Saving and Investment Demand Lecture Notes
(Chapter 9 of the Text)
Definitions
Saving = Current Income – Current Consumption
Note that by this definition saving is measured as a “flow” variable. That means it is
measured over a period of time. For example, one can talk about saving per year, or saving
per month.
However, wealth is defined as the total amount of assets that a person owns at a point in time.
Hence wealth is a “stock” variable, meaning it is a variable measured at a point in time. For
instance, one can talk about the wealth of a person on December 31, 2012.
Since saving is income minus consumption, one can also say that savings is the addition to
assets in a given period of time. This means that wealth is the accumulation of all past
savings.
Investment demand = Addition to Capital
(Capital = the goods that are used in the production of final goods; such as equipment,
machinery, buildings, etc.)
Key Concepts
The saving done by individuals in the economy is the source of funds available for
investment demand in the economy. Individual savings is transferred to business for
investment demand through “financial markets” This is pictured below.
Savings
Financial Markets
Business
Investment
demand
Financial Markets are where savings are transferred to business for investment demands. This
occurs through banks or other financial intermediaries, stock markets, and bond markets.
Investment demand in the economy is very important for the performance of the economy,
both in terms of long-run growth and in terms of short-run fluctuations. Because of this,
financial markets are an important part of the macroeconomy.
Motivation for Individuals to Save
Life-Cycle Saving: People save for future consumption, when they expect to have relatively
little income. For instance, young working adults may save for a time in the future when they
1
are not working. However, older people may not be working, but instead living off of their
past savings. Hence they will not be saving. Thus savings generally follow the life-cycle of
the person, saving more when young and less as they get older.
Note that national savings may therefore depend on the age of the population, with older
countries saving less and younger countries saving more.
Bequest Saving: Bequest, or inheritance, saving is the desire to save due leaving wealth for
one’s children when they die.
Precautionary Saving: People save for unexpected expenses that may arise in the future (such
as medical expenses) or for a sudden loss of income in the future (such as a job loss).
Interest Rate: Even without the above three motivations, people would save if the interest rate
is high enough. The interest rate is the payment for people to give up current consumption in
exchange for future consumption. The higher the interest rate the greater will be savings.
Graphical Analysis of Saving
The relationship between savings and the motivations to save can be pictured in the graph
below. Panel A shows that savings will increase as the interest rate increases. Panel B
demonstrates the effect of an rise in savings and a fall in savings.
Panel A
Panel B
S2
r
S1
S1
S3
S falls
S rises
Funds
Funds
National Savings
The national income identity is
Y = C + I + G+NX
Where Y is national income, C is consumption spending, I is investment demand spending, G
is government spending, and NX is net exports. If we consider a closed economy (i.e. no
international trade) we can set NX = 0, and we have
Y=C+I+G
2
Now let T be taxes. One the right side of the national income identity we will add and
subtract T. This gives us
Y = C + I + T + (G-T)
Rearranging this equation gives us
(Y – C – T) + (T – G) = I
The left side of the equation is savings. More explicitly the term (Y – C – T) is “private
national savings” and the term (T – G) is “public national savings” or government savings,
since T is a source of government funds and G is their spending.
Hence we could write Private National Saving + Public National Savings = Investment
demand. So we can write
𝑆=𝐼
Investment demand
As explained above, investment demand is when businesses purchase new equipment,
machinery, buildings, etc. to increase production or replace existing capital equipment.
Motivation to Invest
Return on Investment demand: The motivation to invest is due to the increase in profits from
investment demand, or the returns on investment demand.
The return on investment demand depends on the technology, government policy, and
whether the international or domestic economy is in expansion or recession.
Interest Rate: The interest rate represents the cost of investment demand. This is because if a
business must borrow money to invest, then they must pay the interest rate on their loan. But
even if a business does not need to borrow and pays for investment demand from their
retained earnings, they could have put those retained earnings in a bank and earned the
interest rate as a rate of return. Hence in that case the interest rate represents an opportunity
cost of investment demand. Either way, the interest rate is the cost of investment demand, so
as the interest rate rises investment demand will fall. Since this represents desired investment
demand, we call this investment demand demand.
Graphical Analysis
The relationship between investment demand and the motivations to invest can be pictured in
the graph below. Panel A shows that investment demand will decrease as the interest rate
3
increases. Panel B demonstrates the effect of a rise in investment demand and a fall in
investment demand.
Panel A
Panel B
r
I rises
I falls
I1
I3
I2
Funds
I1
Funds
A Simple Model of Savings and Investment demand
We stated above that savings will increase with the interest rate while investment demand
decreases with the interest rate. This is graphed below, where the graph represents financial
markets.
Closed Economy
In a closed economy the only funds available for investment demand are national savings,
and the only investment demand is domestic investment demand. Hence the graph below
represents a closed economy where saving MUST equal investment demand. Hence the
equilibrium occurs at the intersection of the two curves, which gives us the equilibrium
interest rate, re.
r
S
re
I
S=I
Funds
Changes in the Equilibrium
4
Below we show the effects of an increase (Panel A) and decrease (Panel B) in savings.
