Expanded Model of Income Determination
The model above does not
include many of the features of a modern market economy. The following model
will add a government sector, an
international sector, and business savings. We will continue to assume that
potential output is fixed, that there is a fixed relationship between output
and employment, and that all investment is carried out by private firms.
Investment Fluctuations
One of the major failings of
the simple model is that it treats investment as stable at all levels of
income. In fact, observations show that investment expenditure is very unstable
over time. Investment expenditure is quantitatively less important than
consumption expenditure (tpical values for I range from 15% to 30% of GNP), but
because I is much more variable over time than C, it has a major role to play
in explaining the short run behavior of income and output.
Investment is undertaken in
the hope and expectation that it be profitable. To assess whether any proposed
investment scheme will be profitable, a business has to arrive at an objective
of subjective judgement of three factors:
(a)
The cost of the
investment;
(b)
The expected
returns from the investment in the form of increased income;
(c)
The cost of
financing the investment.
The first two factors give
the rate of return over cost, which is known as the marginal efficiency of
investment (r) which is the same as the accounting concept of IRR. The third
factor, the cost of financing, is the rate of interest (R). For some
investments, particularly those that are very large or extend over a long
period of time, the cost of the investment can only be estimated at the time of
the initial decision. For other investments, the cost is known with great
accuracy. But for practically all investments, the expected returns involve
uncertainty. Thus a firm must make estimates of the expected returns on its
investments. In addition, for many investments, either the expenditure or the
return are expected to take place over a lengthy period of time.
It is assumed that every firm
faces a list of possible investments and must decide which to undertake. It
would be very unlikely that every investment on the list would have the same
rate of return, so the list will be ordered from highest to lowest expected
rate of return. As the volume of investment undertaken increases or decreases,
the overall return expected will also increase or decrease. In addition, as the
volume of investment increases, it will put greater pressure on the productive
capacity of the capital goods industries, and, as costs in those industries
rise, the increasing cost of capital equipment will lower the marginal
efficiency of investment. This results in a ‘marginal efficiency of investment
schedule’ that shows the expected rate of return for each possible volume of
investment.
However, there is no
convincing historical evidence to suggest that the rate of return has declined
over time even though volume has increased, primarily because technical
knowledge improves over time and shifts the marginal efficiency of investment
schedule to the right.
If the only factors
influencing investment decisions were the expected returns and the costs, then
all investments with a positive rate of return would be undertaken. However,
the funds used for any investment have an opportunity cost, that being the
value of their next best alternative use. For a given rate of interest R, money
can always be lent out at that rate at very low risk. As a result, it is not
rational for any investment to be undertaken where the expected return r is
less than the interest rate R, because more profit would be made by simply
lending the money out. This means that the volume of investment actually
undertaken will equal the point on the marginal efficiency of investment
schedule where R=r, as shown here (assuming, of course, that firms are
economically rational profit maximizers—in reality, these decisions are not
nearly so mechanistic):
The function resulting in the MEI curve (shown above as a straight line) is the investment function, I=f(R). Movements along this curve occur when the rate of interest changes. Shifts in this curve occur when the relationship between rate of interest and total investment expenditure change for all values. Shifts in the MEI curve occur frequently. The two most inportant reasons are:
(a)
business
expectations;
(b)
the degree of
uncertainty.
The calculation of r (rate of
return, aka marginal efficiency of investment) depends on estimates of future
returns. These estimates are fundamentally affected by firms’ expectations and
uncertainty about what the future holds. A firm must make judgements concerning
future costs and prices, technological advance, political disturbances, the
behavior of competitors, changes in government policy, political disturbances,
the actions of consumers, and so forth. The role of expectations in investment
decisions explains why investment is one of the more volatile components of
national income. If the managers who make investment decisions become
pessimistic through fears of a coming recession, the MEI curve will shift to
the left and the volume of investment undertaken for all rates of interest will
be reduced. In addition, the MEI curve is affected by the amount of uncertainty
firms feel in their estimates. Assuming firms estimate conservatively, the MEI
curve will shift to the left as uncertainty increases, and to the right as it
decreases. More investment will be undertaken for all rates of interest when
firms feel that their estimates are comparatively reliable.
Shifts in the MEI curve are
likely to be of more importance than movements along it. Planned investment is
subject to sudden sharp changes rather than smooth, predictable movements. In
fact, some economists question the importance of the rate of interest to the
volume of investment—they claim that changes related to firms’ expectations and
uncertainty are so substantial and frequent that changes related to the rate of
interest are almost trivial by comparison. As a result, it may be difficult to
influence the volume of investment through monetary policy: Investment may be
interest inelastic.
