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ECN115A-Excel代写
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1Asymmetric Information & Credit Rationing
ARE/ECN 115A
November 7, 2023
1
2Readings
Today: Summary of Asymmetric Information & Credit
Markets
Primary Reading: T&L, Ch. 12 pp 262 – 270
Primary Reading: T&L, Appendix 12A & 12B
Optional: Banerjee & Duflo: “The men from Kabul…”
Thursday
Overview of Moral Hazard and Adverse Selection
How do lenders overcome asymmetric information?
Primary Reading: T&L, Ch 12 pp 270 – 275
Optional: “The Microfinance Promise” by Jonathan Morduch
Lots of material on microfinance on Canvas/Module
2
3Business
Midterm
Mean: 77.6
Median: 81
SD: 15
Problem Set 2
Regrading Question 5 for partial credit
Problem Set 3
Available on Canvas
Due Thursday, Nov 16 (Start Early! You can do it all after sections this
week)
3
Academic Integrity & Problem Sets4
4
51. Should students be able to consult answer keys from
prior quarters to complete their problem sets?
2. Provide one or more normative arguments for your
answer to question 1.
3. Provide one or more positive arguments for your answer
to question 1.
5
6Our Policy in 115A
If it appears that you consulted and
plagiarized/copied from a prior answer key, you will
be referred to the Office of Student Support and
Judicial Affairs (OSSJA)
6
71. Should students be able to consult answer keys
from prior quarters to complete their problem
sets?
YES (32%)
NO (68%)
7
8Arguments in support of YES
Can enhance their problem-solving skills. By reviewing previous
solutions, students can gain insights into different problem-solving
approaches, techniques, and strategies.
It can help students with deeper understanding of the material
through self-assessment, and preparing students for real-world
problem-solving scenarios where they have access to various
resources.
I think that it's okay to consult answer keys from prior quarters to help
with the completion of the problem sets. However the answer key
should not be used as a mean to copy and paste directly onto the
problem set and complete the assignment in that manner. The answer
key should be used to help students and provide an aid as to how to
start the problems and resolve any confusion or question that students
may have about a particular problem.
8
9Arguments in support of NO
Negative impacts on yourself
If people use answer keys in homework then they won’t learn the material
Using an old answer key is a waste of time because you don't learn anything from just
copy-pasting correct answers. Even if you get the answer wrong, the process of working
on a problem is the most beneficial experience.
One positive argument is that looking at prior quarters answer keys means students will
not do as well on the midterm because they do not learn the material on their own.
Negative impacts on others
It will confuse the professor on how well each content has been understood by students,
which leads to preparing the class not appropriately.
The students who used past keys for responses affected the grade distribution of the
whole class. It would be logical to assume students who used a key would have more
correct answers than someone who did not. So the students benefiting from using a key,
negatively effect the grades of those who do not.
9
10
Bottom line…
In 115A, problem sets are critical to the learning
process.
They are hard and long.
Struggling through them will help you learn the
material.
Teaching team is here to support you.
If you can’t make it to office hours, let us know
10
Announcements11
11
12
0.5% Extra Credit!!
Just show up and sign-in
12
Clicker Question
Have you seen the movie Shrek?
A. YES
B. NO
13
13
Plan for Today
Review of Market Equilibrium (Market Fundamentals)
Shrek and Credit Markets: Peeling the layers of the asymmetric
information onion
Asymmetric information and the “quality” of a credit contract
Credit Market Equilibrium under Adverse Selection
Plan for Sections this Week
Credit Market Equilibrium under Moral Hazard
14
14
Market Fundamentals15
15
05
10
15
20
25
0 25 50 75 100
Pr
ic
e
Quantity
The Market for Jalapeño Bacon
Burgers
Supply
16
Demand
Why would we
not expect the
equilibrium price
to be $5?
16
05
10
15
20
25
0 25 50 75 100
Pr
ic
e
Quantity
The Market for Jalapeño Bacon
Burgers
Supply
17
DemandExcess Demand
17
18
Pareto Efficiency
An allocation specifies a price, an amount produced
and an amount consumed.
An allocation is Pareto Efficient if:
There is no way to reallocate things to make one person
better off without making at least one person worse off.
Equivalently, no gains from trade are possible.
18
05
10
15
20
25
0 25 50 75 100
Pr
ic
e
Quantity
The Market for Jalapeño Bacon
Burgers
Supply
19
DemandExcess Demand
If current price is
$5, what could we
do to improve
efficiency?
19
20
First Fundamental Theorem of Welfare Economics
A competitive market equilibrium is Pareto Efficient If a bunch of
conditions hold.
Price will adjust to coordinate producer and consumer
plans until = ∗;
Firms produce exactly the amount consumers want
No excess demand or supply.
Policy Implications:
Government intervention cannot improve the efficiency
of the economy.
Government can re-allocate (redistribution, lump-sum tax
and transfer) after market equilibrium is established.
But Government should not interfere with the market
equilibrium by…
…setting prices;
…directly participating in production.
About that fine print…
D
S
Q
P
∗
∗
20
21
First Fundamental Theorem of Welfare Economics
A competitive market equilibrium is Pareto Efficient if a
bunch of conditions hold:
No externalities! (Environmental Economic)
No public goods! (Public Economics)
No asymmetric information! (Contract Theory & Development
Economics)
Some other technical conditions
If even one of these conditions does not hold, all bets are
off.
Market equilibrium may not be Pareto efficient.
It is possible that government intervention in markets can
increase efficiency.
21
22
First Fundamental Theorem of Welfare Economcis
A competitive market equilibrium is Pareto Efficient if a
bunch of conditions hold:
No externalities! (Environmental Economic)
No public goods! (Public Economics)
No asymmetric information! (Contract Theory &
Development Economics)
Some other technical conditions
This is the BIG problem in CREDIT and INSURANCE
markets.
22
23
Clicker Quiz
Bernie made a loan to Isaac so that Isaac could expand his
business. Bernie cannot prevent Isaac from using the loan to buy
food instead of investing the loan in his business. The problem that
Bernie faces is:
A. Adverse Selection
B. Moral Hazard
23
24
Asymmetric Information & Market Failure
Asymmetric Information (AI): One party to a transaction has
greater information about the quality of the good or service being
transacted than the other.
Two types of Asymmetric Information problems
Adverse selection: Lender can’t observe key characteristics of the
borrower.
Moral hazard: Lender can’t observe (or enforce) key actions taken by
the borrower.
Our Goal is to show that AI may lead to a market equilibrium
that…
…is not efficient
…excludes some potentially good borrowers (credit rationing)
24
25
Asymmetric Information and Credit Market Failure
Thanks to A.I….
Interest rate may NOT adjust to
coordinate lenders and borrowers
plans.
May end up stuck at ̅ :
Banks lend less than borrowers want.
(Excess Demand/Credit rationing);
Consumer + Producer surplus is NOT
maximized.
Gains from trade are possible, but
they don’t happen!
There may be roles for
government policy to enhance
efficiency.
