
© 20012003 Douglas A. Ruby
Revised: 01/15/2003
Basic Definitions
Interest Rates
Financial Markets and Instruments
Aggregate Demand
Investment Decisions
Money Market Equilibrium
Overview of Economics
Macroeconomic Principles
Macroeconomic Theory

Savings, Investment, Interest Rates
and the Flow of Funds
A general approach to analyzing changes in the structure of interest rates is via the
Flow of Funds model. This model examines the
broad determinants of savings in a macroeconomy and treats the
real interest rate as the variable that
aligns a given level of savings with investment needs.
Savings represents the source of funds in the model and
domestic Investment Expenditure represents the use of those funds. It is important
to keep in mind that these funds being transferred from lender to borrower represent
scarce resources. These resources are made available via the saver foregoing current consumption allowing
these resources to be used for the creation, accumulation, and replacement of capital  capital that will
allow labor to be more productive in the future.
The model begins with the Income Identity:
Y = C + I + G + NX
rearranging terms:
Y  C  G  NX = I(r)
where the lefthandside of the equation represent the source of funds and the
righthandside, the use of funds. Additionally, we note that Investment decisions
are (negatively) related to the real rate of interest 'r'.
By subtracting and addingin taxes 'T' which represents the transfer of
resources from the private sector to the public sector we have:
[Y  T  C] + [T  G] + [NX] = I(r)
Each term in brackets now represents a separate type of savings defined as follows:
 S_{Private} = [Y  T  C] ... Private savings,
 S_{Public} = [T  G] ... Public Savings and,
 S_{foreign} = [NX] .. Foreign Savings
Note that NX represents the Current Account Balance
within the balance of payments. Thus, its negative, [NX] represents the
Capital Account Balance (see the Balance of Payments
link).
Adding these three terms together we have:
S_{National} = S_{pvt} + S_{pub} + S_{foreign}
This is shown by the vertical line in the diagram below. The real rate of interest will adjust
in competitive financial markets to bring National Savings into an equality with Domestic
Investment as shown by r_{o}.
Before
After
Various shocks can affect the flow of funds and thus the rate of interest. For example, an increase
in investment expenditure perhaps due to an increase in the productivity of capital or due to growth in
the real economy will shift the Investment schedule to the right (click the After button).
Fiscal policy shocks can also affect the flow of funds and real interest rates. For example, suppose that
Government Expenditure G decreases. Holding taxes constant, this will lead to an increase in
Public Savings and National Savings. The savings
function will shift to the right creating an excess supply of funds thus causing
the real rate of interest to fall (click on the Government Exp. button).
Initial Position
Government Exp.
Tax Rate
Changes to the tax rate is a bit more complicated. Changes in taxes affect both consumption expenditure
and thus Private Savings as well as Public Savings directly. However, working through the
Marginal Propensity to Consume, an increase in the tax rate reduces Consumption
Expenditure / Private Savings by less than the increase in Public Savings (press the Tax Rate button).
A Numerical Example
Suppose that we have the following equations:
C = 0.80(Y  T) ... consumption expenditure, MPC = 0.80
T = 0.20(Y) ... Tax Revenue, tax rate = 20%
G = 2,000 ... Government Exp. (billions)
NX = 500 ... Current Acct. Balance (deficit)
I = 2,600  100(r) ... Investment Exp.
Y = 10,000 ... Real GDP (Output in billions) held constant.
Solving (given Y = 10,000), we find that:
T = 2,000
C = 0.80(10,000  2,000) = 6,400
and
S_{pvt} = Y  T  C = 1,600,
S_{pub} = T  G = 0 and,
S_{foreign} = [NX] = 500
thus,
S_{National} = 1,600 + 0 + 500 = 2,100
setting S_{National} = I(r) we have:
2,100 = 2,600  100(r) and
r_{0} = 5% and Investment expenditure = 2,100.
* * *
Now, if the tax rate were to be reduced to 10% (t' = 0.10):
T' = 1,000
C' = 0.80(10,000  1,000) = 7,200 and
ΔC = +800
and
S'_{pvt} = Y  T  C = 1,800 and
ΔS_{pvt} = +200
S'_{pub} = T  G = 1,000 and
ΔS_{pub} = 1,000
S_{foreign} = [NX] = 500 as before.
Thus,
S'_{National} = 1,800  1,000 + 500 = 1,300 and
ΔS_{National} = 800
setting S'_{National} = I(r) we have:
1,300 = 2,600  100(r) or
r_{1} = 13% and Investment expenditure = 1,300.
Reducing the tax rate from 20% to 10% has led to an increase in the
real interest rate from 5% to 13%. With this interest rate increase, private Investment
Expenditure will be reduced (from 2,100 to 1,300).
Concepts for Review:
 Flow of Funds
 Investment Expenditure
 Marginal Propensity to Consume
 National Savings
 Private Savings
 Public Savings
 Real Interest Rate
