From Macroeconomics: Applied Assessments and Policy Options
Evan Tanner
© 2014, all rights reserved
8.3 The Real Interest Rate, Saving, and Investment in Closed Economy: A
Loanable Funds Approach
LO 8.3 Show how the real interest rate, savings, and investment are jointly determined using a model of
supply and demand for loanable funds in a closed economy.
Throughout this book, we have discussed the linkage between savings and investment. When
people save (refrain from consuming), they are able to instead purchases capital goods that will help
them produce more goods tomorrow. In the first chapter we learned several versions of the savings –
investment identity. The most basic version is that for a closed economy with no government.
The most basic version is that for a closed economy with no government. In such a simple economy, the
identity of income with expenditures tells us that:
Y =
Total
Output
C
Consumption
(Private)
+
I
Investment
(Private)
Special case
Closed economy, no govermment
(8.13)
In this case, since the economy’s savings is income minus consumption, investment must be equal to
savings:
I
Investment
(Private)
= S
Savings
(Private)
(8.11)
Special case
Closed economy, no govermment
We expanded this simple case to include a government that could run a surplus or a deficit: GBS (GBS>0
reflects a public surplus; GBS<0 reflects a budget deficit). In this case, capital investment would equal
total domestic savings – private plus government.
The more general case was that of an open economy in which investment was funded by three sources
of saving: private domestic, public domestic and external savings (minus one times the current account
deficit). This case will be discussed in the next section.
Our goal in this section is to show how savings and investment are brought into equality. Starting with a
closed economy (but moving to an open one in the next section), we will see the key price that equates
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From Macroeconomics: Applied Assessments and Policy Options
Evan Tanner
© 2014, all rights reserved
investment with savings is the real interest rate. This idea is summarized in Figure 8.8. In a previous
chapter, we learned that the real interest rate was a reward for saving. Saving should increase when the
real interest rate increases – although “how much” is a question that economists disagree on. In this
chapter, we learned that the real interest rate is the opportunity cost of capital; when the real interest
rate increases, the demand for investment expenditures will fall. In fact, both definitions hold.
As in other markets, supply and demand are equated at an equilibrium price that is set in a market.
Here, we assume that the equilibrium real interest rate equates investment and savings in a market for
loanable funds. For this reason, the model that we will use to analyze this question is often called the
loanable funds model. This model emphasizes the fact that savings from various sources are loaned out
to firms for the purposes of investment; the real interest rate must be the price that brings the desired
amount of investment into equality with the desired amount of savings.
We can most easily see the key intuition of the loanable funds by considering the simplest case: that of a
closed economy where the government runs a balanced budget (GBS =0). In this case, it is domestic
private savings that are equated with investment. This first example, shown in Figure 8.9, illustrates how
desired savings and desired investment are equated. The vertical axis shows the real interest rate, while
the horizontal axis showed savings and investment. The investment demand function is the downward
sloping blue line, reflecting the negative relationship between investment and the interest rate.
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From Macroeconomics: Applied Assessments and Policy Options
Figure 8.9
Evan Tanner
© 2014, all rights reserved
Loanable Funds Model (Closed Economy)
Savings and investment in percent of output
Real interest rate (r ) in percent
7.0%
6.0%
Investment Function
5.0%
Domestic Private Savings
Function
In a closed economy, the
interest rate adjusts to equate
total domestic investment to
total domestic savings.
S > I;
4.0%
3.0%
2.0%
1.0%
S < I;
0.0%
16.0%
16.5%
17.0%
17.5%
18.0%
18.5%
19.0%
19.5%
20.0%
Savings (S) and Investment (I) in percent of output
Real
interest
rate
Ba s eline / Equilibrium
r
4.3%
2.8%
1.3%
Desired
Savings
Ratio
S
18.2%
18.0%
17.9%
Desired
Investment
Ratio
I
17.1%
18.0%
18.9%
This figure shows how the interest rate adjusts to equilibrate savings and
investment under. In the example, savings and investment are equated at
an interest rate of 2.8%.
If the initial interest rate lies above this value, savings will exceed desired
investment (S>I). As the interest rate falls, desired investment spending will
increase and desired savings will fall – until savings and investment are
equated.
If the initial interest rate lies below this value, desired investment will
exceed savings (I>S). As the interest rate rises, desired investment
spending will decrease and desired savings will increase – until savings and
investment are equated.
Where did we get these numbers / Online Feature: Calculating equilibrium saving,
investment, interest rate, and the current account in the LF model. Replicate the
Baseline
alt(i)
alt(ii)
Where did 13260
we get
those
Output
13525
13931
numbers?
Inflation
3
2.4
2.9
ONLINE FEATURE
Interest Rate
4.5
4.7
4.6
numbers under the graphs. Create your own investment / saving scenarios with the LF
model. The method is similar to the supply/demand model of Chapter 3. END Where did we get those
numbers callout.
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From Macroeconomics: Applied Assessments and Policy Options
Evan Tanner
© 2014, all rights reserved
The savings supply function is shown by the upward sloping green line, reflecting the assumption that
higher rates of interest encourage more saving by domestic households (as we learned in a previous
chapter).
In the figure, investment and saving both equal 18% of output when the real rate of interest is 2.8%.
