Regan/Lipsey 11th (Chapter 28)
Question 3
a) We assume in each case that the payments are made at the end of years 1, 2, and 3. The
present values are as follows:
Treasury Bill:
PV = $1000/(1.08) = $925.93
Bond:
PV = $5000/(1.07)3 = $5000/(1.22504) = $4081.49
Bond:
PV = $200/(1.09) + $200/(1.09)2 + $200/(1.09)3 = $506.27
Stock:
PV = $50/(1.10) + $40/(1.10)2 + $60/(1.10)3 = $123.59
b) If the market price is less than the PV, then profits can be made by borrowing money
to buy the asset. The excess demand for the asset will drive up its price. If the market
price is greater than the PV, there will be no demand for it, and the excess supply will
reduce the price. Thus the PV is also the competitive equilibrium market price for the
asset.
Question 4
a) Present Value (PV) = $100/(1.08) + $100/(1.08)2 + $1000/(1.08)3
= $92.59 + $85.73 + $793.83
= $972.15
b) You should not buy the bond at $995 because it is only “worth” $972.15. This is a
different way of saying that if, instead of buying the bond at this high price, you invested
$995 at the market interest rate (8 percent), you would do better than buying the bond.
The implied bond yield (at a price of $995) is less than the market interest rate. In this
situation, since there should be little demand for the bond at this price, we should expect
the bond price to decline in the near future.
c) You should buy the bond at the price of $950 because you can make a profit by doing
so. You could buy the bond for $950 and ought to be able to sell it for $972.15 since that
is the bond’s “worth” in terms of present value. The implied yield at the offered price is
greater than the market interest rate. Since there should be great demand for the bond at
this price, we should expect the bond price to rise in the near future.
d) If the bond price is exactly $972.15, then the implied yield is exactly equal to the
market interest rate, 8 percent.
e) We have just seen that if bond prices differ from their PV, then there will be market
pressures moving the bond price toward the PV. The competitive market equilibrium
price of bonds is exactly the bond’s PV. So, if bond prices tend to equal to PV, then bond
yields tend to equal the market interest rate. Thus market interest rates and bond yields
tend to rise and fall together.
Question 6
a) The MD function is downward sloping because the nominal interest rate is the
opportunity cost of holding money. Thus a fall in the nominal interest rate should lead to an
increase in the quantity of money demanded.
b) At iA, there is excess demand for money balances. Firms and households attempt to sell
their current holdings of bonds (in return for money). This attempt in the aggregate to sell
bonds drives down their price and thus drives the interest rate up. As the interest rate rises,
firms and households reduce the quantity of money demanded. This process continues until
i* is reached, at which point the amount of money available is willingly held.
c) At iB, there is excess supply of money balances. Firms and households attempt to get rid
of their excess money holdings by purchasing bonds. This attempt in the aggregate to buy
bonds drives the price of bonds up and thus reduces the interest rate. As the interest rate
falls, firms and households increase the quantity of money demanded. This process
continues until i* is reached, at which point firms and households are willing to hold the
available supply of money.
d) An increase in the transactions demand for money, caused for example by an increase in
real GDP, is illustrated in the figure by a rightward shift in the MD curve. At i*, there is
excess demand for money. People try to sell some of their current bond holdings to satisfy
their increased demand for cash. But there is only so much cash available. The effort in the
aggregate to sell bonds drives the price of bonds down and thus causes the interest rate to
rise, choking back the quantity of money demanded (an upward movement along the new
MD curve). This adjustment continues until the existing supply of money is willingly held,
at a new higher equilibrium interest rate.
Question 7
a) An increase in the money supply shifts MS0 to the right. At i0, there is now an excess
supply of money. Firms and households try to purchase bonds with their excess money
holdings, and this drives the price of bonds up and the interest rate down. As the interest
rate falls, the quantity of desired investment increases — a movement down and to the right
along the ID curve.
b) A reduction in the demand for money (an increase in the demand for bonds) shifts the
MD curve to the left. At i0, there is now an excess supply of money. As firms and
households try to purchase more bonds, the price of bonds is driven up and the interest rate
is driven down. This adjustment occurs until firms and households are once again willing to
hold the unchanged amount of money balances (because the interest rate is now lower). As
the interest rate falls, the quantity of desired investment increases, a movement down and to
the right along the ID curve.
c) Parts (a) and (b) show that, in terms of the effect on the amount of desired investment, a
reduction in the demand for money looks just like an increase in the supply of money, in
the sense that both shocks lead to a fall in the interest rate. This is an important feature of
the monetary transmission mechanism. Since it is changes in the interest rate, other things
equal, that determine changes in desired investment, changes in the demand for money can
have similar effects as changes in the supply. What matters, ultimately, is what happens to
the interest rate. A reduction in the interest rate coming about from a shock to the money
market will stimulate investment; an increase in the interest rate coming about from a shock
to the money market will reduce investment.