D
S
Q
i
ௌ
̅
“Deadweight
Loss”
“Excess Demand”
25
26
Credit Rationing
D
S
Q
i
ௌ
̅
“Deadweight
Loss”
“Excess Demand”
Credit rationing occurs when:
Excess demand for credit
exists:
Borrowers get less than they
want or;
Some borrowers get what
they want and others get
nothing
But lenders are unwilling to
raise the interest rate to clear
excess demand.
26
Shrek, Moral Hazard & Adverse
Selection
27
27
Structure of our Argument
Access to credit is crucial for poverty reduction &
development (3 crucial roles)
1) Credit allows you to get ahead
Directly allows investments to raise expected income;
2) Credit prevents you from falling behind
Credit for consumption after shock;
Indirectly promotes investment via “credit as insurance”.
3) Credit shifts risk
From households (like Ana & Zimba’s) who can’t afford to take on
much risk, towards banks who can.
28
Structure of our Argument
Credit markets don’t work well in low-income
countries. Poor households, in particular, don’t have
good access to credit. (financial inclusion graphs)
% of Adults with a Bank
Account
% of Adults that Borrowed
from Bank in last Year
29
Structure of our Argument
MYSTERY: Existence of Credit Rationing (Excess Demand)
Plenty of talented, hard-working poor have great ideas for businesses
or productive investments
But lenders are often unwilling to offer loans even though potential
borrowers are willing to pay higher interest rates
Why?? Why won’t lenders accept the higher interest rate and offer these
loans?
30
Structure of our Argument
Answer: Moral Hazard and Adverse Selection
provide (at least a partial) answer to this puzzle
Once we understand Moral Hazard & Adverse
Selection, we can think about solutions to credit
rationing
31
Shrek, Moral Hazard & Adverse SelectionMoral Hazard &
Adverse Selection
M.H. &
A.S.
32
Shrek, Moral Hazard & Adverse Selection
Moral Hazard & Adverse Selection are complicated concepts
– we need to peel the onion!
Let’s first provide an intuitive discussion about them, to get the
general idea.
Indeed we’ll see that these concepts are relevant to a wide variety
of context and decisions
Then we need to be more precise – this is what we do with
economic models – so that we can determine:
How do we incorporate these two concepts in the context of a
credit contract?
Does each concept affect whether or not and at what terms credit
is offered? If so, how?
33
34
General Definitions
Adverse Selection: A situation in which one party has greater
information than the other party about some (fixed) characteristic
or type of the more informed party that affects product quality.
(It’s all about unobserved characteristics)
Moral Hazard: A situation in which one party has more
information than the other about some action that the more
informed party takes that affects product quality.
(It’s all about unobserved or unenforceable actions)
34
35
Volunteer?
Has anybody run their own business (or family has a business)?
What is the business?
Guestimate at annual revenues?
Sources of risk?
35
36
Volunteer?
Has anybody run their own business (or family has a business)?
What is the business?
Guestimate at annual revenues?
Sources of risk?
Now put yourself in the shoes of a lender
Imagine our volunteer comes to you for a loan to expand their
business.
Question 1: What information would you like to know before you
decide to make the loan (or not)?
Question 2: If you decide to make the loan, what types of actions
would you like to monitor and make sure our volunteer
chooses/follows?
36
Moral Hazard & Adverse Selection in
Everyday Life
Homework Groups in 115A: How do M.H. and A.S. relate to
your decision of working in groups in 115A?
Hiring an undergrad as a research assistant: Put yourself in
my shoes. How do M.H. and A.S. relate to my decision of
hiring an undergraduate student as a research assistant?
University admissions: Put yourself in the shoes of the
admissions committee at the MBA program you are applying
to. How do M.H. and A.S. relate to the admission committee’s
decision to admit you and potentially offer you a fellowship?
37
Clicker Question
How are you feeling about the concepts of Moral Hazard & Adverse
Selection?
A. Sd
B. As
C. df
38
38
Next step
OK…hopefully we have the basic idea.
Now let’s peel the onion to the next layer and be very
specific in the context of credit transactions.
39
Asymmetric Info and the QUALITY
of a credit contract
40
40
41
“Asymmetric Information” Paradigm
Field of “Economics of information” emerges in the 1980’s.
Stiglitz, Akerloff, and Spence win Nobel prize in 2001 – primarily for
economics of information.
Powerful framework for understanding how information problems can cause
imperfections in many markets where contracts are critical.
Revolves around two basic notions:
Adverse Selection
Moral Hazard
These two concepts will help us answer the question:
Why won’t the lender raise the interest rate to eliminate excess demand (get
rid of credit rationing)?
In 2 weeks: Why is it so difficult to offer insurance?
41
42
“Asymmetric Information” Paradigm
When you purchase most goods/services, you know exactly what
you are getting.
As a buyer, you can easily evaluate the quality of clothes, a
toothbrush, a potato.
But it’s not so easy for buyers to evaluate the quality of some
other goods/services, such as used cars and, as we will see,
credit and insurance.
When the seller knows the quality, but the buyer cannot easily
evaluate quality, we say the buyer suffers from asymmetric
information.
42
43
“Asymmetric Information” in Credit Markets
Let’s apply this framework to credit markets.
To do so, we need to think about:
Who is the buyer and who is the seller?
What is actually exchanged/sold in a credit contract?
How do we define quality?
43
44
Who is buyer & seller in a credit contract?
Asymmetric information usually is a problem faced by the buyer.
So who is the “buyer” and who is the “seller” in a credit contract?
The lender is the seller, right?
I’m going to flip this: Lender is the buyer; Borrower is the seller.
Why? Because of what is really exchanged in a credit transaction.
44
45
What is Sold in a credit contract?
A credit contract exchanges the inter-temporal use of resources.
Lender gives up resources today in exchange for getting them back (with
interest) tomorrow;
Borrower receives resources today in exchange for giving them back (with
interest) tomorrow
Consider a $100 loan at a 10% interest rate.
Borrower is the seller:
He “sells” a promise to deliver $110 next year.
In return, he gets to use the $100 he borrowed this year.
Lender is the buyer:
She “buys” the borrower’s promise to deliver $110 next year.
In return, she must give up the $100 this year plus any returns (interest earned in a savings
account) she would have earned if she had not made the loan.
45
46
What determines the Quality of a Credit
Transaction?
The lender is buying a promise to get money in the future.
From the lender’s point of view, the quality of the loan contract has two parts:
The interest rate, which determines how much she receives next year if the borrower repays
and;
The probability that the borrower defaults – i.e., does not repay.
Information is asymmetric because the borrower knows this default probability, but
the lender may not!
The probability of default depends on two things that lender cannot easily observe:
BORROWER TYPE: Characteristics/traits of the borrower & borrower’s project (Adverse
Selection);
BORROWER ACTIONS: What the borrower does with the loan (Moral Hazard)
46
47
Adverse Selection
General: A situation in which one party has greater information
than the other party about some (fixed) characteristic of product
quality.
