Saving and Investment
Classical Model
Learning Objectives
• Learn how to derive and shift the investment
demand curve
• Learn how to derive and shift the saving supply
curve.
• Understand the role of interest rates in the
classical model.
• Understand the impact of technology on
investment demand.
• Understand the impact of “animal spirits” on
investment demand.
• Understand the impact of social changes on the
supply of saving.
Business Cycles and Investment:
Classical Model
• Classical economists argue that business
fluctuations are caused by a series of shocks to
technology that alter the productivity of labor in a
random way from one year to the next.
• These shocks are transmitted to the capital market
through changes in investment, causing saving,
investment and the interest rate to fluctuate
during the business cycle in an apparently random
way.
• Business cycles are a necessary and unavoidable
feature of market economies.
Investment Volatility: Classical
Model
• Investment spending is volatile.
– Investment fluctuates much more than GDP over
time.
• In classical theory, output and employment are
determined by fundamentals such as technology,
which can also influence investment.
– For example, new technology can cause an
investment boom in new machines that are designed
to exploit the invention.
Investment Volatility: Keynesian
Model
• In Keynesian theory, changes in investment
represent changes in the mass psychology of
investors or “animal sprits.”
– Greenspan’s use of “irrational exuberance” is a
recent example of this Keynesian idea.
• According to Keynesians, business cycles can be
avoided if investment is more efficiently
coordinated.
• Keynesians favor government policies to stabilize
the business cycle.
Consumption
• Unlike investment, consumption fluctuates
less than GDP over time.
• Consumption is smooth because households
borrow and lend in the capital market in an
effort to redistribute their income more evenly
over time.
• Keynesian economists agree that consumption
is smooth, but they argue that it could be even
smoother.
“Smooth” Consumption
• Keynesian economists argue that consumption is
not as smooth as it could be because households
with low incomes do not have easy access to capital
markets.
• If people who prefer to consume more than their
income are credit constrained, their optimal
decision is to consume all their income.
• Therefore, the presence of credit constrained
individuals implies that aggregate consumption will
fluctuate more than otherwise since the credit
constrained individuals’ consumption will fluctuate
equally with GDP.
Theory of Investment
• Assumptions:
– Individuals consume what they produce.
– As time passes, individuals allocate their
produced commodities between consumption
goods and investment goods.
Intertemporal Production
Possibilities Frontier
Future
Income
D The maximum attainable resources
available for consumption and
E investment = 0A.
If an individual invests 0B and
consumes BA, he will have 0E
available to divide between
consumption and investment in
the future.
Current
0 B A Income
Investment Consumption
The Production Function
• The intertemporal production function slopes
up because the more an individual invests
today, the greater his income in the future.
• The intertemporal production function’s slope
rises at a decreasing rate because of the law of
diminishing returns.
– For every increase in capital, output increases by
smaller amounts.
Investment and Profit Maximization
• Firms invest up to the point where the
output produced by an extra unit of
investment is equal to its cost.
– Firms equate the marginal product of
capital investment with the real rate of
interest.
• At this point, they are investing in the
profit maximizing amount of capital.
Profit: Definition
• A firm’s profit is the value of its produced output
minus the accrued principal and interest on loans
needed to purchase current investment goods.
• Profit = Value of Future Sales – Cost of Borrowing
p = Y – (1+r)I
– Y = value of output tomorrow
– r = market rate of interest
– I = investment of resources today
Investment and Production Function
Yt+1 A
Panel A shows the intertemporal production
function: the amount of output that can be
produced in the future (Yt+1) for any given
investment today (I).
0 I
(1+r)
B Panel B shows the relationship between
the real interest factor (1 + r) and the quantity
of capital investment demanded (I).
I
I
0
Investment and Production Function
A (slope =(1+r))
Yt+1
Panel A: As the firm buys additional capital,
Y
the extra output produced by the last unit of
capital decreases.
The additional output is the marginal product
of capital investment = slope of the production
function.