Some economists also believe
in the accelerator (as distinct and different from the multiplier). The idea
here is that some investments are determined by the rate of change of national
income/output. For example, suppose a firm producing shoes requires $2 million
of capital goods to produce $1 million output of shoes and this capital-output
ratio is fixed at all levels of output. If the firm is selling $1 million in
shoes and economic growth occurs such that the demand for the firm’s shoes
rises to $1.5 million, then the firm must invest an additional $1 million in
new capital for the production of the higher volume of shoes. If growth then
ceases and the firm continues to operate at the $1.5 million level of output,
then no additional capital investment occurs. If demand for the firm’s goods
decreases, the firm is likely to disinvest, or go out of business, or what have
you, so the accelerator principle also applies to reductions in the rate of
growth. The accelerator is related not to national output itself, but to the
rate of change of national output. Hence, DI=aDY where a is the accelerator, aka the capital-output ratio.
The accelerator principle
does not yield a comprehensive explanation of investment, because not all
investment is in capital goods required to produce output. Other types of
investment are not subject to the accelerator principle: replacement
investment, research and development, ‘autonomous’ investment, etc. In
addition, even where the accelerator principle applies, the causeal connection
is often less immediate and simple than the above explanation suggests.
However, empirical evidence does suggest that a significant portion of the
fluctuations in investment observed may be associated with the rate of change
of national output.
As with any change in demand,
a multiplier effect also exists for investment expenditure: DY=kDI, where k is the multiplier. The
causal relationship for the multiplier effect is that changes in investment
result in proportionally larger changes in national output. The causal
relationship is reversed for the accelerator effect: Changes in national output
result in additional changes in investment. The accelerator principle suggests
that the secondary effects of ‘first-round’ investments are likely to be larger
and more complicated than explained by the multiplier effect alone. As with
changes in consumption expenditure, both the multiplier and accelerator effects
can only occur where Y<Q.
The Government Sector
Government taxation and
expenditure (fiscal policy) are analogous to household saving and business
investment. Taxation (and saving) is a withdrawal from the circular flow of
income, and expenditure (and investment) an injection. Equilibrium national
income is reached when S+T=I+G. It follows from this that planned savings and
planned investment can diverge without causing a change in equilibrium income,
if the difference is offset by an inequality of the same magnitude but opposite
sign between taxes and government expenditure.
GNP=C+I+G
GNI=C+S+T
At equilibrium, GNP=GNI;
therefore, S+T=I+G. Alternately, S=I+(G-T). As a result, private investment
varies inversely with government budget defecit. This assumes that C=C, but in
fact there are two different values: C produced and C bought:
GNP=CP+I+G
GNI=CB+S+T
When CP > CB,
unintended inventories will accumulate (in the short run). When CB
> CP, inventories will be depleted faster than planned. These
changes in inventory level are a form of investment, InvU=CP-CB.
So:
GNP=CP+I+InvU+G
GNI=CB+S+T
\ S=I+InvU, given a balanced budget (G=T)
There are two types of
government expenditure. The first, represented by G, is money spent on current
goods and services. The second is transfer expenditure, such as welfare
payments. Transfer expenditure is not part of G; it is deducted from T as a
‘negative tax’. So T does not represent total taxation; it is actually tax
reciepts less transfer payments.
The government purchases
goods and services from the private sector (firms and households) to produce
government services such as defense, law and order, health and education. The
government typically distributes these services to citizens at zero or minimal
charge, and finances them through tax reciepts. If taxes are insufficient to
pay for government services, then the government must borrow money from
households and firms.
The expanded model of income
determination takes the following as exogenous: G, T, I. Note that taking T as
exogenous means that it is a poll tax or otherwise unrelated to income. Also
note that Y cannot increase beyond Q but this is not shown by the model. The
model is defined as:
Solving for Y produces:
From this can be derived the
change in Y that will result from a change in any of the exogenous variables
representing government expenditure, taxes less transfers, and investment:
The next step is to build a
model where investment (I) is not entirely exogenous. Suppose some part of I is
a function of income. (Note that we actually think investment should depend on
some combination of the rate of interest or on the rate of change of income.)
The model then becomes:
And the solution becomes:
Next, we can consider the
effects of an income tax. The previous model took T as exogenous, unrelated to
income, for example a poll or head tax. However, modern economies generally
feature an income tax:
The solution for this model,
for which I is again considered exogenous, is:
The difference here is that
the income tax reduces the value of the multiplier, where the poll tax did not.
This is because the poll tax is a simple subtraction (YD=Y-T), but
the income tax takes a cut from each round of the multiplier effect.
Suppose that unemployment
exists and the government wishes to reach full employment. To do so through
fiscal policy, it can decrease taxes or increase government expenditure. If it
increases government expenditure, it has simply increased demand by the amount
of the increased expenditure. The full multiplier effect applies. However, if
it reduces taxes, the tax reduction by itself does not produce any additional
demand. The tax cut winds up in the hands of consumers, who will spend a
portion of it determined by the marginal propensity to consume (b). This is why
DY/DT is different from DY/DG. The consequence of this is that
if the government’s budget is balanced, and G and T must increase in lock-step,
the multiplier for additional government spending is 1 – the negative
multiplier effect from the increase in taxes exactly cancels out the multiplier
effect from the additional expenditure, so the change in Y is equal to the
change in G.
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