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Chapter 10
We have seen that the level of real GDP produced by
the economy depends on the quantity of labor
employed, holding constant the quantity of capital,
other factors of production and the state of
technology. Along the aggregate production function,
the quantity of capital is fixed.
If the quantity of capital increases, the aggregate
production function shifts up: with the same quantity
of labor employed, the economy is now able to
produce more real GDP.
In this chapter we study what determines the quantity
of capital employed in the economy.
Physical capital is the equipment, buildings,
machinery, and other durable goods that have
already been produced in the past and are used
today to produce goods and services.
Financial capital is the funds that firms use to
purchase physical capital. The quantity of physical
capital therefore depends on the quantity of financial
capital.
Growth of physical capital enables the economy to
produce more real GDP over time. Thus, growth of
the physical capital stock (together with human
capital and technology) is the main engine of
economic growth.
But growth of physical capital requires growth of
financial capital to enable firms to purchase more
physical capital.
The total quantity of financial capital is determined
by the interplay between saving and investment
decisions in financial markets.
Recall that investment is expenditure by firms on
capital goods.
Investment expenditures can be on either new capital
goods or on additions to inventory.
Investment expenditures on new capital goods can
be either:
Replacement of worn out capital goods, which is
called depreciation
or
Net additions to the stock of capital, which is
called net investment.
The total amount spent on new capital goods is called
gross investment.
Thus,
Gross investment = Net investment + Depreciation.
Therefore,
Net investment, which is the change in the stock of
capital = Gross investment – Depreciation.
Numerical example:
A firm’s equipment at the beginning of the year is valued at
$10,000.
During the year, the market value of this equipment falls by
$6,000 (depreciation = $6,000), so that the firm’s existing
equipment is worth only $4,000.
During the year, the firm spends $8,000 on new equipment
(gross investment = $8,000).
At the end of the year the firm’s capital is worth $4,000 +
$8,000 = $12,000.
The value of the firm’s capital has increased from $10,000 at
the beginning of the year to $12,000 at the end. Therefore, net
investment, defined as the change in the firm’s capital stock, is
$2,000.
Alternatively: Net investment = Gross investment – Depreciation
= $8,000 – $6,000 = $2,000.
Investment is financed out of saving – either the
firm’s own savings, or by borrowing from other
people’s savings.
Recall that saving is that portion of income that is not
spent on consumption or paid in taxes. Saving
means forgoing present consumption in order to
attain a higher level of consumption in the future.
Wealth is the value of all of the assets that an
individual owns.
Saving adds to wealth. Wealth also increases when
the value of assets rises, which is called capital
gains.
Thus, Wealth = Saving + Net capital gains
In financial markets, or loanable funds markets,
borrowers sell bonds or stocks in order to raise
funding to finance investment expenditures.
Lenders, or savers, buy bonds or stocks, i.e., they
make some of their income available to others to
spend, and receive interest or dividends as a reward
for doing so.
A bond is a claim on future income or consumption,
i.e., a promise to pay a specified amount of money
at a specified date in the future.
A stock is an ownership share in a firm that entitles
the holder to receive a portion in the firm’s future
profits.
Investment demand
Investment demand is the amount of funds that all
firms in the economy plan to spend on investment.
The quantity of funds demanded for investment
purposes depends on the real interest rate.
Other things remaining the same, the higher the real
interest rate, the smaller is the quantity of funds
demanded for investment spending; and the lower the
real interest rate, the greater is the quantity of funds
demanded for investment spending.
Firms effectively rank different investment projects
in declining order in terms of expected rate of profit
or rate of return:
Thus, for this firm, the investment project with the
highest expected rate of return yields a 24% profit.
The investment project with the next highest
expected rate of return yields 22%, etc.
Now, the firm compares these expected rates of
profit with the real interest rate.
The real interest rate is the opportunity cost of the
funds used to purchase the capital goods needed for
the investment project.
The real interest rate is the opportunity cost of funds
whether the firm borrows the funds in the financial
market, or uses its own funds, which are called
retained earnings.
The firm will undertake an investment project only if
the expected rate of return on that project is greater
than or equal to the real interest rate.
If the expected rate of rate of return is less than the
real interest rate, the firm will not undertake that
investment project, either because
the cost of the funds is greater than the profit the
firm will obtain from the investment (if the firm is
borrowing the funds)
or
the firm could earn more by lending the funds in
the financial market than spending them on the
investment project (if the firm is using its own
funds).
Suppose that the real interest rate is 12%.
