Other Applications
 “Equilibrium in Competitive Insurance Market:
An Essay on the Economics of Imperfection”,
by Rothschild and Stiglitz, 1976 Quarterly
Journal of Economics
 “Credit Rationing in Markets with Imperfect
Information”, by Stiglitz and Weiss, American
Economic Review, June 1981
ECON3014 - The Economics of Information
1
Insurance Market with Asymmetric Info
 Price (premium) for insurance: Not just a
price, but both a price and a quantity together
due to asymmetric information
 Insurance sellers cannot distinguish high-risk
or low-risk insurance buyers (policy holders)
 If insurance buyers are willing or able to
reveal their information, both buyers and
sellers are better off
ECON3014 - The Economics of Information
2
What is Full Insurance
• Moving from E to A means
reduction in uncertainty
• A means no uncertainty
• An insurance move you from E to
A is a Full Insurance/Coverage
𝑊
45 degree line:
Certainty Line
A: Certainty state
𝑊
E: Uninsured state, (𝑊 , 𝑊 )
𝑊
ECON3014 - The Economics of Information
𝑊
3
What is Full Insurance?
1) Good-State:
2) Bad-State:
 Insurance premium (price), you have to pay
no matter in Good-State or Bad-State:
 Therefore, if you CAN buy full insurance (i.e.
no uncertainty in wealth):
1) At Good state:
2) At Bad state:
 Given A is on the certainty line, the insurance
is full insurance
ECON3014 - The Economics of Information
4
What is Full Insurance?
• Insurance policy, you give up 𝛼 in both states and receive a
compensation of 𝑑 at Bad-State, or
• You give up 𝛼 at Good-State for 𝛼 at Bad-State
• Therefore, the blue line represents the Supply of Insurance
45 degree line:
Certainty Line
A: Certainty state
𝛼
𝑊
𝑑
E: Uninsured state, (𝑊 , 𝑊 )
𝛼
𝛼
𝑊
ECON3014 - The Economics of Information
𝑊
5
What is Full Insurance?
 In other words, an insurance buyer is selling
his wealth at good state to exchange for
wealth in bad state or in other words, selling
his/her risk in wealth
 Similarly for insurance sellers
ECON3014 - The Economics of Information
6
Insurance Seller’s Decision
• Should the Supply of Insurance line be the red or blue
line?
?
A: Certainty state
𝛼
𝑊
𝑑
E: Uninsured state, (𝑊 , 𝑊 )
𝛼
𝛼
ECON3014 - The Economics of Information
𝑊
7
Supply of Insurance Contracts
 Expected Profit for insurance sellers, given
is the probability of Bad-State, is:
 Assuming perfect competitive insurance
market, then
, therefore

tells you the “exchange ratio” between
wealth in good state and bad state
 Therefore, slope of supply of insurance line is
more step for smaller
ECON3014 - The Economics of Information
8
Supply of Insurance Contracts
 Stiglitz assumed perfect competitive
insurance market for simplicity: Zero profit
 Question: Above or below of the supply of
insurance line means?
ECON3014 - The Economics of Information
9
Supply of for Insurance Contracts
• Given 𝜋 , the Supply of Insurance is denoted by the blue line, with
slope =
• An insurance policy at B means a loss (negative profit) for the
insurance sellers
• An insurance policy at C means a loss (positive profit) for the
insurance sellers
• A competitive market will drive profit to zero for insurance sellers
B
risk-averse
A: Certainty state
𝛼
𝑊
𝑑
C
E: Uninsured state, (𝑊 , 𝑊 )
𝛼
𝛼
ECON3014 - The Economics of Information
𝑊
10
Demand of Insurance Contracts
 Utility of Individual with no insurance:

is the utility function,
refers to level of
wealth($), where
 If there is full insurance, which:
 Individuals will choose a insurance contract
which max their
 An individual can choose to buying no
insurance, when he purchases a contract
ECON3014 - The Economics of Information
11
Insurance Market with Perfect Info
 Assume are two type of insurance buyers:
High risk (H-R): High chance to get into BadState and file a claim (ask for compensation)
Low risk (L-R): Low chance to get into Bad-State
and file a claim (ask for compensation)
 How individuals trade-off wealth between
Good-State and Bad-State?
 Ans: Indifference curves
 First we focus on one type first (e.g. H-R
type)
ECON3014 - The Economics of Information
12
Insurance Market with Perfect Info
•
Slope of the indifference curve represents the trade-off
between Good-State and Bad-State
•
Given up the same amount at Good-State, how many to
receive in Bad-State to be equally happy
A: H-R type, full insurance
risk-neutral curve?
