The IS Curve
In the simple income-expenditure model there was no
explanation for what determined investment--it was imply
assumed fixed. However, investment decisions are not
arbitrary, but are determined by businessmen calculating the
costs and benefits of additions to their capital stock and
inventories, and by consumers calculating the costs and
benefits of purchasing houses. Thus the model will be a
better model if it can incorporate reasons for investment
rather than leaving it outside the model.
Though the calculations determining the amounts of
various categories of investment are each a bit different,
all involve the interest rate. We will consider only the
sort of calculation behind the decision to purchase new
machinery, and will leave the decisions about inventory and
housing to more advanced courses.
When a business decides whether or not to invest in new
equipment, it estimates as best it can the future returns
that will flow from the new equipment. Then it must compare
these benefits to the costs of the investment. Suppose, for
example, that a business can buy a new machine that it
believes will add output worth $20,000 each year for five
years. One might assume that the firm would decide to buy
the machine if it costs less than $100,000. For example, if
the machine costs $95,000, the firm could make a profit of
$5000. However, this conclusion is wrong because it ignores
the interest rate and the concept of present value.
If the firm must borrow the $95,000 in the above example
and the interest rate is 10%, the machine would never earn
enough to pay both the original cost and the interest on
that cost. One could use the first year's returns of $20,000
to pay off part of the debt, but in the first year the
amount owed would have grown by 10% or $9500. Thus after one
year the business would owe $95,000-$20,000 + 9500 =
$84,500. Continuing with future years, one sees that the
business will lose money by purchasing the machine.
One might at this point argue that the conclusion would
be different if the firm financed the machine from retained
earnings. The argument is wrong. The firm has a choice of
investing its $95,000 either in the machine or in a
financial asset that will earn interest. Unless the firm is
run by fools (in which case its future is not bright), it
will use its funds where returns are highest.
In determining how much to invest, the firm must consider
both the cost of the machinery and the cost of financing the
investment. This latter cost depends on the interest rate.
It also considers the potential returns on the investment,
which depends on expected future spending in the economy.
Thus in 1933, when there was massive unemployment of men and
machines, there were few investment purchases which could
have offered much of a return in future years. Even if the
cost of financing new investment had been close to zero (it
was not for most businesses, though it was for the
government--interest rates that a borrower faces depend on
how risky he seems to the lender), it would have made no
sense for most businesses to add equipment. They already had
plenty idle, and it served no purpose to build more to sit
idle.
One could also argue that interest rates should affect
consumption. Changes in interest rates affect the benefits
from saving and the cost of borrowing. They also affect the
value of financial wealth, and wealth should affect
consumption. A rise in the interest rate causes the value of
existing bonds to fall and a fall in the interest rate
causes the value of existing bonds to rise. However, to keep
the discussion simple, we will continue assuming that
consumption is unaffected by changes in interest rates.
The modification that the above discussion makes to the
simple income-expenditure model is illustrated below. In
this table there are two columns that show investment. One
column shows what investment will be at each level of income
if the interest rate is 5%, while the other shows what
investment will be if the interest rate is 4%. If the
interest rate is 5%, equilibrium income is 600. If the
interest rate drops to 4%, equilibrium income will rise to
700. Similarly, different levels of investment would exist
for all other levels of interest rates, and for each
interest rate, there would be an equilibrium level of
income. We expect that lower interest rates would spur
investment, and thus be associated with higher levels of
equilibrium income.
The Income-Expenditure
Model when Investment Depends on Interest
Rate
|
If Expected Income Is:
|
People will Pay Taxes
|
People will Spend
|
People Will Save
|
Government Spends
|
Investment @ 5%
|
Investment @ 4%
|
500
|
20
|
450
|
30
|
20
|
45
|
60
|
600
|
20
|
530
|
50
|
20
|
50
|
65
|
700
|
20
|
610
|
70
|
20
|
55
|
70
|
800
|
20
|
690
|
90
|
20
|
60
|
75
|
When we construct a graph showing equilibrium income is
for each level of interest rate, we get a curve similar to
that graphed below. It is called the IS curve, and
its name comes from the condition for equilibrium when there
is no government in the model: investment (I) must equal
savings (S).
The addition of the interest rate to the
income-expenditure model opens a way for monetary policy to
influence spending within the logic of this model. When the
central bank allows the banking system to create more money,
banks increase their lending. This additional supply of
funds reduces interest rates. Lower interest rates increase
investment, which has a multiplier effect on total spending.
A contraction of money will have opposite results.
Next we take a closer look at how money
can be included in our synthesis.
Copyright
Robert Schenk
|