Hence, the equilibrium real interest rate is 2.8%. To see how the market for loanable funds equilibrates,
suppose that the initial interest rate is greater than 2.8%. Recall from a previous discussion that, for
savers, the interest rate may be thought of as a reward for consuming less and saving more. Here, when
the interest rate exceeds its equilibrium value, that savers are asking for a reward that is “too high”
relative to the interest rate that the marginal firm is willing to pay. Hence, we start from a position
where desired savings exceeds desired investment (S>I).
To clear the market, savers will accept progressively lower interest rates as their reward for saving. As
this happens, some savings will be withdrawn; at lower interest rates, some individuals will choose to
consume more and save less. At the same time, as the interest rate falls, desired investment increases -firms expand their capital expenditures. Hence, the interest rate will continue to fall until the gap
between savings and investment is eliminated – as shown by equilibrium in Figure 8.9.
From the other direction, suppose that the initial interest rate is less than 2.8%. In this case, savers are
asking for a reward that is “too low” relative to the interest rate that demanders are willing to pay.
Hence, desired investment will exceed desired saving (I>S). In this case, competition amongst
demanders will bid up the interest rate.
When this happens, savers will be encouraged to save even more than previously, while desired
investment falls – as firms cut back on their desired capital expenditures. The interest rate will continue
to rise until the gap between investment and investment is once again eliminated; this example is
symmetric with the previous one.
Do Public Deficits ‘Crowd-out’ Private Investment?
We will now expand our example by adding government spending to the national accounts identity (as
previously shown in Chapter 1):
Y =
Total
Output
C
+
Consumption
(Private)
I
Investment
(Private)
Special case
Closed economy
4

G
Government
spending
(8.14)
From Macroeconomics: Applied Assessments and Policy Options
Evan Tanner
© 2014, all rights reserved
Thus, the savings-investment identity now becomes:
I(r;....) = S(r;...) +
Investment
(Private)
Savings
(Private)
T-G
Government
Budget
Surplus
(Public savings)
(8.15)
Special case: closed economy
This identity tells us that, in a closed economy, there are two sources of funding for private investment:
private savings and the government budget surplus (T-G). Figure 8.10 shows how the interest rate,
investment, and private savings would respond to an increase in the government budget deficit from a
loanable funds perspective. In the figure, there is a baseline and one alternative scenario. Under the
baseline, public savings is zero – no deficit, no surplus. As before, private savings and private investment
equal 18% of output at the equilibrium interest rate -- 2.8%.
Under the alternative scenario (alt(i)) the government increases its spending by 1% of output – but
leaves taxes alone. Since the total supply of savings – private plus public – falls, the total savings supply
curve must shift to the left. As we saw in the balance sheet example, the public sector may be viewed as
competing with private firms to be funded with private savings.
For this reason, there is pressure on the interest rate to rise. Higher interest rates mean that fewer
investment projects will take place. Thus, under the alternative scenario, the interest rate rises from
2.8% to 4.2%. The cutback of investment is substantial – from 18% to 17.14% of output. At the same
time, higher interest rates have encouraged a small amount of extra saving – from 18% to 18.14% of
output.
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From Macroeconomics: Applied Assessments and Policy Options
Evan Tanner
© 2014, all rights reserved
Figure 8.10
Loanable Funds Model: Closed Economy
Savings and Investment, in percent of output
Real interest rate (r) in percent
7.0%
Tota l Savings (Pri vate plus Public)
6.0%
5.0%
When government reduces
savings, total savings curve
shifts to the left.
4.0%
3.0%
2.0%
Investment Function
1.0%
0.0%
16.0%
16.5%
17.0%
17.5%
18.0%
18.5%
19.0%
19.5%
20.0%
Savings (S) and Investment (I) in percent of output
S(public)
S(private)
S(total)
req
I
baseline
0.0%
18.0%
18.0%
2.8%
18.0%
alt(i)
-1.0%
18.14%
17.14%
4.2%
17.14%
Public savings falls.
Small increase in private savings.
Decrese in total savings.
Interest Rate Increases
Investment Spending Falls
This figure shows how the interest rate adjusts to equilibrate total
savings (private plus public) and private investment. Under the
baseline, public savings is zero, while private savings and investment
equal 18% of output at the equilibrium interest rate of 2.8%.
Under the lone alternative scenario (alt(i)), the government increases
its spending, but not its taxes, by 1% of output. This shifts the total
savings supply curve (public plus private) to the left.
This pushes the interest rate upward: the public sector is now
competing with private firms for private savings. Higher interest rates
mean that fewer investment projects will take place; some
investment is ‘crowded out’. At the same time, higher interest rates
encourage some extra private saving – but only a small amount.
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From Macroeconomics: Applied Assessments and Policy Options
Evan Tanner
© 2014, all rights reserved
Thus, this scenario shows one of the principal consequences of higher government budget deficits – the
displacement or crowding out of private sector investment. (Key term: crowding out: the displacement
of investment that takes place when there is a decrease in savings – typically public sector savings]. The
crowding out effect occurs precisely because investment expenditures are interest sensitive – an
increase in the interest rate will crowd-out some investment projects. In this scenario, we do see private
savings increase. However, this effect is not very large: savings is less sensitive than investment to
changes in the interest rate.
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