𝑊
E: Uninsured state, (𝑊 , 𝑊 )
ECON3014 - The Economics of Information
𝑊
13
Indifference Curves
 At point A (on 45 degree line), MRS =
 On 45 degree line, i.e.
,
, which equals the slope of supply of
insurance (profit zero)
ECON3014 - The Economics of Information
14
Indifference Curves
 How to derive MRS? Total derivative
 Move along an indifference curve means
ECON3014 - The Economics of Information
15
Indifference Curves
•
•
Red: H-R type
Blue: L-R type
𝑊
ECON3014 - The Economics of Information
E: Uninsured state, (𝑊 , 𝑊 )
𝑊
16
Insurance Market with Perfect Info
 If insurance sellers can tell who is H-R and
who is L-R type
 H-R type:
 L-R type:
 Insurance sellers can offer two different
insurance policy for H-R (A) and L-R type (B)
 The supply of insurance line for L-R will be
steeper than that of H-R, given slope:
ECON3014 - The Economics of Information
17
Insurance Market with Perfect Info
1. move to certainty case
2. not at any cost
3. red line is fair
Blue:good Red: Bad
slope=buyer's exchange cost
B: L-R type, full insurance
A: H-R type, full insurance
single－crossing property
substitution of good-state
and bad-state income
𝑊
E: Uninsured state, (𝑊 , 𝑊 )
ECON3014 - The Economics of Information
𝑊
18
Insurance Market with Perfect Info
 Both H-R and L-R types are better off than if
there is no insurance available
 Full insurance makes insurance buyers the
most happiest
 Insurance sellers make zero profit
ECON3014 - The Economics of Information
19
A h P
Another
Perspective:
i
The
Th D
Demand
d off
Insurance
 Insurance Buyers max its expected utility,
subject to the supply of insurance
 There is one choice variable:
ECON3014 - The Economics of Information
20
A h P
Another
Perspective:
i
The
Th D
Demand
d off
Insurance
 F.O.C.
ECON3014 - The Economics of Information
21
A h P
Another
Perspective:
i
The
Th D
Demand
d off
Insurance
 Assume zero profit for supply of insurance:
 Given
, further solve the F.O.C of
buyers
 Which means full insurance will be bought
under “fair insurance”
ECON3014 - The Economics of Information
22
Insurance Market with Asymmetric Info
 How about if insurance sellers cannot tell
who is H-R and L-R type, and still offer policy
A an B
 Which policy will H-R and L-R choose?
 L-R type will choose B (zero profit for
insurance sellers)
 Will H-R type choose A?
 No! H-R type will choose B as well!!!
 However, when H-R type choose B,
insurance sellers will get into loss
 Consequence: Collapse of market (negative
profit)
ECON3014 - The Economics of Information
23
Insurance Market with Asymmetric Info
 Solution?
 Collect more information: Health check,
medical history
 May not be adequate or effective
 If we can “make” different buyers to tell their
truth type!
 Truth-telling device!!!
 Insurance sellers can redesign the insurance
policy (terms and quantity)
ECON3014 - The Economics of Information
24
Insurance Market with Asymmetric Info
•
C is on the Supply of Insurance line for L-R type, and a
little bit below the indifference curve of H-R type
-Hurt the good type
insurance company cannot
offer full insurance to the
good-type because the badtype will pretend
no in perfect competition
Competitors wil push up
the dot up the blue line
below the intersection
point
A: H-R type, full insurance
C: L-R type, Partial Insurance
𝑊
E: Uninsured state, (𝑊 , 𝑊 )
ECON3014 - The Economics of Information
𝑊
25
Insurance Market with Asymmetric Info
 If A and C is offered, then H-R type will go for
A and L-R type will go for C: We call this
Separating Equilibrium
 A and C is a truth-telling screening device to
separate the different type of insurance
buyers
 However, H-R type gets complete insurance
and L-R type gets partial insurance
 Partial insurance: Insurance policy does not
buy all uncertainty for the buyers
 Asymmetric information hurts the L-R type
ECON3014 - The Economics of Information
26
Moral Hazard in Insurance
 The above is related to adverse selection,
different contracts serve as a screening
device
 To due with moral hazard, usually insurance
policy comes with deductible and co-payment
Deductible: A deductible of $x, means the first $x
damage will not be borne by the insurer
Co-payment: A co-payment of x% means the
insurer will compensate (1-x%) of the damage
high-risk say no to deductible--> bad-type
truth telling
ECON3014 - The Economics of Information
27
Credit Rationing
 According to Demand-Supply framework,
when there is disequilibrium: QD ≠ QS, P will
adjust until the market reaches equilibrium
again: QD = QS
 Credit Rationing: In lending market, QD is
found very often larger than QS at the interest
rate asked by banks (lenders)
Based on demand-supply analysis, market fails?
