𝑦)
𝑑𝑦 𝑥
𝑦
=
=
= elasticity
𝑑𝑙𝑛(𝑥) 𝑑𝑥 𝑑𝑥 𝑦
𝑥
Constant elasticity demand curve
𝛾 𝑥′𝛽
𝑞=𝑝 𝑒
ln 𝑞 = 𝛾 ∗ ln 𝑝 + 𝑥 ′ 𝛽
Even if this function is correct, in practice there will be noise in the data
ln 𝑞 = 𝛾 ∗ ln 𝑝 + 𝑥 ′ 𝛽 + error
R-squared and related measures tell you how much of the data is “explained by the
model” vs. in the error term
Constant elasticity demand curve
• Simple functional form, gives a useful baseline
• Elasticity may often be constant in the “relevant range” of prices
• Statistical tests should be used to see if different functional forms
provide better fit to the data
Assignment
Data: 83 Chicago-area stores
At weekly level:
• Sales (“log move”)
• Average sales price
• Whether advertised (“feat”)
At store level:
• Various demographics of the shoppers
Data taken from:
“Determinants of Store-Level Price Elasticity” Stephen J. Hoch, Byung-Do
Kim, Alan L. Montgomery and Peter E. Rossi
Journal of Marketing Research Vol. 32, No. 1 (Feb., 1995), pp. 17-29
Data available here:
www.justinmrao.com/econ404/oj.csv
Data
Log of quantity sold
each week
Price is not logged
Demographics of
shoppers by store
We’ll study 3 brands,
“dominicks” is the
store’s brand
1 if advertised that week
by that store, 0 if not
For the purposes of the assignment
• Assume the store randomly changes the price of various brands of
orange juice, and then chooses to pair the price change with
advertising or not (so advertising and price can be correlated)
• Start by assuming a constant elasticity of demand function
Linear Regression in R
regoutput = glm(y ~ var1 + var2 + … + varK, data=mydata)
Formula to estimate, y is
the LHS, the RHS is a linear
function of the vars
The data frame that
contains the variables in
the estimating equation
regoutput is an object with many useful outputs
Summary(regoutput) prints the coefficients and basic diagnostics
Coef(regoutput) gives a vector of the coefficients
Fitted.values(regoutput) gives a vector of the fitted values of y
Predict(regoutput, newdata=mynewdata) predicts new values for “scenarios” given
in new data sets
Using R for the Assignment
myfirstmodel = glm(logmove ~ log(price)+ vars, data=oj)
• In the assignment, you will estimate and interpret models of this type