The firm will undertake all of the investment projects
whose expected rate of profit is greater than or equal
to 12%.
This means that the firm will undertake the first
seven investment projects but not the eighth:
If the real interest rate were now to decrease to 8%,
the number of investment projects that are
worthwhile for the firm to undertake will increase.
With a real interest rate of 8%, the firm will undertake
the first nine investment projects, but not the tenth:
This example illustrates that, for an individual firm,
the lower the real interest rate, the greater is the
number of investment projects that are worthwhile for
the firm to undertake.
Therefore, the lower the real interest rate, the greater
is the quantity of funds demanded for investment
purposes.
This same inverse relationship between the quantity
of funds demanded for investment and the real
interest rate holds true, not only for an individual firm,
but for all of the firms in the economy.
For the whole economy, the relationship between the
quantity of funds demanded for investment and the
real interest rate, holding everything else constant, is
called investment demand:
In this example, if the real interest rate decreases
from 5% to 4%, the quantity of funds demanded for
investment increases from $6 trillion to $7 trillion.
This is a movement down along the investment
demand curve.
Vice versa, if the real interest rate increases from 4%
to 5%, the quantity of funds demanded for
investment decreases from $7 trillion to $6 trillion.
This is a movement up along the investment demand
curve.
Shifts of investment demand
When there is a change in the expected rate of profit,
investment demand changes, i.e., the investment
demand curve shifts.
If the expected rate of profit increases, the quantity of
funds demanded for investment at any given real
interest rate increases; the investment demand curve
shifts to the right.
If the expected rate of profit decreases, the quantity
of funds demanded for investment at any given real
interest rate decreases; the investment demand curve
shifts to the left.
Factors that influence the expected rate of
profit:
In a business cycle expansion, income increases,
demand for goods and services increases, and
therefore firms expect higher profits.
Anticipating higher profit rates in the future, firms will
want to produce more output in the future, which
means they must expand productive capacity.
To expand productive capacity, firms must invest in
plant and equipment. Therefore investment
spending at each and every real interest rate
increases; the investment demand curve shifts to the
right.
Technological change lowers costs, raises labor
productivity, and brings new and profitable products.
But to implement these new technologies, firms must
first invest in the equipment that uses them.
Therefore, technological advances cause an increase
in the quantity of funds demanded for investment at
any given real interest rate; the investment demand
curve shifts to the right.
Population growth causes increased demand for
goods and services. To respond to this demand, firms
must increase output and thus expand their productive
capacity, which means investing in additional capital.
Again, the quantity of funds demanded for
investment at each real interest rate increases and
the investment demand curve shifts to the right.
The supply of saving
The higher the real interest rate, the greater is the
quantity of saving supplied, other things remaining
the same. The lower the real interest rate, the
smaller is the quantity of saving supplied, other
things remaining the same.
The real interest rate is the opportunity cost of
consumption expenditure. A dollar spent on
consumption is a dollar not saved.
Therefore the opportunity cost of consumption is the
interest earnings that are forgone as a result of
consuming some amount of income instead of
saving it and earning interest.
The higher the real interest rate, the greater is the
amount of interest earnings forgone when income is
spent on consumption instead of saved. Therefore
the opportunity cost of consumption is high, and
individuals will choose to spend less on consumption
and supply more saving.
Therefore the quantity of saving supplied increases
when the real interest rate increases.
The lower the real interest rate, the lower is the
amount of interest earnings forgone when income is
spent on consumption instead of saved. Therefore
the opportunity cost of consumption is low, and
individuals will choose to spend more on consumption
and supply less saving.
Individuals who are in debt will also save more when
the real interest rate increases. A higher real interest
rate means an increase in the cost of paying off a
given amount of debt, therefore debtors are likely to
increase their saving to pay off their debt as quickly
as possible when interest rates rise.
The relationship between the quantity of saving
supplied and the real interest rate, holding everything
else constant, is called saving supply:
In this example, if the real interest rate increases from
4% to 5%, the quantity of saving supplied increases
from $5 trillion to $6 trillion. This is a movement up
along the saving supply curve.
Vice versa, if the real interest rate decreases from
5% to 4%, the quantity of saving supplied decreases
from $6 trillion to $5 trillion. This is a movement
down along the saving supply curve.
Shifts of saving supply
When any influence on saving other than the real
interest rate changes, there is a change in saving
supply, i.e., the saving supply curve shifts.
