ECON 2160 Lecture Notes - Lecture 5: Adverse Selection, Risk Premium, Risk Neutral
2 May 2018
School
Department
Course
Professor
“a
Adverse
selection
-
The
Lemon
Problem
One
of
the
big
suppositions
In
the
theory
on
perfectly
competitive
markets
and
our
work
with
game
theory
to
this
point
is
that
all
the
participants
have
complete
and
equal
information
regarding
the
transaction.
When
players
have
a5ymmetric
information,
this
can
lead
to
a
market
or
game
resulting
suffering
from
adverse
selection.
Asymmetric
information
can
be
any
information
inequality
between
parties.
it
does
not
always
have
to
be
one
knows
something
and
the
other
doesn't.
It
can
also
be
the
situation
where
one
knows
more
than
the
other
or
where
there
is
common
knowledge
between
the
players
and
private
Information
as
well.
You
can
visualize
the
Information
set
as
a
Venn
Diagram.
Any
situation
where
the
circles
for
two
players
are
not
exactly
on
top
of
each
other
(concentric
with
equal
radii),
there
is
Information
asymmetry.
Asymmetric
Information
most
often
leads
to
the
market
failure
named
Adverse
Selection.
The
term,
Adverse
Selection,
comes
from
the
insurance
Industry
and
is
one
of
the
biggest
challenges
in
insurance
underwriting.
If
the
people
you
are
trying
to
insure
have
an
incentive
(lower
premium)
to
either
lie
or
hide
information,
then
the
Insurer
can
miss
assign
the
risk
premium
needed
to
properly
insure
those
people.
As
a
result,
if
the
Insurer
wants
to
stay
in
business
in
the
long
run,
it
must
charge
a
premium
where
It
assumes
some
of
the
information
it
is
getting
on
coverage
risk
is
wrong.
Thus,
it
has
to
charge
a
premium
that
is
higher
than
the
truthful,
low-risk
people
would
want
to
pay.
Hence,
all
the
insurer
gets
are
those
people
with
high
risk
to
buy
the
policy.
However,
those
who
may
believe
they
are
truly
low
risk
may
be
high
risk
or
become
high
risk.
Therefore,
an
efficient
insurance
market
where
everyone
to
be
covered
has
some
probability
of
being
very
risk
needs
to
have
everyone
be
able
to
buy
the
policy.
We
can
see
this
play
out
in
health
insurance.
Some
may
be
easily
categorized
as
high
risk
due
to
past
issues
or
simple
test
and
observations,
while
others
may
appear
to
below
risk
are,
in
fact,
high
risk
(e.g.
hidden
genetic
disease)
or
become
high
risk
(e.g.
traffic
accident).
A
classic
model
looking
into
this
circumstance
is
called
the
Lemon
Model
(Akerlof,
1970).
The
situation
is
there
are
two
types
of
used
cars.
Good
ones:
Oranges
and
Bad
ones:
Lemons
Sellers
of
Oranges
will
sell
at
$12,500
and
up.
Sellers
of
Lemon’s
will
sell
for
at
least
$3000.
The
maximum
buyers
are
willing
to
pay
for
an
Orange
is
$16,000
and
the
maximum
for
3
Lemon
is
$6,000.
In
the
market,
regardless
of
whether
the
car
is
an
Orange
or
a
Lemon,
it
will
have
the
same
price.
To
help
the
model
come
to
specific
results,
without
losing
its
applicability,
we
assume
there
are
enough
buyers
in
the
market,
compared
to
cars
available,
where
the
price
will
be
bid
up
to
the
buyer’s
maximum
wiliness
to
day.
This
assumption
removes
any
uncertainty
about
the
price
paid
and
whether
the
market
will
clear.
It
is
possible
to
relax
this
assumption.
Doing
so
doesn’t
shed
more
light
on
the
basic
concept,
but
the
math
does
get
messier.
Our
numbers
in
table.
tam—.-
sewerswnme
ear-.m-
As
we
can
see,
any
otter
irom
a
Buyer
below
$12,500
will
guarantee
the
car
is
a
Lemon,
as
Orange
sellers
will
not
put
their
car
up
lor
sale
at
that
prrc‘e.
However,
an
oller
above
$12,500
does
not
guarantee
that
the
car
offered
for
sale
is
an
Orange.
There
is
just
the
possibility
that
it
is
one.
As
this
is
the
case,
the
Buyer
then
needs
to
think
of
their
expected
value
or
the
car
they
purchased.
An
important
concept
is
the
level
of
risk
a
buyer,
in
this
case,
is
willing
to
assume.
To
help
ease
the
model,
we
are
going
to
say
our
buyers
are
"risk
neutral."
Risk
neutrality
simple
means
as
long
as
the
value
or
expected
value
received
is
greater
than
Its
cost,
the
transaction
takes
placemp'ly
put,
lfthere
l
thbflu'm,
the
rlslt
neutral
agent
does
thinlvltyfihere
is
no
compensation
for
the
risk
taken.
it
is
possible
to
include
risk
aversion
in
to
models.