Credit Markets: Borrower has greater information about
characteristics of herself and her project that affect the probability
of default -- than the lender.
Implication: The lender may be unwilling to raise the interest rate
even if there exists excess demand.
Why? Because, by increasing the interest rate, the lender may adversely
affect the quality of the applicant pool and thus lower her own profit.
47
48
Moral Hazard
General: A situation in which one party has more information than
the other about some action that the more informed party takes that
affects product quality.
Credit Market: Borrower has greater information about the actions
that she takes after receiving the loan that affect the probability of
default -- than the lender.
Implication: The lender may be unwilling to raise the interest rate
even if there exists excess demand.
Why? Because by increasing the interest rate, the lender may induce
the borrower to take actions that reduce the probability of
repayment and thus lower her own profit.
48
49
Looking forward…
Our goal is to understand how Moral Hazard and Adverse
Selection may affect the credit market.
In the real world, lenders face these two problems simultaneously.
In order to learn the concepts, we will always deal with them
separately.
In order to understand the impact of M.H. and A.S., we will:
First find the credit market equilibrium under symmetric information
(lenders face neither M.H. nor A.S.)
Then find the credit market equilibrium under asymmetric information
If there is a difference in the equilibrium, we can attribute this difference
to asymmetric information.
49
50
Structure of our Analysis Today
(similar to sections & PS3)
Information
Environment
Symmetric Asymmetric
Market
Structure
Perfect
Competition A B
Monopoly C D
Information
Environment
Symmetric Asymmetric
Market
Structure
Perfect
Competition A B
Monopoly C D
TODAY: ADVERSE SELECTION (Multiple TYPES)
SECTION: MORAL HAZARD (Multiple ACTIONS)
Monopoly
Single lender with all
market power
Lender will earn highest
possible ()
Borrower must earn
() ≥ 0
Perfect Competition
Many lenders competing
against each other
Borrower earns highest
possible ()
Lender must earn () ≥0
50
Intro to Adverse Selection51
51
52
Types of Potential Borrowers
From lender’s point of view, high quality means low probability of
default.
Lender knows that two types of potential borrowers exist:
SAFE Types (High Quality):
Have projects/investments that are low risk.
Might not be super-successful, but low probability that they fail
So Safe types have low default probability
RISKY Types (Low Quality):
Have projects/investments that are high risk.
Occasionally they strike it rich, but high probability that they fail
So Risky types have high default probability
52
53
Clicker Question
If the lender CAN distinguish between SAFE versus
RISKY types, she would:
A. Charge higher interest rate to SAFE type than RISKY type
B. Charge higher interest rate to RISKY type than SAFE type
C. Charge same interest rate to both SAFE and RISKY types
53
54
Under Symmetric Information
If lenders could perfectly distinguish between high quality and low
quality borrowers, we don’t have a problem.
Lender could offer different interest rates to each type. The interest
rate will reflect each type’s risk of default.
Lender charges safe types a low interest rate
Lender charges risky types a high interest rate
So the equilibrium contracts would specify two terms: TYPE & Interest
Rate:
(SAFE type, LOW interest rate)
(RIKSY type, HIGH interest rate)
54
55
Under Asymmetric Information
When lenders CANNOT distinguish between high quality (Safe) and
low quality borrowers (Risky) things get complicated.
Lender could offer the low interest rate and high interest rate
contracts and announce:
“If you are a Safe type, please apply for the low interest rate contract”
“If you are a Risky type, please apply for the high interest rate contract”
Question: What do you think would happen?
55
56
Under Asymmetric Information
When lenders CANNOT distinguish between high quality (Safe) and
low quality borrowers (Risky) things get complicated.
Lender could offer the low interest rate and high interest rate
contracts and announce:
“If you are a Safe type, please apply for the low interest rate contract”
“If you are a Risky type, please apply for the high interest rate contract”
What do you think would happen?
Risky types would lie to get the lower interest rate intended for Safe types.
So under asymmetric information, the lender has to offer a single interest
rate.
56
57
Under Asymmetric Information
When lenders CANNOT distinguish between high quality and low
quality borrowers:
Lender has to be very careful picking the interest rate, why?
Because the interest rate she picks will determine which types of borrowers
apply for loans!
Will end up having two choices for the interest rate:
OPTION 1: Set it low enough so that BOTH types will want the loan.
OPTION 2: Give up on SAFE types and instead set it high and deal only
with RISKY types
So there will be a single equilibrium contract and it will only have
one term: Interest Rate
But lender will know which types of borrowers will apply at that interest rate;
So lender will know exactly what her () is.
57
“A Tale of Two Types”
Example 1: Adverse Selection58
58
59
We’re going to make assumptions about:
Projects and risk for two TYPES of borrowers;
Opportunity cost of lenders
Use those assumptions to find equations for the following as functions
of the interest rate:
ௌ : Expected income of Safe Type of borrower
ோ : Expected income of Risky Type of borrower
ௌ : Expected profit of lender on a loan to a Safe Type of borrower
ோ : Expected profit of lender on a loan to a Risky Type of borrower
Graph these four functions to visually understand the equilibrium in the
specific context (symmetric vs asymmetric; monopoly vs competition)
Mathematically find the specific interest rate(s) and what borrowers and
lenders will earn in equilibrium
General Strategy
59
60
Two Types of Entrepreneurs
Both have $0 in liquidity/savings
Both need $100 loan to start a business
Both want to maximize ()
Both must earn () ≥ 0, otherwise won’t take a loan.
Half are Safe Types
Revenues = 180 with probability 1 (always succeed)
Half are Risky Types
Revenues = 260 with probability 0.5 (success)
Revenues = 0 with probability 0.5 (failure)
Entrepreneurs
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Risky Types:
Revenues = 260 with probability 0.5 (success)
Revenues = 0 with probability 0.5 (failure)
The expected value of Revenues of a Risky Type is:
A. 0
B. 130
C. 150
D. 260
Clicker Question
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62
Wants to maximize ()
Opportunity cost:
She could earn 10% interest if she kept the $100 in the bank
instead of lending.
So her opportunity cost is 100*(1 + 0.1) = $110
Offers limited liability loans
Borrower doesn’t have to repay anything if project fails
(careful in PS3: pay attention to liability rule!)
Must earn () ≥ 0, otherwise won’t offer a loan.
Lender
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63
We now want to see how the interest rate affects:
Expected income earned by each type of borrower;
The lender’s expected profit.