0 I1 I
(1+r)
B The firm invests up to the point where (1+r)
just equals the marginal product of capital
investment. At this point, profits are maximized.
(1+r)1
Panel B shows the investment schedule. At
I higher rates of interest, investment is less and
0
at lower rates of interest, investment is greater.
I1 I
Deriving the Investment Schedule:
Math
• Max p = AI – (½)(I)2 – (1 + r)I
AI – (½)(I)2 = Total Product in t+1
(1 + r)I = Total Borrowing Cost
A = Technology induced shifts in
investment.
Find the derivative of profit with respect to I, set it equal
to zero, and solve for the marginal product of investment.
• dp/dI = A – I – (1 + r) = 0
• A–I = (1 + r)
Households and Saving
• Intertemporal utility theory forms the basis
for most modern explanations of how
income is divided between consumption and
saving.
• This theory argues that, given the choice,
families would prefer that consumption be
evenly distributed over time.
Intertemporal Budget Constraint
• Assumptions:
– Households consume part of its income and
saves part.
– They put their savings into the capital market
by lending to another household or firm and
receive future resources with interest.
• The amount of additional goods that households can
buy in the future grows with the rate of interest.
Present Value
• The capital market can be used to transfer
resources from the present to the future.
• It can also be used to transfer resources
from the future to the present.
– When an individual borrows against future
income, he/she borrows its present value.
Present Value
• Present value tells us how much an
expected future payment is worth today.
– For example, if we expect to inherit $10,000
next year, but wish to spend it today, we can
borrow some amount less than $10,000 today.
– The amount that we can borrow is determined
by the interest rate.
Present Value Formula
• The formula for present value can be found
by rearranging the compounding formula.
FV = PV(1 + i) Compounding
• Solve for PV
FV/(1 + i) = PV Present Value
Intertemporal Budget Constraint
• Households can use capital markets to
redistribute resources over time.
• The intertemporal budget constraint places a
bound on the amount of consumption that is
available over a household’s lifetime.
• C1 + C2/(1 + r) S, causing r to rise to r2.
I1 I2
0 I1(r1) I2(r1) I Equilibrium occurs at Point 3.
Saving and Investment: Open
Economy
• In an open economy, domestic saving does
not have to equal domestic investment.
– It can be less than domestic investment or more
than domestic investment.
• When I S, a country must borrow from abroad.
Saving and Investment: Open
Economy
• Y = CNAT + INAT + NX
• Y – CNAT – INAT = NX
• SNAT – INAT = NX
– If SNAT = INAT, NX =O, trade balance
– If SNAT > INAT, NX >0, trade surplus
– If SNAT M, a country has excess funds to lend to
the ROW, or S > I.
– If X 0 over domestic saving is paid for by
I
0 S1 S,I borrowing NB1 in the world capital
I1
rw B
market.
SKROW
At r1 in Panel B, net borrowing from the
ROW equals NB1 = I1 – S1.
A
r1 Point A represents one point on the USA
DK USA
demand for ROW capital curve.
0 NB1 K
USA Demand for Capital from the
A
Rest of the World Curve
r
At r2 in Panel A, national domestic
S
r2
NB20 domestic investment results in negative
I borrowing = NB2 in the world capital
0 S1 I2 S2 I1 S,I
r2 market.
B
B SKROW
At r2 in Panel B, negative net borrowing
from the ROW equals NB2 = I2 – S2.
A
r1 Point B represents another point on the
DK USA USA demand for ROW capital curve.
NB2 0 NB1 K
Equilibrium in the World Capital
A
Market
r
S
NB20 equals the world supply of capital to the USA.
r1
NB1>0
I Point C in Panel B represents equilibrium
0 S1 I2 S2 I1 S,I in the world capital markets.
r2 B
B SKROW
At this point, USA investment exceeds
C domestic savings. The difference is made up
req
by borrowing NBE from abroad
A
r1
DKUSA
NB2 0 NBE NB1 K