Interest rate (P) is not used to clear the market!
If credit rationing just exist for a short period of
time, you can regard it as taking time to reach
equilibrium. However, if not ……
ECON3014 - The Economics of Information
28
Credit Rationing
 Credit Rationing in two perspectives:
1) Some borrowers are completely rationed out
of the market (zero loan) at the interest rate
2) Borrower receives less loan than he/she
wants at the interest rate
 Both are supply-side phenomenon to handle:
Adverse selection
Moral hazard
 Stiglitz and Weiss focuses on the 2)
 Credit Rationing is a persistent equilibrium
phenomenon due to imperfect information
ECON3014 - The Economics of Information
29
Why Credit Rationing is Important
 (1) The role credit rationing might play in the
transmitting the macroeconomic effects of
monetary policy
 Monetary policy operates through a “credit
channel”:
Change in Money Supply (Central bank) →
Funds available for banks to lend → Terms of
lending (including interest rate and quantity
available)
 Therefore, credit rationing may play an
important role in the transmission of
monetary policy
ECON3014 - The Economics of Information
30
Why Credit Rationing is Important
 During the bad time, such as financial crisis
 Central banks may adopt expansionary
monetary policy or increase the money
supply/liquidity available in the market
 However, history tells us that banks may
have no intention to lend out money!
Too risky! Loan default!
 Or, banks try to do short-term lending with
heavy collateral
 So, these short-term lending cannot help
much firms/businessmen to survive their
business during the bad time
ECON3014 - The Economics of Information
31
Why Credit Rationing is Important
 Even worse, some of the short-term lending
get into financial market for speculation
purposes
 (2) There is lacking institutions/device to tell
who is good borrowers or bad borrowers
Especially for developing countries
Especially for minority groups
 This leads to financial underdevelopment and
a barrier for the development of particular
groups in a society
Evidence that black and Hispanic minority loan
applicants are denied more frequently than
ECON3014 - The Economics of Information
comparable whites in US
32
Credit Rationing – Stiglitz & Weiss
 Assumptions:
1) Borrowers and lenders are both risk neutral
2) Borrowers are characterized by their
projects, which are assumed to have the
same investment, same expected returns
but differ from one another in their risk
3) Borrowers are with limited liability
ECON3014 - The Economics of Information
33
Credit Rationing – Stiglitz & Weiss
 Lending is not an “easy” business! In good
time, lenders earn the interest payment (% on
the loan amount); however, in bad time, you
earn zero interest payment and may lose the
whole amount of loan!!!
 Lenders decide what projects (borrowers) to
finance (lend). Expected profit of a project
portfolio:
 : Average chance for loan default (bad time)
 : Total loan amount – portfolio size
 : Average Interest rate
ECON3014 - The Economics of Information
34
Credit Rationing – Stiglitz & Weiss
 Given all assumptions, at any given :
 A subset of the least risky borrowers will drop
out of the market, choosing instead to forgo
their projects
Still remember the market for used cars?
 Result: Higher the , more low risk borrowers
will driven out the market and more risky
borrowers stays, which means:
Lower quality of lending portfolio
Chance for default increases
 Adverse selection in borrowers
ECON3014 - The Economics of Information
35
Credit Rationing – Stiglitz & Weiss
Expected
Profit
Interest
Rate
 Increase in affects lender’s return in two
ways: (1) Higher return (direct effect); but (2)
Lower average quality of lending portfolio and
(indirect effect)
 Adverse Selection: Borrowers willing to pay
higher interest rate may mean a have higher
chance to default
ECON3014 - The Economics of Information
36
Beyond Stiglitz & Weiss
 Moral Hazard: Level of interest rate affects
borrowers’ action: Higher interests induce
lenders to take more risky projects
 Credit rationing to a particular borrower is a
way to reduce the problem of moral hazard
To hold borrower to partial responsible for the
chance of big loss/bankrupt
ECON3014 - The Economics of Information
37
Remedies for Credit Rationing
 Credit rationing is a problem of selection and
control (due to imperfect information)
 Remedies for credit rationing (adverse
selection and moral hazard):
Sufficient collateral (Firm’s net worth)
Project value if default happens – Mortgage is
relatively safe
Credit scores/rating (To identify high-risk, low-risk
type)
Long-term relationship – Better information and
closer monitoring
% of borrower’s own investment in a project
ECON3014 - The Economics of Information
38