Need to find equations for the following as functions of the
interest rate:
ௌ : Expected income of Safe Type of borrower
ோ : Expected income of Risky Type of borrower
ௌ : Expected profit of lender on a loan to a Safe Type of
borrower
ோ : Expected profit of lender on a loan to a Risky Type of
borrower
Objective functions as a function of
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64
Expected Income of Safe Type:
ௌ = Pr ∗ + Pr ∗ ( )
“Setup Equation”
ௌ = 1 ∗ 180 − 100 ∗ 1 + + 0 ∗ [0 − 0 ∗ 100 ∗ (1 + )]
“Final Equation”
ௌ = −
Expected Income of Risky Type:
ோ = Pr ∗ + Pr ∗ ( )
“Setup Equation”
ோ = .5 ∗ 260 − 100 ∗ 1 + + 0.5 ∗ [0 − 0 ∗ 100 ∗ (1 + )]
“Final Equation”
ோ = −
Borrowers’ Expected Income as a Function of
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65
Expected Income of Safe Type: ௌ = −
Expected Income of Risky Type: ோ = −
Interpretation
Each type of borrower’s expected income is decreasing in
interest rate.
Question: Why does an increase in the interest rate lower
expected income more for Safe type than risky type?
Borrowers’ Expected Income as a Function of
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66
Lender’s Expected Profit on loan to Safe type:
ௌ = Pr ∗ + Pr ∗
Setup Equation
ௌ = 1 ∗ 100 ∗ 1 + − 100 ∗ 1 + .1 + 0 ∗ [0 − 100 ∗ 1 + .1 ]
Final Equation
ௌ = − +
Lender’s Expected Profit on loan to Risky type:
ௌ = Pr ∗ + Pr ∗ ( )
Setup Equation
ோ = 0.5 ∗ 100 ∗ 1 + − 100 ∗ 1 + .1 + 0.5 ∗ 0 − 100 ∗ 1 + .1
Final Equation
ோ = − +
Lender’s Expected Profit as a Function of
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67
Expected Profit on loan to Safe type: ௌ = − +
Expected Profit on loan to Risky type: ோ = − +
Interpretation
Lender’s expected profit is increasing in interest rate.
Question: Why does an increase in the interest rate raise lender’s
expected profit more on loan to Safe than risky type (i.e. slope is
higher 100 vs 50)?
Let’s graph these 4 functions and find equilibrium under symmetric
information…
She can tell Safe & Risky apart and offer them separate contracts.
Lender’s Expected Profit as a Function of
67
-200
-150
-100
-50
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
(_)
(_)
Interest rate
(_)
(_)
68
Expected profit and income
0.1
68
-200
-150
-100
-50
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
(_)
(_)
(_)
〖(〗_))
69
-- Clicker Question --
Under symmetric information, what interest rate would
a monopolistic lender charge to the SAFE type?
A. 0.1
B. 0.6
C. 0.8
D. 1.4
E. 1.6
0.1
69
-200
-150
-100
-50
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
(_)
(_)
(_)
(_)
70
Equilibrium Under Symmetric Info? (monopoly)
What interest rate would she charge to Safe Type?
If she can only make 1 loan, to whom does she offer it?
Max she can charge to Safe
Max she can charge to Risky
2.2
What interest rate would she charge to Risky Type?
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71
Now Lender cannot tell the two types apart.
She just knows that 50% are Safe Types and 50% are Risky Types
What is the opportunistic behavior the lender is concerned about?
Risky types will pretend to be safe types to get a lower interest rate.
So…When she picks an interest rate, she must ask herself: At this
interest rate, who -- which type(s) – will apply for a loan?
Equilibrium under Asymmetric Information?
71
-200
-150
-100
-50
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
(_)
(_)
(_)
(_)
72
How does affect who applies for loan?
Over what range will both types apply?
Over what range will only 1 type apply?
What happens if lender raises a bit higher?
What happens if lender raises a bit higher?
2.2
Both types apply Only Risky apply Nobody applies
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Who wants a loan?
≤ 0.8: Both Types
0.8 < ≤ 1.6: Only Risky Types
> 1.6: Nobody
So Lender’s expected profit as function of interest rate is different for these
three ranges:
≤ 0.8: Both Types apply
= Pr ∗ ௌ + Pr ∗ ோ
= 0.5 ∗ −10 + 100 + 0.5 ∗ −60 + 50
= − +
0.8 < ≤ 1.6: Only Risky Types apply
= ோ = − +
> 1.6: Nobody applies
=
Lender Expected Profit under Asymmetric
Information
These probabilities are just the fraction of
each type in the population!
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Equilibrium Under Asymmetric Info?
You’re a monopolistic lender. You can pick 1 interest rate to charge.
What interest rate do you pick?
-40
-30
-20
-10
0
10
20
30
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
Lender Expected Profit under Asymmetric Information
Both Types Apply Only Risky Types Apply Neither Type Applies
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In this case, Lender would charge the highest possible interest rate that
would keep BOTH safe and risky types in the market (i = 0.8)
What if the lender only has $100 to loan out, but two people want a
loan?
i.e., there exists “excess demand” for the loan
Would she be willing to lend to somebody who offered to pay a
slightly higher interest rate?
No!!
Safe types would drop out of the market
Lender would be left with only Risky types, so expected profit falls
In this case, when she raises the interest rate as high as possible to Risky types,
she earns less profit compared to keeping both Safe and Risky types in the
market
So…lender actually is better off NOT increasing the price
Cost of Asymmetric Information
DISCUSS…she would NOT be willing to raise the interest rate.
• She knows that only risky type would be willing to pay more than 80% interest rate.
• So if she raises interest rate, Safe types drop out of market.
• She’s left only with Risky type.
• She might be willing to do this IF she could raise interest rate very high so that she earns
big profit with only Risky types (possible when the revenue of success is very high for the
Risky types).
• But in this example, she would not be willing to do it.
75
76
D
S
Q
i
ௌ <
∗
Excess Demand
Our Goal: Solve the Mystery!!
Why would lenders choose to
NOT raise the interest rate even
though some people are willing
to pay a higher interest rate?
ௌ
76
77
Summary: Adverse Selection
Lender cannot observe borrower
“type”
Lender must consider how her choice of
affects which type(s) apply!
For low interest rates ( ≤ 0.8):
Both types apply
Not sure to which type loan was given;
Just know 50% chance it went to Safe and
50% chance it went to Risky (fraction of
each type in the population)
is weighted average of expected
profits on a loan to each type
For intermediate interest rates (0.8 <
≤ 1.6):
Lender knows that only Risky types apply
= ோ
For high interest rates ( > 1.6):
Neither type applies
So = 0 = .5 ௌ + .5 ோ =
− 35 + 75
= ோ = −60 + 50
= 0
77
78
Equilibrium: Adverse Selection
Under monopoly
Lender just picks that gives highest value of
Given the parameter values we picked for
this problem, monopolist will pick = 0.8.
(careful on PS or exam: different parameter
values could lead to different outcome)
Under perfect competition??
Pick that makes borrowers as best off as
possible while allowing lender to earn
≥ 0
This occurs at the lowest such that = 0.
i.e., where −35 + 75 = 0
So = ଷହ = 0.47
What about the other such that = 0?
(i.e., where −60 + 50 = 0 )
Cannot be equilibrium! Another lender
would offer a slightly lower interest rate
and steal all the borrowers.
