Homework Assignment 3
Economics 333
Money and Banking
Assigned: November 4th, 2014
Due: November 11th , 2014
1.
Monetary Policy An economy can be represented as a linear function of gaps.
The aggregate expenditure curve represents the output gap as a linear function of the
difference between the real interest rate and the long-term level,
Output Gapt  at  d   rt  r  where at is an expenditure shock and d is the interest
sensitivity of demand. The monetary policy reaction function is rt  r  b   t   TGT  .
The supply curve is given by Output Gapt  f   t   tE  where f is the inflation
sensitivity of supply. Assume that d is 2 and f is 1. The inflation target is 2% (i.e.  TGT
=.02) and the long-term interest rate is r = .04.
a.
Assume that inflation expectations are co-ordinated around the target,  tE   TGT .
Write inflation and the output gap as a function of at. Assume a 1% positive demand
shock, i.e. at = .01. Solve inflation and the output gap when b = .1 and b = 1000. Which
policy results in a smaller shift in inflation? Which policy results in a smaller shift in the
output gap? Demonstrate your results on a graph.

Y
Set at = 0, but assume that inflation expectations are suddenly shifted upward,
    ct . Write inflation and the output gap as a function of ct. Assume a 1%
b.
E
t
TGT
positive expectation shock, i.e. ct = .01. Solve inflation and the output gap when b = .1
and b = 1000. Which policy results in a smaller shift in inflation? Which policy results
in a smaller shift in the output gap?
2.
Adverse Selection. You are an investor in the market for junk bonds (which by
custom have a face value of 100). There are a number of a number of firms that have
projects that they would like to finance. Some of these projects are risky and some are
relatively safe. Firms with risky projects are willing to sell discount bonds to investors to
finance risky projects if they can sell their bonds for at least 80. Firms with safe projects
are only willing to sell their bonds to if they can get a price of at least 90. Investors put a
value on risky bonds of 75 and will offer to buy bonds issued by risky firms at a price of
75. Investors put a value on safe bonds of 95 and will offer to buy bonds issued by safe
firms at a price of 95.
a.
Perfect Information. If everyone has perfect information, then no risky projects
would be financed because the price offered by investors will be less than the minimum
price accepted by firms. What will be the average yield to maturity on bonds?
b.
Symmetric Information. Assume that no one, not even the firms themselves, are
able to distinguish between risky and safe firms. Everyone believes that there is a 50%
chance that a given firm is risky and a 50% chance that a given firm is safe. Assume that
all firms are willing to accept the expected values of the minimum prices of safe and
risky firms. Assume that all investors are willing to offer a price equal to the expected
value of bonds. What is the yield to maturity on bonds if the price is the price that
investors are willing to offer?
c.
Asymmetric information Assume that investors are not able to distinguish between
risky and safe firms. Investors look at any given firm and believe that there is a 50%
chance that firm is risky and a 50% chance that firm t is safe. However, firms can identify
with certainty whether they themselves are risky or safe. Will any bonds be sold in this
market?
d.
Less Asymmetry Assume that an investment banker named Milken is able to get
enough information about firms so that he can identify a group of firms which is 80%
likely to be safe and only 20% likely to be risky. What is the expected value of bonds
from this group of firms to investors? Will firms that know they are safe be willing to sell
at this price?
3.
Moral Hazard. An entrepreneur wants to open a textile factory which costs
$100,000. You lend him $100,000 at a 10% interest rate and he promises to pay you back
$110,000 in 1 years’ time. If he defaults, he must pay you all the income from the plant.
A.
The entrepreneur considers two sales plans. The first sales plan will be to
produce athletic socks. This safe investment will generate income of $130,000 with a
probability of 80% and income of $120,000 with probability of 20%. What is the
expected value of income? What is the expected value of the pay-off to your bond? What
is the expected pay-off for the entrepreneur?
B.
The second sales plan is to produce trendy fashions for the Japanese market. If
the plan successfully predicts a trend, it can produce large income, but could very easily
go bad. Producing trendy fashions will generate income of $250,000 with a probability of
20% but produce only income of $50,000 with probability of 80%. What is the expected
value of income? What is the expected value of the pay-off to your bond? What is the
expected pay-off for the entrepreneur?
C.
Which project offers the greatest amount of profits at the level of society? Which
will the entrepreneur choose if they have total control of the funds and are risk neutral?
Explain the difference.
D.
Assume that the entrepreneur own an apartment which you estimate can be resold
for $30,000. Before you make the loan, you demand that he puts up this apartment as
collateral. If the entrepreneur defaults, his payoff is -$30,000 but your payoff will be the
income from the plant plus $30,000. Go back and calculate the expected value of the payoff to the entrepreneur and to the bond holder under the second sales project. Would the
entrepreneur invest in this risky project if they had money at risk?