Increases in savings causes a fall in the interest rate, while decreases in savings cause a rise in
the interest rate.
Panel A
Panel B
S2
r
S1
S1
S2
S rises
S falls
r2
r1
r1
r2
I
I
Funds
Funds
Below we show the effects of an increase (Panel A) and decrease (Panel B) in investment
demand demand. Increases in investment demand causes a rise in the interest rate, while
decreases in investment demand causes a fall in the interest rate.
Panel A
Panel B
r
S
S
r1
r2
r2
r1
I2
I1
I1
I2
Funds
Funds
Open Economy
National Income Accounts
In an open economy domestic businesses can find funds from both domestic savings and
foreign savings. Similarly, domestic savings can be used to fund domestic investment
demand or foreign investment demand. When funds for investment demand flow into a
country we call it a capital inflow. When funds for investment demand flow out of a country
we call it a capital outflow.
5
This can be seen using the national income accounts. Recall the national income identity is
Y = C + I + G+NX.
Now rearrange to show
𝑌 − 𝐶 − 𝐺 = 𝐼 + 𝑁𝑋
Or, lettings savings again be given by 𝑆 = 𝑌 − 𝐶 − 𝐺, we have
𝑆 = 𝐼 + 𝑁𝑋
Or,
𝑆 − 𝐼 = 𝑁𝑋
Notice if 𝑁𝑋 > 0, it must be 𝑆 > 𝐼. That is, there must be a capital outflow. The trade surplus
is being used to finance investment by the domestic country in foreign countries.
If 𝑁𝑋 < 0, it must be 𝑆 < 𝐼. That is, there must be a capital inflow. The trade deficit is
financed by foreign countries investing in the domestic country,.
Open Economy and the Loanable Funds Model
To capture these ideas in our model of loanable funds, we imagine that there is a “world”
interest rate at which businesses can borrow and at which savers can lend. Because of this the
domestic interest rate must equal the world interest rate. The panel of financial market graphs
below shows three possible cases. In Panel A, at the world interest rate domestic savings
exceed domestic investment demand. This implies there is capital outflow from the country
of the amount indicated. In Panel B, at the world interest rate domestic investment demand
exceeds domestic savings. This implies there is capital inflow into the country of the amount
indicated. In Panel C there is the special case in which domestic savings equals domestic
investment demand. In this case there is neither an inflow nor outflow of capital.
6
Panel A
r
Capital
Outflow
Panel B
SD
Panel C
r
r
SD
rW
rW
rW
ID
ID
Funds
I
S
Funds
S
I
Funds
S=I
Capital
Inflow
Changes in Equilibrium
Changes in Savings
Below we show the effects of an increase and decrease in savings. To make the result simple
to understand, we begin from an initial point in which domestic savings equals domestic
investment demand demand; that is, neither an inflow nor outflow of capital.
As one can see in Panel A of the graph, when savings increases, there is a capital outflow.
That is, at the initial equilibrium at point E1, there is neither capital inflow nor outflow as
savings equals investment demand demand. When savings increases, at the world interest rate
there will be a capital outflow as savings is greater than investment demand demand.
In panel B, when savings decreases there is a capital inflow. That is, at the initial equilibrium
at point E1, there is neither capital inflow nor outflow as savings equals investment demand
demand. When savings decreases, at the world interest rate there will be a capital outflow as
savings is less than investment demand demand.
7
Panel A
Panel B
r
S2
S1
S2
S1
E1
E1
rw
rw
I
Funds
Funds
Changes in Investment Demand
Below we show the effects of an increase and decrease in investment demand. To make the
result simple to understand, we begin from an initial point in which domestic savings equals
domestic investment demand; that is, neither an inflow nor outflow of capital.
As one can see in Panel A of the graph, when investment demand increases, there is a capital
inflow. That is, at the initial equilibrium at point E1, there is neither capital inflow nor
outflow as savings equals investment demand. When investment demand increases, at the
world interest rate there will be a capital inflow as investment demand is greater than savings.
And in panel B, when investment demand decreases there is a capital outflow. That is, at the
initial equilibrium at point E1, there is neither capital inflow nor outflow as savings equals
investment demand. When investment demand decreases, at the world interest rate there will
be a capital outflow as investment demand is less than savings.
Panel A
Panel B
r
S1
S1
E1
rw
rw
I2
E1
I1
I1
I2
Funds
Funds
Changes in the World Interest Rate
8
The graph below shows the effect of an increase and decrease in the interest rate. For
simplicity, we begin at a world interest rate in which there is neither capital inflow nor
outflow. In Panel A an increase in the world interest rate results a capital outflow, as the
higher world interest rate decreases investment demand and increases savings, so that savings
is greater than investment demand. In Panel B a decrease in the world interest rate results a
capital inflow, as the higher world interest rate increases investment demand and decreases
savings, so that investment demand is greater than savings.
Panel A
Panel B
r
S1
S1
rw2
rw1
rw1
rw2
I1
I1
Funds
Funds
9