The three main factors that influence saving supply
are:
Disposable income
The purchasing power of net assets
Expected future disposable income
Disposable income is income earned minus net
taxes. The greater a household’s disposable
income, other things remaining the same, the
greater is its saving.
Therefore, an increase in disposable income causes
the quantity of saving supplied at each and every real
interest rate to increase; the saving supply curve
shifts to the right.
Net assets are the assets a household owns minus
the debts that it owes. The purchasing power of net
assets is the amount of goods and services that
those assets can buy. The greater the purchasing
power of the net assets a household has
accumulated, other things remaining the same, the
less it will save.
Therefore, an increase in the purchasing power of
net assets causes a decrease in the quantity of
saving supplied at any given real interest rate; the
saving supply curve shifts to the left.
The higher a household’s expected future
disposable income, other things being equal, the
less it will save.
Therefore an increase in expected future disposable
income causes the quantity of saving supplied at
each real interest rate to decrease and the saving
supply curve shifts to the left.
Thus, an increase in disposable income, a decrease
in the purchasing power of net assets, or a decrease
in expected future disposable income will cause an
increase in saving supply. The saving supply curve
will shift to the right.
Vice versa, a decrease in disposable income, an
increase in the purchasing power of net assets, or an
increase in expected future disposable income will
cause a decrease in saving supply. The saving
supply curve will shift to the left.
Financial market equilibrium
Financial market equilibrium occurs when the
quantity of funds supplied by the savers in the
economy is exactly equal to the quantity of funds
demanded for investment purposes by the firms in
the economy.
Therefore financial market equilibrium occurs at the
intersection of the saving supply curve and the
investment demand curve:
When the real interest rate is 6% per year, the
quantity of saving supplied is greater than the
quantity of funds demanded for investment. There is
an excess supply of funds in the market.
Competitive market forces will drive the interest rate
down toward equilibrium at point E, eliminating the
excess supply.
When the real interest rate is 4% per year, the
quantity of funds demanded for investment is greater
than the quantity of saving supplied. There is an
excess demand for funds in the market.
Competitive market forces will drive the interest rate
up toward equilibrium at point E, eliminating the
excess demand.
When the real interest rate is 5%, the quantity of
funds supplied by the savers is exactly equal to the
quantity of funds demanded for investment, i.e., the
market clears.
Therefore 5% is the market clearing equilibrium real
interest rate.
Changes in investment and saving
Shifts of the investment demand curve or the saving
supply curve cause changes in the market clearing
equilibrium real interest rate and the equilibrium levels
of investment and saving.
For example, a decrease in investment demand:
The investment demand curve shifts from ID0 to ID1.
At the initial equilibrium real interest rate of 5%, there
is now an excess supply of funds.
Competitive market forces will drive the real interest
rate down to a new market clearing equilibrium at 4%.
The new equilibrium level of saving and investment is
$5 trillion.
As another example, suppose there were a decrease
in the supply of saving:
The saving supply curve shifts from SS0 to SS1. At
the initial equilibrium real interest rate of 5%, there is
now an excess demand for funds.
Competitive market forces will drive the real interest
rate up to a new market clearing equilibrium at 6%.
The new equilibrium level of saving and investment is
$5 trillion.
Investment demand and saving supply fluctuate, so
that the market clearing equilibrium real interest rate
sometimes increases and sometimes decreases. But
in the long run, the trend is for both investment
demand and saving supply to increase. However,
they increase at about the same rate, so that in the
long run the equilibrium real interest rate stays more
or less constant.
Government budget and government
saving
The government borrows funds from financial
markets and also supplies saving. Therefore the
government budget affects market equilibrium interest
rates and the equilibrium quantity of saving and
investment in the economy.
Recall that, according to the expenditure approach,
real GDP is measured in terms of total expenditure on
final goods and services.
Following the expenditure approach, therefore, GDP,
Y, is the sum of consumption expenditure, C,
investment, I, government purchases, G, and net
exports, NX.
Ignoring the foreign sector, i.e., excluding net exports:
Y=C+I+G
Recall that, according to the income approach, real
GDP can also be measured in terms of the total
value of income paid to households for the factors of
production they supply.
Therefore, real GDP equals total income.
There are three things that households can do with
their income: consume it, save it, or pay it to the
government as net taxes (taxes net of transfer
payments). Therefore:
Y = C + S + NT
Thus, we have:
Y=C+I+G
and
Y = C + S + NT.
Therefore,
C + I + G = C + S + NT.
