Economics 345
Prof. Irina Telyukova
Fall 2008
Homework Assignment 3 SOLUTIONS
1.
(a) Analyze what happens to the interest rate in the bond market in the case of an
economic (business cycle) recession. Remember that there are both demand and
supply effects to cover. Explain in detail in words, and in graphs, all relevant
effects.
For this question, we use the bond demand-supply framework. When there is an
economic recession, output and income in the economy is falling. Thus, in
general, wealth among households is dropping. This means that households will
demand fewer bonds, and the bond demand curve will shift to the left, causing
prices to fall and the interest rate to rise.
Simultaneously, however, the contraction in the economy means that firms are
also willing to borrow less, because new investment is not expected to pay off
when the overall economy is suffering (consumers do not want to buy as much,
etc.). This means that bond supply will also fall, shifting the bond supply curve to
the left, which will in turn raise prices and lower interest rates.
What is the total effect? This theory is actually ambiguous on the answer.
Depending on how far the two curves shift, we could observe an increase,
decrease or no change in the interest rate: an equal increase in demand and
supply (so an equal shift in the curves) would produce no overall change in the
interest rate; if the demand effect is stronger (demand shifts by more than supply),
then prices drop and the interest rate rises; if the supply effect stronger, then
prices will increase, and interest rates decrease. (The two graphs demonstrate
two of the three scenarios). So according to the theory, interest rates could be
procyclical (move with output), countercyclical (move against output), or
acyclical (not react to movements in output).
P
Supply effect dominates: P up, i down
BS
B
P’
P
B
BD
Q
P
Demand effect dominates: P down, i up
BS’
BS
P
P’
BD
BD’
Q
The data, of course, point to procyclical interest rates – so when the business
cycle swings down, so that output contracts, we would expect from the data that
interest rates would contract too. From our diagrams, this would imply that the
supply effect might dominate the demand effect.
(b) Now do the same analysis using the liquidity preference framework.
In the liquidity preference framework, we are just shifting money demand and
supply curves. When there is a contraction, incomes move down, so by our money
demand theory, we expect that people will want to hold less money – so money
demand curve will shift to the left. That would lead to an unambiguous move
down of the interest rates.
Given that in this theory, we assume money supply to be fixed by the central
bank, this is the end as far as liquidity preference theory goes. It actually gives a
more unambiguous prediction on the interest rates. Of course, you could then try
to guess what a central bank might do in a recession. It could contract or expand
money supply – it has done both in the past; if it contracts money supply, that
would lead to an increase in the interest rate.
So this theory could also produce an ambiguity with respect to the interest rate
movement that results from a business cycle contraction, but in general, it points
more definitively to a procyclical interest rate.
(c) According to each of the theories, are interest rates procyclical or
countercyclical? That is, do they move with the business cycle (rise when
output rises, fall when output falls) or against the business cycle?
Answered above.
2. Mishkin and Serletis, ch.5, p. 117 – 1,3-6, 9-12, 16, 18. In problem 5, “Rembrandts”
really does refer to Rembrandt paintings.
(1) (a) Declining wealth leads people to invest less, so demand for a given stock falls;
(b) Appreciation of stock value is equivalent to rising expected returns of the stock, so
you would be more willing to buy; (c) Less, because the stock has just become less
liquid; (d) Relative returns (and expected returns) of the stock will decline, so you
will be less willing to buy it; (e) This implies increased risk in the bond market, so the
stock you are considering is relatively safer now – you would be more willing to buy
it as a result.
(3) (a) More, because it has become more liquid; (b) less, because it has become
more risky; (c) more, because its expected return has risen; (d) less, because its
expected return has fallen relative to the expected return on bonds, which has
increased.
(4) Answer in the book.
(5) The rise in the value of stocks would increase people’s wealth and therefore the
demand for Rembrandts would rise.
(6) Answer in the book. Be sure to practice drawing the curves for both frameworks
(bond and liquidity preference).
(9) An increase in savings rates implies an increase in wealth. This in turn means an
increase in bond demand. As the BD curve shifts right, the interest rates on the bonds
will fall. (What is the corresponding effect on the prices?) Draw the graph. This is the
opposite of the example we discussed in class.
(10) Interest rates fall. The increased volatility of gold prices makes bonds relatively
less risky relative to gold and causes the demand for bonds to increase. The demand
curve, Bd, shifts to the right and the equilibrium interest rate falls.
(11) In the book.
(12) Interest rates might rise. The large federal deficits require the government to
issue more bonds; thus the supply of bonds increases. The supply curve, Bs, shifts to
the right and the equilibrium interest rate rises. Some economists believe that when
the government issues more bonds, the demand for bonds increases because the issue
of bonds increases the public’s wealth. In this case, the demand curve, Bd, also shifts
to the right, and it is no longer clear that the equilibrium interest rate will rise. Thus
there is some ambiguity in the answer to this question. (Draw the graphs!)
(16) If the public believes the governor’s program will be successful, interest rates
will fall. The governor’s announcement will lower expected inflation so that, for a
given nominal interest rate, the real interest rate will rise, raising the cost of
borrowing, so that the supply of bonds falls. The resulting leftward shift of the supply
curve, Bs, causes the equilibrium interest rate to fall.
(18) Interest rates will rise. The expected increase in stock prices raises the expected
return on stocks relative to bonds and so the demand for bonds falls. The demand
curve shifts to the left and the equilibrium interest rate rises.