Interest rate will be driven down until =ଷହ
= 0.47 = ோ − 60 + 50
= 0
= .5 ௌ + .5 ோ =
− 35 + 75
78
ARE/ECN 115A
November 7, 2023
1
2Readings
Today: Summary of Asymmetric Information & Credit
Markets
Primary Reading: T&L, Ch. 12 pp 262 – 270
Primary Reading: T&L, Appendix 12A & 12B
Optional: Banerjee & Duflo: “The men from Kabul…”
Thursday
Overview of Moral Hazard and Adverse Selection
How do lenders overcome asymmetric information?
Primary Reading: T&L, Ch 12 pp 270 – 275
Optional: “The Microfinance Promise” by Jonathan Morduch
Lots of material on microfinance on Canvas/Module
2
3Business
Midterm
Mean: 77.6
Median: 81
SD: 15
Problem Set 2
Regrading Question 5 for partial credit
Problem Set 3
Available on Canvas
Due Thursday, Nov 16 (Start Early! You can do it all after sections this
week)
3
Academic Integrity & Problem Sets4
4
51. Should students be able to consult answer keys from
prior quarters to complete their problem sets?
2. Provide one or more normative arguments for your
answer to question 1.
3. Provide one or more positive arguments for your answer
to question 1.
5
6Our Policy in 115A
If it appears that you consulted and
plagiarized/copied from a prior answer key, you will
be referred to the Office of Student Support and
Judicial Affairs (OSSJA)
6
71. Should students be able to consult answer keys
from prior quarters to complete their problem
sets?
YES (32%)
NO (68%)
7
8Arguments in support of YES
Can enhance their problem-solving skills. By reviewing previous
solutions, students can gain insights into different problem-solving
approaches, techniques, and strategies.
It can help students with deeper understanding of the material
through self-assessment, and preparing students for real-world
problem-solving scenarios where they have access to various
resources.
I think that it's okay to consult answer keys from prior quarters to help
with the completion of the problem sets. However the answer key
should not be used as a mean to copy and paste directly onto the
problem set and complete the assignment in that manner. The answer
key should be used to help students and provide an aid as to how to
start the problems and resolve any confusion or question that students
may have about a particular problem.
8
9Arguments in support of NO
Negative impacts on yourself
If people use answer keys in homework then they won’t learn the material
Using an old answer key is a waste of time because you don't learn anything from just
copy-pasting correct answers. Even if you get the answer wrong, the process of working
on a problem is the most beneficial experience.
One positive argument is that looking at prior quarters answer keys means students will
not do as well on the midterm because they do not learn the material on their own.
Negative impacts on others
It will confuse the professor on how well each content has been understood by students,
which leads to preparing the class not appropriately.
The students who used past keys for responses affected the grade distribution of the
whole class. It would be logical to assume students who used a key would have more
correct answers than someone who did not. So the students benefiting from using a key,
negatively effect the grades of those who do not.
9
10
Bottom line…
In 115A, problem sets are critical to the learning
process.
They are hard and long.
Struggling through them will help you learn the
material.
Teaching team is here to support you.
If you can’t make it to office hours, let us know
10
Announcements11
11
12
0.5% Extra Credit!!
Just show up and sign-in
12
Clicker Question
Have you seen the movie Shrek?
A. YES
B. NO
13
13
Plan for Today
Review of Market Equilibrium (Market Fundamentals)
Shrek and Credit Markets: Peeling the layers of the asymmetric
information onion
Asymmetric information and the “quality” of a credit contract
Credit Market Equilibrium under Adverse Selection
Plan for Sections this Week
Credit Market Equilibrium under Moral Hazard
14
14
Market Fundamentals15
15
05
10
15
20
25
0 25 50 75 100
Pr
ic
e
Quantity
The Market for Jalapeño Bacon
Burgers
Supply
16
Demand
Why would we
not expect the
equilibrium price
to be $5?
16
05
10
15
20
25
0 25 50 75 100
Pr
ic
e
Quantity
The Market for Jalapeño Bacon
Burgers
Supply
17
DemandExcess Demand
17
18
Pareto Efficiency
An allocation specifies a price, an amount produced
and an amount consumed.
An allocation is Pareto Efficient if:
There is no way to reallocate things to make one person
better off without making at least one person worse off.
Equivalently, no gains from trade are possible.
18
05
10
15
20
25
0 25 50 75 100
Pr
ic
e
Quantity
The Market for Jalapeño Bacon
Burgers
Supply
19
DemandExcess Demand
If current price is
$5, what could we
do to improve
efficiency?
19
20
First Fundamental Theorem of Welfare Economics
A competitive market equilibrium is Pareto Efficient If a bunch of
conditions hold.
Price will adjust to coordinate producer and consumer
plans until = ∗;
Firms produce exactly the amount consumers want
No excess demand or supply.
Policy Implications:
Government intervention cannot improve the efficiency
of the economy.
Government can re-allocate (redistribution, lump-sum tax
and transfer) after market equilibrium is established.
But Government should not interfere with the market
equilibrium by…
…setting prices;
…directly participating in production.
About that fine print…
D
S
Q
P
∗
∗
20
21
First Fundamental Theorem of Welfare Economics
A competitive market equilibrium is Pareto Efficient if a
bunch of conditions hold:
No externalities! (Environmental Economic)
No public goods! (Public Economics)
No asymmetric information! (Contract Theory & Development
Economics)
Some other technical conditions
If even one of these conditions does not hold, all bets are
off.
Market equilibrium may not be Pareto efficient.
It is possible that government intervention in markets can
increase efficiency.
21
22
First Fundamental Theorem of Welfare Economcis
A competitive market equilibrium is Pareto Efficient if a
bunch of conditions hold:
No externalities! (Environmental Economic)
No public goods! (Public Economics)
No asymmetric information! (Contract Theory &
Development Economics)
Some other technical conditions
This is the BIG problem in CREDIT and INSURANCE
markets.
22
23
Clicker Quiz
Bernie made a loan to Isaac so that Isaac could expand his
business. Bernie cannot prevent Isaac from using the loan to buy
food instead of investing the loan in his business. The problem that
Bernie faces is:
A. Adverse Selection
B. Moral Hazard
23
24
Asymmetric Information & Market Failure
Asymmetric Information (AI): One party to a transaction has
greater information about the quality of the good or service being
transacted than the other.
Two types of Asymmetric Information problems
Adverse selection: Lender can’t observe key characteristics of the
borrower.
Moral hazard: Lender can’t observe (or enforce) key actions taken by
the borrower.
Our Goal is to show that AI may lead to a market equilibrium
that…
…is not efficient
…excludes some potentially good borrowers (credit rationing)
24
25
Asymmetric Information and Credit Market Failure
Thanks to A.I….
Interest rate may NOT adjust to
coordinate lenders and borrowers
plans.
May end up stuck at ̅ :
Banks lend less than borrowers want.
(Excess Demand/Credit rationing);
Consumer + Producer surplus is NOT
maximized.
Gains from trade are possible, but
they don’t happen!
There may be roles for
government policy to enhance
efficiency.