Because C appears on both sides of this equation,
we can subtract C from both sides and simplify the
equation to:
I + G = S + NT.
Now subtract G from both sides of this equation to
obtain:
I = S + (NT – G).
This equation tells us that investment is financed
either by private saving, S, or by government saving,
NT – G.
If NT – G > 0, the government is collecting more tax
revenue than it is spending: the government has a
budget surplus.
If NT – G < 0, the government is spending more than
it is collecting in tax revenue: the government has a
budget deficit.
A government budget surplus
If the government has a budget surplus, this means
that government saving is positive and therefore
adds to private saving.
Assume that the government has a budget surplus
of $2 trillion, i.e., government saving is $2 trillion.
The total supply of saving increases by $2 trillion:
Government saving is a constant $2 trillion at each
real interest rate, therefore the total saving supply
curve, SS, lies $2 trillion to the right of the private
saving supply curve, PS. The horizontal distance
between the PS and SS curves is $2 trillion.
The market clearing equilibrium real interest rate
decreases from 5% to 4%.
The equilibrium level of saving and investment
increases from $6 trillion to $7 trillion.
Note that the equilibrium level of saving and
investment increases by less than the amount of
government saving, i.e., BE1 < AE1.
This is because the market clearing equilibrium real
interest rate decreases from 5% to 4%, causing the
quantity of private saving supplied to decrease as
we move down the PS curve from E0 to A.
The decrease in the quantity of private saving
supplied, from $6 trillion to $5 trillion, partially offsets
the $2 trillion of added government saving, but, on
net, the equilibrium quantity of saving and
investment still increases by $1 trillion.
A government budget deficit
If the government has a budget deficit, this means
that government saving is negative, i.e., the
government is dissaving. In this case, total saving
equals private saving minus the budget deficit.
Assume that the government has a budget deficit of
$2 trillion.
The total supply of saving decreases by $2 trillion:
Government dissaving is a constant $2 trillion at each
real interest rate, therefore the total saving supply
curve, SS, lies $2 trillion to the left of the private saving
supply curve, PS. The horizontal distance between
the PS and SS curves is $2 trillion.
The market clearing equilibrium real interest rate
increases from 5% to 6%.
The equilibrium level of saving and investment
decreases from $6 trillion to $5 trillion.
Note that the equilibrium level of saving and
investment decreases by less than the amount of
government dissaving, i.e., BE1 < AE1.
This is because the market clearing equilibrium real
interest rate increases from 5% to 6%, causing the
quantity of private saving supplied to increase as we
move up the PS curve from E0 to A.
The increase in the quantity of private saving
supplied, from $6 trillion to $7 trillion, partially offsets
the $2 trillion decrease in total saving due to the
budget deficit, but, on net, the equilibrium quantity of
saving and investment still decreases by $1 trillion.
The tendency for a government budget deficit to
cause a decrease in total investment is called the
crowding-out effect.
In our example, when the market clearing equilibrium
real interest rate increased from 5% to 6%, the
quantity of funds demanded for investment decreased
from $6 trillion to $5 trillion. This would be
represented as a movement up along the ID curve
from E0 to E1.
Thus increased government spending that causes a
budget deficit comes at the expense of reduced
private investment expenditure – the increased
government spending “crowds out” private investment
spending.
The Ricardo-Barro effect
Some economists believe, contrary to the crowdingout theory, that a government budget deficit will have
no effect on the market equilibrium real interest rate
or on the level of investment.
According to this view, the public realizes that a
budget deficit financed by borrowing will result in a
higher level of government debt in the future. The
public anticipates that the government will need to
raise taxes in the future in order to pay off the debt.
Higher taxes in the future mean a decrease in
expected future disposable income. Therefore private
saving increases.
In effect, the Ricardo-Barro effect is based on the
idea that the public will prepare for higher future taxes
by immediately increasing their saving by an amount
equal to the amount of government dissaving.
Therefore, at the same time that the total saving
supply curve shifts to the left due to the decrease in
government saving, private saving supply increases
by the same amount and the total saving supply
curve shifts back to the right.
Overall, the total saving supply curve remains in its
initial position and the market clearing equilibrium real
interest rate and the equilibrium quantity of saving and
investment remain unchanged:
The total saving supply curve, SS, shifts to the left
due to the government’s budget deficit, i.e.,
government dissaving, but then immediately shifts
back to its initial position due to the increase in
private saving.
The market clearing equilibrium real interest rate
remains at 5% and the equilibrium level of saving
and investment remains at $6 trillion.