SI 425: Introduction to User Modeling
Lecture B3: Prices and Price Discrimination
Tanya Rosenblat
University of Michigan
September 18, 2016
Demand and Supply
In order to derive prices we have to understand both demand
(what consumers want) and supply (how much does it cost to
produce a good).
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Since the focus on this course are consumers we will adopt a
very simple specification of supply.
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Firms can produce goods at a constant cost c per item.
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For example, a cloud storage provider might provide 1GB of
online storage at a cost of 10 cents per GB and year.
“Many firms”: Competitive Equilibrium
When there are many firms (such as Google Drive, OneDrive,
Dropbox) firms have little to no pricing power.
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They cannot set prices below their cost c because they would
otherwise make a loss.
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They cannot set prices above c either because their
competitors would undercut them and steal their market.
The supply curve specifies that any amount Q is provided at cost
c per unit.
“Many firms”: Competitive Equilibrium
Equilibrium price and
quantity is determined by
the intersection of supply
and demand.
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P = $0.10
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equilibrium quantity
Q
PGB
Demand curve
Supply curve
P = $0.10
Q
Storage (in GB)
“One firm”: Monopoly
When there is only one firm firms have pricing power and can set a
price higher than marginal cost:
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The monopolist maximizes total profit:
max (P(Q) − c) Q
Q
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We can use the first-order condition to find Q:
P(Q) − c + QP 0 (Q) = 0
Aside: Point Elasticity of Demand
Assume that we want to
calculate the elasticity of
demand at point A on
demand curve where we
change price and quantity
just slightly.
E
=
PGB
A
∆P
∆Q
∆Q
Q
− ∆P
P
= −
P 1
∆P
Q ∆Q
≈ −
P
QP 0 (Q)
Storage (in GB)
“One firm”: Monopoly
We can simplify the first-order condition:
P − c + QP 0 (Q) = 0
P
= 0
P −c −
E
P = c · E /(E − 1)
Monopolist sets price above marginal cost for elastic demand.
Note:
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The more elastic demand is, the closer the price is to the
competitive price P = c
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when prices are inelastic the monopolist will increase price
indefinitely because every 1% price increase raises her profits
by Q(1 − E )%.
Price Discrimination
In many cases, different customers of a monopolist have more or
less elastic demand.
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In these cases, the monopolist would like to set higher prices
for consumers with inelastic demand.
We distinguish between 3 types of price discrimination.
First-degree Price Discrimination
Monopolist can set a different price for each consumer.
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This is rarely possible.
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It requires (a) a lot of information about customers and (b)
the ability to prevent any resale between high-price and
low-price customers.
Third-degree Price Discrimination
Monopolist can set a different price for certain identifiable
types of consumers.
Examples:
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Student discounts (with student ID)
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Senior discounts in movie theaters
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Family memberships versus Individual memberships (verify
last names and age).
Second-degree Price Discrimination
Monopolist cannot identify consumers types but can create
variants of the product which appeal to different consumer
types.
Examples:
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Business class airline tickets can be exchanged while other
tickets have high change fees.
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Intel sells unlocked CPUs at a high price (for gamers) and
locked CPUs for everyone else.
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Printer manufacturers sell consumer printers at low price with
high ink costs and business printers at high price with lower
ink costs.
Second-degree Price Discrimination
Second-degree price discrimination often involves degrading the
variants that are intended for high-elasticity consumers.
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This prevents low-elasticity/high value consumers from
defecting to the lower-price variants.
Case study: Hubspot
Hubspot was founded in 2006 and focuses on inbound marketing.
I Inbound marketing draws consumers in rather than distract
them through advertising.
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recipes on the Whole Foods website
company blogs
Twitter feeds and Facebook pages
Hubspot provides the tools to run inbound marketing
campaigns.
Case study: Hubspot
Case study: Hubspot
Lower-cost plans are degraded to prevent switching of high-value
customers.