D
S
Q
i
ௌ
̅
“Deadweight
Loss”
“Excess Demand”
25
26
Credit Rationing
D
S
Q
i
ௌ
̅
“Deadweight
Loss”
“Excess Demand”
Credit rationing occurs when:
Excess demand for credit
exists:
Borrowers get less than they
want or;
Some borrowers get what
they want and others get
nothing
But lenders are unwilling to
raise the interest rate to clear
excess demand.
26
Shrek, Moral Hazard & Adverse
Selection
27
27
Structure of our Argument
Access to credit is crucial for poverty reduction &
development (3 crucial roles)
1) Credit allows you to get ahead
Directly allows investments to raise expected income;
2) Credit prevents you from falling behind
Credit for consumption after shock;
Indirectly promotes investment via “credit as insurance”.
3) Credit shifts risk
From households (like Ana & Zimba’s) who can’t afford to take on
much risk, towards banks who can.
28
Structure of our Argument
Credit markets don’t work well in low-income
countries. Poor households, in particular, don’t have
good access to credit. (financial inclusion graphs)
% of Adults with a Bank
Account
% of Adults that Borrowed
from Bank in last Year
29
Structure of our Argument
MYSTERY: Existence of Credit Rationing (Excess Demand)
Plenty of talented, hard-working poor have great ideas for businesses
or productive investments
But lenders are often unwilling to offer loans even though potential
borrowers are willing to pay higher interest rates
Why?? Why won’t lenders accept the higher interest rate and offer these
loans?
30
Structure of our Argument
Answer: Moral Hazard and Adverse Selection
provide (at least a partial) answer to this puzzle
Once we understand Moral Hazard & Adverse
Selection, we can think about solutions to credit
rationing
31
Shrek, Moral Hazard & Adverse SelectionMoral Hazard &
Adverse Selection
M.H. &
A.S.
32
Shrek, Moral Hazard & Adverse Selection
Moral Hazard & Adverse Selection are complicated concepts
– we need to peel the onion!
Let’s first provide an intuitive discussion about them, to get the
general idea.
Indeed we’ll see that these concepts are relevant to a wide variety
of context and decisions
Then we need to be more precise – this is what we do with
economic models – so that we can determine:
How do we incorporate these two concepts in the context of a
credit contract?
Does each concept affect whether or not and at what terms credit
is offered? If so, how?
33
34
General Definitions
Adverse Selection: A situation in which one party has greater
information than the other party about some (fixed) characteristic
or type of the more informed party that affects product quality.
(It’s all about unobserved characteristics)
Moral Hazard: A situation in which one party has more
information than the other about some action that the more
informed party takes that affects product quality.
(It’s all about unobserved or unenforceable actions)
34
35
Volunteer?
Has anybody run their own business (or family has a business)?
What is the business?
Guestimate at annual revenues?
Sources of risk?
35
36
Volunteer?
Has anybody run their own business (or family has a business)?
What is the business?
Guestimate at annual revenues?
Sources of risk?
Now put yourself in the shoes of a lender
Imagine our volunteer comes to you for a loan to expand their
business.
Question 1: What information would you like to know before you
decide to make the loan (or not)?
Question 2: If you decide to make the loan, what types of actions
would you like to monitor and make sure our volunteer
chooses/follows?
36
Moral Hazard & Adverse Selection in
Everyday Life
Homework Groups in 115A: How do M.H. and A.S. relate to
your decision of working in groups in 115A?
Hiring an undergrad as a research assistant: Put yourself in
my shoes. How do M.H. and A.S. relate to my decision of
hiring an undergraduate student as a research assistant?
University admissions: Put yourself in the shoes of the
admissions committee at the MBA program you are applying
to. How do M.H. and A.S. relate to the admission committee’s
decision to admit you and potentially offer you a fellowship?
37
Clicker Question
How are you feeling about the concepts of Moral Hazard & Adverse
Selection?
A. Sd
B. As
C. df
38
38
Next step
OK…hopefully we have the basic idea.
Now let’s peel the onion to the next layer and be very
specific in the context of credit transactions.
39
Asymmetric Info and the QUALITY
of a credit contract
40
40
41
“Asymmetric Information” Paradigm
Field of “Economics of information” emerges in the 1980’s.
Stiglitz, Akerloff, and Spence win Nobel prize in 2001 – primarily for
economics of information.
Powerful framework for understanding how information problems can cause
imperfections in many markets where contracts are critical.
Revolves around two basic notions:
Adverse Selection
Moral Hazard
These two concepts will help us answer the question:
Why won’t the lender raise the interest rate to eliminate excess demand (get
rid of credit rationing)?
In 2 weeks: Why is it so difficult to offer insurance?
41
42
“Asymmetric Information” Paradigm
When you purchase most goods/services, you know exactly what
you are getting.
As a buyer, you can easily evaluate the quality of clothes, a
toothbrush, a potato.
But it’s not so easy for buyers to evaluate the quality of some
other goods/services, such as used cars and, as we will see,
credit and insurance.
When the seller knows the quality, but the buyer cannot easily
evaluate quality, we say the buyer suffers from asymmetric
information.
42
43
“Asymmetric Information” in Credit Markets
Let’s apply this framework to credit markets.
To do so, we need to think about:
Who is the buyer and who is the seller?
What is actually exchanged/sold in a credit contract?
How do we define quality?
43
44
Who is buyer & seller in a credit contract?
Asymmetric information usually is a problem faced by the buyer.
So who is the “buyer” and who is the “seller” in a credit contract?
The lender is the seller, right?
I’m going to flip this: Lender is the buyer; Borrower is the seller.
Why? Because of what is really exchanged in a credit transaction.
44
45
What is Sold in a credit contract?
A credit contract exchanges the inter-temporal use of resources.
Lender gives up resources today in exchange for getting them back (with
interest) tomorrow;
Borrower receives resources today in exchange for giving them back (with
interest) tomorrow
Consider a $100 loan at a 10% interest rate.
Borrower is the seller:
He “sells” a promise to deliver $110 next year.
In return, he gets to use the $100 he borrowed this year.
Lender is the buyer:
She “buys” the borrower’s promise to deliver $110 next year.
In return, she must give up the $100 this year plus any returns (interest earned in a savings
account) she would have earned if she had not made the loan.
45
46
What determines the Quality of a Credit
Transaction?
The lender is buying a promise to get money in the future.
From the lender’s point of view, the quality of the loan contract has two parts:
The interest rate, which determines how much she receives next year if the borrower repays
and;
The probability that the borrower defaults – i.e., does not repay.
Information is asymmetric because the borrower knows this default probability, but
the lender may not!
The probability of default depends on two things that lender cannot easily observe:
BORROWER TYPE: Characteristics/traits of the borrower & borrower’s project (Adverse
Selection);
BORROWER ACTIONS: What the borrower does with the loan (Moral Hazard)
46
47
Adverse Selection
General: A situation in which one party has greater information
than the other party about some (fixed) characteristic of product
quality.
Credit Markets: Borrower has greater information about
characteristics of herself and her project that affect the probability
of default -- than the lender.