However,
it
doesn’t
add
much
more
to
our
understanding
of
the
underlying
concept
at
this
point.
Would
there
be
a
used
car
market,
including
both
types
of
cars,
if
there
are
3
Oranges
for
every
2
Lemons
for
sale,
or
the
used
car
supply
is
60%
Oranges?
What
would
be
a
car
buyers
expected
value
of
any
randomly
drawn
car?
"but,"
:2
Probablity
of
Orange
*
Value
of
Orange
+
Probablity
of
Lemon
1:
Value
of
Lemon
For
our
numbers,
we
get
EVbuyer
=
.6(16,000)
+
.4(6,000)
=
12,000
The
risk
neutral
car
buyer
will
offer
a
seller
no
more
than
her
expected
value
of
the
car.~"|n
this
case,
the
offer
of
$12,000
isn’t
enough
to
have
an
Orange
be
sold.
Therefore.
only
lemons
will
be
for
offer
-
there
a
is
no
market
with
both
types
of
cars
for
sale
at
this
proportion
of
Oranges
to
Lemons.
How
do
we
find
the
’cut
off
point’
or
the
minimum
proportion
of
Oranges
available
to
have
a
functioning
market?
If
we
say
the
probability
of
an
Orange
is
"f",
then
the
probability
of
a
Lemon
is
(1-f).
We
would
rewrlt'e
our
buyer's
expected
value
as
Eme,
=
f(16,000)
+
(1-f)(6,000)
=
10,000f
-
6000
As
the
Expected
value
of
any
random
car
needs
to
be
more
than
12,500
to
guarantee
there
being
Oranges
for
sale
EVbuyer
—>
orangereservation
price
10,000f
—
6000
_>
12500
10,000f
>._
6500
[2.65
in
order
tor
the
martet
to
function.
there
need
to
be
at
least
a
65%
chance
at
any
randomly drawn
car
tor
sale
being'
an
Orange,
We
can
then
use
our
simple
model
to
see
what
happens
when
we
have
changes
to
demand
for
Orange
can,
An
increase
in
demand
lor
Oranges
would
rais'e
the
maximum
willingness
to
pay
of
them
-
let’s
say
to
180m.
f(i8.000)+
(1
—
[)(6.000)
2
12500
12,000;
2
6500
f
z
.54
Now
that
may
seem
a
little
counterinturt‘ive.
The
demand
for
good
cars
increasing
actually
means
the
number
of
good
cars
for
sale
can
decrease
and
the
market
still
functions.
Why
do
you
think
this
is?
What
happens
if
the
sellers
feel
their
Oranges
are
more
valuable?
Now
they
require
14,500
to
sell.
We
will
go
back
to
the
original
values
for
buyers.
[(16,000)
+
(1
—
f)(6,000)
2
14500
10,000f
—
6000
>_
14500
f
>_.
.85
The
increase
in
value
from
the
sellers
perspective
increases
the
number
of
good
cars
needed
to
make
the
market
function.
Why
do
you
think
this
is
the
case?
Now,
to
be
good
economists,
we
would
be
reticent
to
do
both
changes
in
the
same
model
as
we
cannot
fully
ascribe
causality,
but,
let’s
do
it
anyway.
f(18,000)
+
(1
—
f)(6,000)
>_
14500
12,000f
>_
8500
f
>_
.71
Now
we
may
have
assumed
the
two
factors
would
have
canceled
each
other
out,
but
we
see
the
increase
in
the
price
from
the
sellers
point
of
view
is
more
impactful
than
that
of
the
buyer’s
increase
in
demand.
Thus,
we
see
more
good
cars
on
the
market.
We
can
see
what
price
the
sellers
can
ask
for
if
they
see
the
increase
of
demand,
when
they
have
65%
of
the
cars
on
the
lot
being
Oranges.
.65(18,000)
+
(.
35)(6,000)
=
X
13,800
=
X
This
is
that
we
would
expect.
An
increase
in
demand
would
increase
the
price
of
the
item,
given
a
constant
supply.
And
this
makes
more
sense
as
it
would
be
easier
for
sellers
to
change
the
price
of
a
car
than
to
change
the
proportion
of
cars
on
their
lot.
Document Summary
One of the big suppositions in the theory on perfectly competitive markets and our work with game theory to this point is that all the participants have complete and equal information regarding the transaction. When players have a5ymmetric information, this can lead to a market or game resulting suffering from adverse selection. Asymmetric information can be any information inequality between parties. it does not always have to be one knows something and the other doesn"t. It can also be the situation where one knows more than the other or where there is common knowledge between the players and private. You can visualize the information set as a venn diagram. Any situation where the circles for two players are not exactly on top of each other (concentric with equal radii), there is. Asymmetric information most often leads to the market failure named adverse selection. Adverse selection, comes from the insurance industry and is one of the biggest challenges in insurance underwriting.
