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2. Suppose there are two types of potential borrowers. Half are Type A borrowers who have projects that require an investment of 1 unit. They have an equal probability of returning 3 or 0 gross in one year. The other half are Type B borrowers, who have projects that also require 1 unit investment and a gross return of 8 with probability 1/8 or 0 with probability 7/8 in one year. Lenders require one unit gross in one year on one unit loaned (i.e. they will lend if they receive a net interest rate of 0). Assume that there is perfect competition so that lenders must earn their minimum (0 net) in any equilibrium.

First, find the equilibrium interest rates on the loans to each in the case of symmetric information. (Note that they will differ.) Under asymmetric information, where the lenders cannot distinguish between types but know the distribution of potential borrowers, what equilibrium interest rate will be charged and who will borrow? Explain. Characterize the inefficiency that results from asymmetric information.

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Chika Ilonah
Chika IlonahLv10
28 Sep 2019

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Related questions

An entrepreneur needs funds for a project. He has funds of his own, but enough to cover the required investment of $100. If the entrepreneur doesn't misbehave, the project will succeed with a probability of .9, yielding a gross return of 120 in one year. With probability .1, it fails and yields nothing. If the entrepreneur misbehaves, on the other hand, he obtains a private benefit of $14 in one year, while lowering the probability of success to .5. Lenders require a gross expected return of $1 in one year on $1 loaned today, and the lenders are competitive and so receive no more than this. So, for example, if they lend $1 and there is no misbehavior, they must be given 1/.9 = $1.11 dollars if the project succeeds. Show that if the entrepreneur borrowed the entire $100, he or she would have the incentive to misbehave. Since lenders realize this, they will not lend the entire $100. What are the most that they will lend and why? Put another way, what is the minimum amount the entrepreneur must put up in order to have the incentive to behave? Explain.

Three students have each saved $\$$1,000. Each has an investment opportunity in which he or she can invest up to $\$$2,000. Here are the rates of return on the students' investment projects:

Harry $\quad$ 5 percent

Ron $\quad$ 8 percent

Hermione $\quad$ 20 percent

a. If borrowing and lending are prohibited, so each student uses only personal savings to finance his or her own investment project, how much will each student have a year later when the project pays its return?

b. Now suppose their school opens up a market for loanable funds in which students can borrow and
lend among themselves at an interest rate $r$. What would determine whether a student would choose to be a borrower or lender in this market?

c. Among these three students, what would be the quantity of loanable funds supplied and quantity
demanded at an interest rate of 7 percent? At 10 percent?

d. At what interest rate would the loanable funds market among these three students be in equilibrium? At this interest rate, which student(s) would borrow and which student(s) would lend?

e. At the equilibrium interest rate, how much does each student have a year later after the investment projects pay their return and loans have been repaid? Compare your answers to those you gave in part (a). Who benefits from the existence of the loanable funds market$-$the borrowers or the lenders? Is anyone worse off?

(Karloff) Consider the following market for used cars. There are many sellers of used cars. Each seller has exactly one used car to sell and is characterized by the quality of the used car he wishes to sell. Let θ ∈ [0, 1] index the quality of a used car and assume that θ is uniformly distributed on [0, 1]. If a seller of type θ sells his car (of quality θ) for a price of p, his utility is us (p,θ). If he does not sell his car, then his utility is 0. Buyers of used cars receive utility θ − p if they buy a car of quality θ at price p and receive utility 0 if they do not purchase a car. There is asymmetric information regarding the quality of used cars. Sellers know the quality of the car they are selling, but buyers do not know its quality. Assume that there are not enough cars to supply all potential buyers.

(a) Argue that in a competitive equilibrium under asymmetric information, we must have E(θ | p) = p

(b) Show that if us (p,θ) = p − θ/2, then every p ∈ (0, 1/2] is an equilibrium price.

(c) Find the equilibrium price when us (p,θ) = p − √θ. Describe the equilibrium in words. In particular, which cars are traded in equilibrium? (d) Find an equilibrium price when us (p,θ) = p − θ 3. How many equilibrium are there in this case? (e) Are any of the preceding outcomes Pareto efficient? Describe Pareto improvements whenever possible.

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