Implication: The lender may be unwilling to raise the interest rate
even if there exists excess demand.
Why? Because, by increasing the interest rate, the lender may adversely
affect the quality of the applicant pool and thus lower her own profit.
47
48
Moral Hazard
General: A situation in which one party has more information than
the other about some action that the more informed party takes that
affects product quality.
Credit Market: Borrower has greater information about the actions
that she takes after receiving the loan that affect the probability of
default -- than the lender.
Implication: The lender may be unwilling to raise the interest rate
even if there exists excess demand.
Why? Because by increasing the interest rate, the lender may induce
the borrower to take actions that reduce the probability of
repayment and thus lower her own profit.
48
49
Looking forward…
Our goal is to understand how Moral Hazard and Adverse
Selection may affect the credit market.
In the real world, lenders face these two problems simultaneously.
In order to learn the concepts, we will always deal with them
separately.
In order to understand the impact of M.H. and A.S., we will:
First find the credit market equilibrium under symmetric information
(lenders face neither M.H. nor A.S.)
Then find the credit market equilibrium under asymmetric information
If there is a difference in the equilibrium, we can attribute this difference
to asymmetric information.
49
50
Structure of our Analysis Today
(similar to sections & PS3)
Information
Environment
Symmetric Asymmetric
Market
Structure
Perfect
Competition A B
Monopoly C D
Information
Environment
Symmetric Asymmetric
Market
Structure
Perfect
Competition A B
Monopoly C D
TODAY: ADVERSE SELECTION (Multiple TYPES)
SECTION: MORAL HAZARD (Multiple ACTIONS)
Monopoly
Single lender with all
market power
Lender will earn highest
possible ()
Borrower must earn
() ≥ 0
Perfect Competition
Many lenders competing
against each other
Borrower earns highest
possible ()
Lender must earn () ≥0
50
Intro to Adverse Selection51
51
52
Types of Potential Borrowers
From lender’s point of view, high quality means low probability of
default.
Lender knows that two types of potential borrowers exist:
SAFE Types (High Quality):
Have projects/investments that are low risk.
Might not be super-successful, but low probability that they fail
So Safe types have low default probability
RISKY Types (Low Quality):
Have projects/investments that are high risk.
Occasionally they strike it rich, but high probability that they fail
So Risky types have high default probability
52
53
Clicker Question
If the lender CAN distinguish between SAFE versus
RISKY types, she would:
A. Charge higher interest rate to SAFE type than RISKY type
B. Charge higher interest rate to RISKY type than SAFE type
C. Charge same interest rate to both SAFE and RISKY types
53
54
Under Symmetric Information
If lenders could perfectly distinguish between high quality and low
quality borrowers, we don’t have a problem.
Lender could offer different interest rates to each type. The interest
rate will reflect each type’s risk of default.
Lender charges safe types a low interest rate
Lender charges risky types a high interest rate
So the equilibrium contracts would specify two terms: TYPE & Interest
Rate:
(SAFE type, LOW interest rate)
(RIKSY type, HIGH interest rate)
54
55
Under Asymmetric Information
When lenders CANNOT distinguish between high quality (Safe) and
low quality borrowers (Risky) things get complicated.
Lender could offer the low interest rate and high interest rate
contracts and announce:
“If you are a Safe type, please apply for the low interest rate contract”
“If you are a Risky type, please apply for the high interest rate contract”
Question: What do you think would happen?
55
56
Under Asymmetric Information
When lenders CANNOT distinguish between high quality (Safe) and
low quality borrowers (Risky) things get complicated.
Lender could offer the low interest rate and high interest rate
contracts and announce:
“If you are a Safe type, please apply for the low interest rate contract”
“If you are a Risky type, please apply for the high interest rate contract”
What do you think would happen?
Risky types would lie to get the lower interest rate intended for Safe types.
So under asymmetric information, the lender has to offer a single interest
rate.
56
57
Under Asymmetric Information
When lenders CANNOT distinguish between high quality and low
quality borrowers:
Lender has to be very careful picking the interest rate, why?
Because the interest rate she picks will determine which types of borrowers
apply for loans!
Will end up having two choices for the interest rate:
OPTION 1: Set it low enough so that BOTH types will want the loan.
OPTION 2: Give up on SAFE types and instead set it high and deal only
with RISKY types
So there will be a single equilibrium contract and it will only have
one term: Interest Rate
But lender will know which types of borrowers will apply at that interest rate;
So lender will know exactly what her () is.
57
“A Tale of Two Types”
Example 1: Adverse Selection58
58
59
We’re going to make assumptions about:
Projects and risk for two TYPES of borrowers;
Opportunity cost of lenders
Use those assumptions to find equations for the following as functions
of the interest rate:
ௌ : Expected income of Safe Type of borrower
ோ : Expected income of Risky Type of borrower
ௌ : Expected profit of lender on a loan to a Safe Type of borrower
ோ : Expected profit of lender on a loan to a Risky Type of borrower
Graph these four functions to visually understand the equilibrium in the
specific context (symmetric vs asymmetric; monopoly vs competition)
Mathematically find the specific interest rate(s) and what borrowers and
lenders will earn in equilibrium
General Strategy
59
60
Two Types of Entrepreneurs
Both have $0 in liquidity/savings
Both need $100 loan to start a business
Both want to maximize ()
Both must earn () ≥ 0, otherwise won’t take a loan.
Half are Safe Types
Revenues = 180 with probability 1 (always succeed)
Half are Risky Types
Revenues = 260 with probability 0.5 (success)
Revenues = 0 with probability 0.5 (failure)
Entrepreneurs
60
61
Risky Types:
Revenues = 260 with probability 0.5 (success)
Revenues = 0 with probability 0.5 (failure)
The expected value of Revenues of a Risky Type is:
A. 0
B. 130
C. 150
D. 260
Clicker Question
61
62
Wants to maximize ()
Opportunity cost:
She could earn 10% interest if she kept the $100 in the bank
instead of lending.
So her opportunity cost is 100*(1 + 0.1) = $110
Offers limited liability loans
Borrower doesn’t have to repay anything if project fails
(careful in PS3: pay attention to liability rule!)
Must earn () ≥ 0, otherwise won’t offer a loan.
Lender
62
63
We now want to see how the interest rate affects:
Expected income earned by each type of borrower;
The lender’s expected profit.
Need to find equations for the following as functions of the
interest rate:
ௌ : Expected income of Safe Type of borrower
ோ : Expected income of Risky Type of borrower
ௌ : Expected profit of lender on a loan to a Safe Type of
borrower
ோ : Expected profit of lender on a loan to a Risky Type of
borrower
Objective functions as a function of
63
64
Expected Income of Safe Type:
ௌ = Pr ∗ + Pr ∗ ( )
“Setup Equation”
ௌ = 1 ∗ 180 − 100 ∗ 1 + + 0 ∗ [0 − 0 ∗ 100 ∗ (1 + )]
“Final Equation”
ௌ = −
Expected Income of Risky Type:
ோ = Pr ∗ + Pr ∗ ( )
“Setup Equation”
ோ = .5 ∗ 260 − 100 ∗ 1 + + 0.5 ∗ [0 − 0 ∗ 100 ∗ (1 + )]
“Final Equation”
ோ = −
Borrowers’ Expected Income as a Function of
64
65
Expected Income of Safe Type: ௌ = −
Expected Income of Risky Type: ோ = −
Interpretation
Each type of borrower’s expected income is decreasing in
interest rate.
