G 
= T + ΔB + ΔH
where G is government expenditure, T is taxes,
ΔB is the sale of bonds and ΔH
is an increase in the stock of base or high-powered money. Note that
Δ refers to the per-period change in the variable
that follows.
Suppose that the government finances the tax cut by printing money.
Since consumption, as noted above, depends on permanent income this
raises the question: Does this increase the public's permanent income?
Consider first the less-than-full-employment case. Since the price level
does not increase, the growth of nominal money holdings will increase real
money holdings, putting an increased flow of resources at private
individuals' disposal. This income flow will be temporary, of course, as
long as the cut in taxes is temporary.
This is little more than simple expansionary monetary policy. The
government can expand the money supply by buying
bonds from the public with freshly printed money or giving that
money to private individuals by cutting their taxes. If people
feel that their permanent income has increased they will spend
more on consumption. Since the tax cut is temporary, the
objective being to temporarily increase aggregate demand, the
effect on consumption will be much smaller than postulated by the
simple traditional Keynesian analysis. If the exchange rate is
fixed there will be some expansion of output and employment due
to the effect of the increase in consumption on the IS curve.
Under flexible exchange rates there will be no ultimate effect on
the IS curve but the monetary expansion will shift the LM curve
and result in an expansion of output and employment.
Ultimately, of course, full employment will be reached and
beyond that point the price level must rise in proportion to the
monetary expansion. The real money supply will not increase.
The public gives goods to the government in return for money
whose value is immediately eliminated by a rise in the price
level. The public has, it turns out, given goods to the government
for nothing in return. This is exactly what was happening when the
government was levying taxes to financed its expenditure rather than
printing money.
Since each member of the public wants to maintain her money
holdings at the equilibrium level in the face of the rise in
prices, she must give to the government sufficient goods to
acquire an amount of nominal money proportional to her existing
holdings. The government is simply substituting a proportional
tax on existing money holdings for conventional forms of taxation.
Since the public is paying the same real taxes whether
the government is printing money or using conventional taxation,
the switch from tax to monetary finance of government expenditure
has no effect on permanent income. It therefore will have no
effect on consumption and the fiscal policy will be ineffective
---that is, it will not shift the IS curve---once full-employment is
reached.
When there is less than full employment the money acquired
as a result of the tax cut does constitute a temporary increase
in current income and therefore should have some (albeit small)
effect on consumption and on the IS curve. The size of this effect
is limited not only by the temporary nature of the tax cut, but by
private individual's understanding that as soon as full-employment is
reached the tax saving will be automatically replaced by a tax on
money holdings. There is thus no possibility that the public
could view the tax cut as an equal corresponding permanent
income flow.
We must conclude that if the exchange rate is fixed it will
be better for the government to increase the money supply by
cutting taxes rather than by having the central bank buy bonds
from the public. To the extent that the recipients of the tax
cut feel wealthier and spend more---some rightward effect on the
IS curve will result and output and employment will therefore
rise. The effect of the monetary expansion on the LM curve will
be eliminated by the reduction in official foreign exchange
reserves necessary to keep the domestic currency from devaluing.
When the exchange rate is flexible---and equilibrium is therefore
determined by LM and ZZ---straight-forward open market operations in
bonds will be the best policy since the IS curve will be independent
of fiscal policy and other shocks to the real goods market.
Its time for a test. Be sure to think up your own answers to the
questions before looking at the ones provided.
We now turn to an analysis of the situation where the
government cuts taxes and finances the short-fall of taxes
relative to expenditure by printing money.
Consider the government's budget constraint developed previously.
The government must finance its expenditure either through taxes,
the sale of bonds or the printing of money: