MARK 7397
Spring 2007
Customer Relationship Management:
A Database Approach
Class 12
Lemons and Signals
James D. Hess
C.T. Bauer Professor of Marketing Science
375H Melcher Hall
jhess@uh.edu
713 743-4175
Noah
Hess
Noah
Noah
Hess
Hess
Noah
Lemons and Peaches
Number of
Computers
b=part-worth
of quality for
owners
bV - P  0
N
Supply
of Lemons
P/b
1
V, Value of
Remaining
Product Life
Demand for
Computer of
Value V
Number of
Computers
V - P  0
N
N
Demand
P/V
1

Taste for
Quality
V
1
P
Price
Suppose Quality is Observable
Price depends on value of computer: PV
A mutually beneficial exchange is possible if
bV < PV < V for some .
Suppose the highest value computer is sold to buyer with highest
taste for quality at the highest willingness to pay. Then all V above
b will be sold, and total exchange will be (1-b)N.
Suppose Quality is Known only by Seller
Price is the same for all computers, P.
PN / b if P b
Supply is 
1 if P  b
Number of
Computers
Expected quality= ½ P/b
Buy if  ½ P/b - P  0
N
Demand is
Supply
of Lemons
P/b
1
 N(1  2b)if b 1 / 2

 0if b  1 / 2.
V, Value of
Remaining
Product Life
Equilibrium Price and Exchanges:
If b < ½ , P*=b(1-2b) and Supply=Demand=(1-2b)N
If b > ½ , P*=0 and Supply=Demand= 0
Akerlof’s Theorem: Differences in information about the quality of products
cause the market to perform poorly or even stop operation entirely.
George Akerlof, Nobel Prize Winner 2001
"I submitted it (“The Market for Lemons”) in June, 1967 to the American Economic Review. I got a reply from the editor
which said that the article was interesting but the American Economic Review did not publish such trivial stuff." The
article next went to the Journal of Political Economy. Again it was rejected. Akerlof kept trying. "I next sent the article to
the Review of Economic Studies. I had been urged by one of its co-editors to do that. Instead it went to another editor
whose view of 'The Market for 'Lemons" was decidedly less favorable. It was rejected on the grounds again that it was
'trivial.' Finally I sent it to the Quarterly Journal of Economics which accepted it with some degree of enthusiasm."
Akerlof believes that journal editors refused the article both because they feared the introduction into economics of
informational considerations and “...they also almost surely objected to the style of the article which did not reflect the
usual solemnity of economic journals."
Talk is cheap,
but cheaper for high quality brands
A new brand is about to be introduced that can have high or low quality: VH=2
or VL=1. The company learns the quality of its brand from pre-test markets
but the general consumer does not and thinks the probability of a high quality
brand is .
Cost of advertising: A/2 for the high quality firm
A for the low quality firm,
where A is the target advertising rating points.
Profit p(A,P|V)=P-A/V, where V{1,2}.
P
Iso-profit of V=1
Iso-profit of V=2
2
1
1/2
1
A
 P  A / 1 for V  1
p
P  A / 2 for V  2
Separating Low and High Quality
P
Iso-profit of V=1
Iso-profit of V=2
2
1
H
L
A
 P  A / 1 for V  1
p
P  A / 2 for V  2
Separating Equilibrium
P
Iso-profit of V=1
Iso-profit of V=2
2
1
A
 P  A / 1 for V  1
p
P  A / 2 for V  2
Spence’s Theorem: The only intuitive Nash equilibrium in the signaling game is the separating
strategies (AL,PL)=(0,1) and (AH,PH)=(1,2).
Michael Spence won the 2001 Nobel Prize in Economic Science (sharing it with George Akerlof and Joseph Stiglitz).
This was unusual because the award cited his doctoral dissertation, Market Signaling. Unlike Akelof, whose “Market for
Lemons” was not well-received immediately, Spence was a superstar out of the gate. He wrote his dissertation in 1972
and by 1975 was a Full Professor at Harvard; normally this takes a dozen years. In fact, after that dozen years, Spence
was the Dean of the Faculty at Harvard.
Spence’s work created lots of heat. Why?
The total welfare of the economy is the sum of expected profits of the company
and the consumer surplus: TW=Ep+CS=(2-1/2)+(1-0)(1-) + 0=1+/2.
Suppose that advertising was not legally permitted. Then the total welfare would
come from a pooled equilibrium where price is 1+. It is always the case that
1+/2 < 1+, so
•The use of advertising by the seller as a signal of quality dissipates
society’s resources.
•The use of higher education as a signal of personal talent dissipates
society’s resources.
Capital One: Signaling Model
T=teaser rate for transfer of balances
CA=checking account balance (signal)
Cost of funds=10%
Segment 1: size=a, would contribute beyond a 0% teaser year by holding debt for 2 more years
Segment 2: size=1-a, would break even with teaser rate of 10% and payoff all balances
Cost of maintaining checking account balances: for segment 2 twice as high as
for segment 1.
U1 = V – T – ½ CA versus U2 = V –T – 1.0 CA
T
.10
A
C
D
CA
.00
B
.10
.20
T
.10
A
C
D
CA
.00
B
.10
.20
Offer A and B: both segments choose B (pooling)
profit = a(-.10+.10+.10)+(1-a)(-.10) = -.10 + .20a
Offer A and D: segment 1 chooses D and segment 2 chooses A (separating)
profit = a(-.10+.10+.10)+(1-a)(.10-.10) = .10a
Separating is preferred to pooling by CapOne so long as a<1.
Competition may force D down to C.