Question: Why does an increase in the interest rate lower
expected income more for Safe type than risky type?
Borrowers’ Expected Income as a Function of
65
66
Lender’s Expected Profit on loan to Safe type:
ௌ = Pr ∗ + Pr ∗
Setup Equation
ௌ = 1 ∗ 100 ∗ 1 + − 100 ∗ 1 + .1 + 0 ∗ [0 − 100 ∗ 1 + .1 ]
Final Equation
ௌ = − +
Lender’s Expected Profit on loan to Risky type:
ௌ = Pr ∗ + Pr ∗ ( )
Setup Equation
ோ = 0.5 ∗ 100 ∗ 1 + − 100 ∗ 1 + .1 + 0.5 ∗ 0 − 100 ∗ 1 + .1
Final Equation
ோ = − +
Lender’s Expected Profit as a Function of
66
67
Expected Profit on loan to Safe type: ௌ = − +
Expected Profit on loan to Risky type: ோ = − +
Interpretation
Lender’s expected profit is increasing in interest rate.
Question: Why does an increase in the interest rate raise lender’s
expected profit more on loan to Safe than risky type (i.e. slope is
higher 100 vs 50)?
Let’s graph these 4 functions and find equilibrium under symmetric
information…
She can tell Safe & Risky apart and offer them separate contracts.
Lender’s Expected Profit as a Function of
67
-200
-150
-100
-50
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
(_)
(_)
Interest rate
(_)
(_)
68
Expected profit and income
0.1
68
-200
-150
-100
-50
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
(_)
(_)
(_)
〖(〗_))
69
-- Clicker Question --
Under symmetric information, what interest rate would
a monopolistic lender charge to the SAFE type?
A. 0.1
B. 0.6
C. 0.8
D. 1.4
E. 1.6
0.1
69
-200
-150
-100
-50
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
(_)
(_)
(_)
(_)
70
Equilibrium Under Symmetric Info? (monopoly)
What interest rate would she charge to Safe Type?
If she can only make 1 loan, to whom does she offer it?
Max she can charge to Safe
Max she can charge to Risky
2.2
What interest rate would she charge to Risky Type?
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71
Now Lender cannot tell the two types apart.
She just knows that 50% are Safe Types and 50% are Risky Types
What is the opportunistic behavior the lender is concerned about?
Risky types will pretend to be safe types to get a lower interest rate.
So…When she picks an interest rate, she must ask herself: At this
interest rate, who -- which type(s) – will apply for a loan?
Equilibrium under Asymmetric Information?
71
-200
-150
-100
-50
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
(_)
(_)
(_)
(_)
72
How does affect who applies for loan?
Over what range will both types apply?
Over what range will only 1 type apply?
What happens if lender raises a bit higher?
What happens if lender raises a bit higher?
2.2
Both types apply Only Risky apply Nobody applies
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Who wants a loan?
≤ 0.8: Both Types
0.8 < ≤ 1.6: Only Risky Types
> 1.6: Nobody
So Lender’s expected profit as function of interest rate is different for these
three ranges:
≤ 0.8: Both Types apply
= Pr ∗ ௌ + Pr ∗ ோ
= 0.5 ∗ −10 + 100 + 0.5 ∗ −60 + 50
= − +
0.8 < ≤ 1.6: Only Risky Types apply
= ோ = − +
> 1.6: Nobody applies
=
Lender Expected Profit under Asymmetric
Information
These probabilities are just the fraction of
each type in the population!
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74
Equilibrium Under Asymmetric Info?
You’re a monopolistic lender. You can pick 1 interest rate to charge.
What interest rate do you pick?
-40
-30
-20
-10
0
10
20
30
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Interest Rate (i)
Lender Expected Profit under Asymmetric Information
Both Types Apply Only Risky Types Apply Neither Type Applies
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75
In this case, Lender would charge the highest possible interest rate that
would keep BOTH safe and risky types in the market (i = 0.8)
What if the lender only has $100 to loan out, but two people want a
loan?
i.e., there exists “excess demand” for the loan
Would she be willing to lend to somebody who offered to pay a
slightly higher interest rate?
No!!
Safe types would drop out of the market
Lender would be left with only Risky types, so expected profit falls
In this case, when she raises the interest rate as high as possible to Risky types,
she earns less profit compared to keeping both Safe and Risky types in the
market
So…lender actually is better off NOT increasing the price
Cost of Asymmetric Information
DISCUSS…she would NOT be willing to raise the interest rate.
• She knows that only risky type would be willing to pay more than 80% interest rate.
• So if she raises interest rate, Safe types drop out of market.
• She’s left only with Risky type.
• She might be willing to do this IF she could raise interest rate very high so that she earns
big profit with only Risky types (possible when the revenue of success is very high for the
Risky types).
• But in this example, she would not be willing to do it.
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76
D
S
Q
i
ௌ <
∗
Excess Demand
Our Goal: Solve the Mystery!!
Why would lenders choose to
NOT raise the interest rate even
though some people are willing
to pay a higher interest rate?
ௌ
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77
Summary: Adverse Selection
Lender cannot observe borrower
“type”
Lender must consider how her choice of
affects which type(s) apply!
For low interest rates ( ≤ 0.8):
Both types apply
Not sure to which type loan was given;
Just know 50% chance it went to Safe and
50% chance it went to Risky (fraction of
each type in the population)
is weighted average of expected
profits on a loan to each type
For intermediate interest rates (0.8 <
≤ 1.6):
Lender knows that only Risky types apply
= ோ
For high interest rates ( > 1.6):
Neither type applies
So = 0 = .5 ௌ + .5 ோ =
− 35 + 75
= ோ = −60 + 50
= 0
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Equilibrium: Adverse Selection
Under monopoly
Lender just picks that gives highest value of
Given the parameter values we picked for
this problem, monopolist will pick = 0.8.
(careful on PS or exam: different parameter
values could lead to different outcome)
Under perfect competition??
Pick that makes borrowers as best off as
possible while allowing lender to earn
≥ 0
This occurs at the lowest such that = 0.
i.e., where −35 + 75 = 0
So = ଷହ = 0.47
What about the other such that = 0?
(i.e., where −60 + 50 = 0 )
Cannot be equilibrium! Another lender
would offer a slightly lower interest rate
and steal all the borrowers.
Interest rate will be driven down until =ଷହ
= 0.47 = ோ − 60 + 50
= 0
= .5 ௌ + .5 ோ =
− 35 + 75
78
