Credit Market Equilibrium under Multiple Activity/Investment Choice
Sunghun is an entrepreneur who is considering between two investment projects. Both projects
are risky and both require an investment of $100. Project 1 is opening an Economics Consulting
Firm. Since Sunghun is an excellent economist, this project is pretty safe: with 80% probability
Sunghun will be a successful consultant and earn $250 of revenues, and with 20% probability
Sunghun will fail and earn only $100 of revenues. Project 2 is opening a “Klassic Korean
Kimchee” Food Truck. Although Sunghun is a master chef, this project is much riskier. With
20% probability the Food Truck is successful and generates $600 of revenues. With 80%
probability the Food Truck fails and generates only $60 of revenues.
Cristina is a banker who may offer Sunghun a loan. Cristina’s opportunity cost of money is 30%.
In other words, she would earn a 30% interest rate if she invested the money in a bank instead of
lending it to Sunghun.1 In questions 1 – 4, we will explore the equilibrium contract that Cristina
will offer under different assumptions about liability, competition and asymmetric information.
1. Standard Debt Contract and Symmetric Information. In this problem Cristina offers
Standard Debt Contracts, also known as unlimited liability credit contracts. Under this type
of contract, Sunghun always has to repay the loan (full principal plus interest) whether his
project succeeds or fails. We also assume symmetric information. This means that in the
credit contract, Cristina can specify and enforce the project that Sunghun must do. A credit
contract thus specifies two terms: the Project and the interest rate. Let <Project, Interest
Rate> denote the contract. For example, the contract <Project 1, 0.1> means that Sunghun
must do Project 1 and the interest rate is 10%.
a. Let ! and ! denote Sunghun’s income from Projects 1 and 2 respectively under a
standard debt contract. Derive expressions for (! ) and (! ), the expected value of
Sunghun’s income under the two projects, as functions of the interest rate, i. Your
expressions should take the form: (! ) = + where you have to find the
“intercept”, A, and “slope”, B.
b. Let ! and ! denote Cristina’s profit from an UNLIMITED liability loan which
finances Sunghun’s Project 1 and 2 respectively. Derive expressions for (! ) and
(! ), the expected value of Cristina’s profits from loans that finance Projects 1 and 2
respectively. Similar to part (1a), you should express these two expected profit functions
as functions of the interest rate
c. In Excel, graph (! ), (! ), (! ) and (! ) as functions of the interest rate, i (i.e.,
put i on the horizontal axis and graph over the range i = 0 to i = 2). Title this graph
“Figure 1: Credit Market under Standard Debt Contract”.
d. What will the equilibrium contract be if Cristina is a monopolist? (A monopolist will
maximize her own expected profit while allowing the borrower to earn at least zero
expected income.)
e. What is Cristina’s expected profit from this equilibrium contract? What is Sunghun’s
expected income?
f. What will the equilibrium contract be if the credit market is instead characterized by
perfect competition? (Under perfect competition, the equilibrium contract will make the
borrower as well off as possible while allowing the lender to earn at least zero expected
profit).
1
Equivalently, Cristina borrows in order to lend to Sunghun and has to pay 10% interest on her loan (even
if Sunghun defaults).
g. What is Cristina’s expected profit from this equilibrium contract? What is Sunghun’s
expected income?
2. Standard Debt Contract and Asymmetric Information. Now assume that Cristina cannot
observe and/or enforce Sunghun’s project choice. Now a credit contract can only specify the
interest rate.
a. What type of asymmetric information problem does Cristina face?
b. Now what will the equilibrium interest rate be if Cristina is a monopolist? What
project will Sunghun choose?
c. How much expected profit will Cristina earn under asymmetric information? How
much expected income does Sunghun earn? (continue to assume Cristina is a
monopolist).
d. Compare your answers for part 2b and 2c to your answers to 1d and 1e above
(monopolist under symmetric information). If they are different, why are they
different? If they are the same, why?
3. Limited Liability Contract and Symmetric Information. Now we return to our assumption
of symmetric information (Cristina can enforce Sunghun’s project choice) as in problem 1,
but change our assumption about the contract structure. Specifically, we now assume that
Cristina must offer a Limited Liability Contract. This means that the borrower does not have
to fully repay the loan when their project fails. In general, limited liability contracts can take
many forms. We will assume the following: If Sunghun’s project succeeds he must fully
repay the loan (principal plus interest). If his project fails, he only has to repay 50% of the
total debt obligation (For example, if the interest rate is 50%, he would have to repay
0.5*(1+.5)*100 if his project fails).
a. Derive expressions for (! ) and (! ), the expected value of Sunghun’s income under
the two projects, as functions of the interest rate, i, under the limited liability contract
described above. Again, your expressions should take the form: (! ) = + where
you have to find the “intercept”, A, and “slope”, B.
b. Derive expressions for (! ) and (! ), the expected value of Cristina’s profits from
limited liability loans that finance Projects 1 and 2 respectively.
c. In Excel, graph (! ), (! ), (! ) and (! ) as functions of the interest rate, i. Title
this graph “Figure 2: Credit Market under Limited Liability”.
d. What will the equilibrium contract (remember to specify both Project & interest rate) be
if Cristina is a monopolist? Which project does Sunghun choose?
e. What is Cristina’s expected profit from this equilibrium contract? What is Sunghun’s
expected income?
f. What will the equilibrium contract if the credit market is instead characterized by perfect
competition?
g. What is Cristina’s expected profit from this equilibrium contract? What is Sunghun’s
expected income?
4. Limited Liability Contract and Asymmetric Information. Finally, we look at the implication
of asymmetric information when we have Limited Liability Contracts. Assume that contracts
are limited liability as in question 3. But now Cristina cannot observe/enforce Sunghun’s
choice of project.
a. To generate intuition about the impact of asymmetric information, in a separate figure,
graph Cristina’s expected profit as a function of the interest rate. Title this graph “Figure
3: Lender’s Profit under Asymmetric Information and Limited Liability”. Discuss the
b.
c.
d.
e.
f.
shape of your graph. (Make sure that you – like Cristina – consider how the interest rate
affects Sunghun’s choice of project!).
Find the equilibrium interest rate be if Cristina is a monopolist? Which project does
Sunghun choose?
What is Cristina’s expected profit from this equilibrium contract? What is Sunghun’s
expected income?
What will the equilibrium interest rate be if the credit market is instead characterized by
perfect competition?
What is Cristina’s expected profit from this equilibrium contract? What is Sunghun’s
expected income?
Compare the total surplus generated under symmetric versus asymmetric information
(question 3 versus question 4). Discuss your findings.
