Review

1
Review

• Own price elasticity
• Empirical estimation of demand curve
• Linear and log-log model
• Interpretation of coefficient and computation of
  price elasticity.

2
Lecture 11Price Discrimination 1
3
Introduction

• Price dispersion different prices for the same
  product - is prevalent in the marketplace
• The law of one price is dead
• Example Microsoft software version and upgrade
  prices
• Example Prices of 1/3 liter Coca-Cola cans in
  Germany

4
Prices of 1/3 liter Coca-Cola cans
Point of Sale Price (DM) Index
1. Large supermarket 0.64 100
2. Grocery store 0.69 108
3. Bakery 0.80 125
4. Vending m/c university 0.90 141
5. Gas station 1.20 188
6. Vending m/c street 1.50 243
7. Newsstand - street 1.60 250
8. Newsstand airport 2.00 312
9. Newsstand Train station 2.20 344
5
Example Student rates

• Why do software manufacturers have lower rates
  for students?
• One explanation is that they have lower
  willingness to pay higher elasticity than
  business users.
• Charging two prices is more profitable

6
Example Airline pricing

• Why do airlines have first class rates often
  2-3 times higher than cabin?
• There is a small group of elite customers who
  are less price elastic than regular customers
• It is more profitable to charge two prices
• The elites must be fenced in from buying
  cabin seats by making cabin seats uncomfortable

7
Illustration of benefits of price customization
Price ()
100
Demand curve
Gross Margins (p-c)q
p
c10
0
1000
q
8
Remember the meaning of the demand curve
The demand curve is an aggregation of the demands
of individual or segment, who have different
reservation prices (max. willingness to pay)
Price ()
q
0
Ideally, charge each customer their reservation
price (as long as it is above c) (i) no
profitable customer is excluded from buying and
(ii) no money left on table.
9
A single price is inefficient
Money left on the table
Price ()
100
Profit (p-c)q
No trade deadweight loss
p
c10
0
q
1000
10
Calculation

• The demand function is
• p 100 0.1q
• The profit-maximizing price is
• The demand at the profit maximizing price is
• The profit (gross margins) is

11
Demonstration of benefits using 2 price points
Price ()
Rule of 1/3 for linear demand functions
100
p1
p2
c
0
1000
q1
q2
12
Calculation
p a bq
q A Bp

• Assume that we can put a fence that prevents
  higher price customers from paying the lower
  price, also, c10
• The demand function is q D(p) 1000 10p
• Profit at prices p1 and p2 are
• The profit-maximizing prices are
• The maximized profit is

(p1-c)D(p1)(p2-c)(D(p2)-D(p1))
p2 40, p170
(70-10)300(40-10)(600-300)27000
13
Calculation
p a bq
q A Bp

• In general, in the case of the linear demand,
  constant variable cost and two prices, the
  profit-maximizing prices are
• p2 (2c a)/3, or p2 (2cB A)/3B
• p1 (2a c)/3, or p1 (2A cB)/3B

14
This is price discrimination

• Charging different prices to different people for
  the same (or similar) product.
• Since discrimination has a negative
  connotation, call it price customization
• A useful result - Most of the benefit of price
  customization may be realized with relatively few
  price points

15
Implementation

• Key problem How do we prevent higher
  willingness-to-pay customers from paying the
  price meant for lower willingness-to-pay
  customers?
• Place fences that corral customers

16
Next Lecture

• Price Discrimination 2 - Implementation