Consider an economy with a shrinking sto ck of at money. Let N t = N , a constan
ID: 1169835 • Letter: C
Question
Consider an economy with a shrinking sto ck of at
money. Let
N
t
=
N
, a constant, and
M
t
=
zM
t
1
for every p erio d
t
, where
z
is p ositive
and less than 1. The government taxes each old p erson
go o ds in each p erio d, payable
in at money. It destroys the money it collects so that the sto ck of money decreases.
(a) Find and explain the rate of return in a monetary equilibrium.
(b) Prove that the monetary equilibrium do es not maximize the utility of the future
generations.
Hint:
Follow the steps of the equilibrium with a subsidy, noting that
a tax is like a negative subsidy.
(c) Do the initial old prefer this p olicy to the p olicy that maintains a constant sto ck
of at money? Explain
Explanation / Answer
A....
In money markets, an interest rate at which the demand for money and supply of money are equal. When a central bank setsinterest rates higher than the equilibrium rate, there is an excess supply of money, resulting in investors holding less money andputting more into bonds. This causes the price of bonds to rise, driving down the interest rate toward the equilibrium rate. The oppositeoccurs when interest rates are lower than the equilibrium rate: there is excess demand for money, causing investors to sell bonds toraise cash. This decreases the price of bonds, causing the interest rate to rise to the equilibrium point. Central banks can use theequilibrium rate of interest as a tool in determining the appropriate money supply.
As the most recent statement of the Federal Open Market Committee (FOMC) made clear, the U.S. economy appears to have moved out of the soft patch that characterized the second quarter. Supported by ongoing advances in productivity and the attendant increases in real incomes, household spending has picked up. Businesses, for their part, seem to have shaken off at least some of their hesitancy to spend, although the subdued pace of hiring may signal that they still retain a wary attitude toward making important commitments. But the strengthened balance sheets of the business sector, along with buoyant cash flow, should provide firms with the wherewithal to fund a healthy expansion of the capital stock in coming quarters. No doubt the recent run-up in energy prices poses some challenges, but the evidence indicates that, without some further material shock, aggregate demand is on a track consistent with sustained economic growth. That should gradually return the economy to full utilization of its resources, while inflation remains subdued.
B... that there is no time subscript on the tax, . This tax will be independent of time in a stationary equilibrium. This tax must satisfy the government budget constraint = vt(Mt1 Mt) N = vt(1 z)Mt1 N = vt 1 z 1 Mt N . The lifetime budget constraint would be c1 + vt vt+1 c2 y vt vt+1 . Build this lifetime constraint from the individual period constraints on your own. (Note that the tax must be subtracted from the endowment in the second-period constraint.) The rate of return on fiat money will be (in a stationary equilibrium with a constant population) vt+1 vt = Nt+1(yc1) Mt+1 Nt(yc1) Mt = Mt Mt+1 = 1 z > 1.
Here, since z < 1, the value of money increases over time (alternatively, the price level decreases over time—deflation). Given this information, the lifetime budget set becomes c1 + zc2 y z
C.....We've seen that the real rate of interest is the difference between expected inflation and the nominal rate of interest that we see quoted in the paper
Now suppose we do the same thing with money. This is unrealistically simple (remember, we're doing theory now!) but suppose the government were to replace every dollar with two new dollars, marked so we can tell the difference between old and new dollars. Then you'd expect, I think, that prices in terms of new dollars would be twice as high. In short, changes in the money supply executed in this way will be associated with proportionate changes in prices, with no effect on output or employment.
Application: Friedman's Money Growth Rule
The quantity theory was the basis (or a big part of it) for one of the sharpest policy debates in the postwar period. Then, as now, there were many businessmen, economists, and government officials who thought that monetary policy should be chosen to micro-manage or fine tune the economy: to help smooth out the recurrent ups and downs that we've labeled the business cycle. Milton Friedman, who made a career out of playing devil's advocate, advocated precisely the opposite: that the Federal Reserve should follow a policy consistent with (we'll leave the operational aspects for later) a constant rate of money growth of about 4 percent a year. Given output growth of about three percent, on average, that would be expected to lead to average inflation of about 1 percent a year.
Over the years Friedman provided many arguments for constant money growth rates. Here are a few of them (stated as hypotheses to think about, not self-evident truths):