Transcript The Saving Supply Curve

Chapter 6
Saving and Investment
Saving, Investment, and the Capital
Market
• Saving occurs when households choose not
to spend part of their income.
• Investment occurs when firms purchase
new capital equipment.
• A mechanism for channeling funds from
savers to investors is the capital market.
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Smoothness
• Standard Deviation: the average difference
from the average.


• Formula:
  xi  x
 x   i 1

n 1


n

2
1/ 2






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Consumption and GDP in the United States
Figure 6.1A
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Investment and GDP in the United States
Figure 6.1B
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Table 6.1
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Why Is Investment So Volatile?
• Fundamental Explanation (Classical):
Investment fluctuates because firms respond
to changes in technology.
Ex. New Invention.
• This is the basis for the RBC school.
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Why Is Investment So Volatile?
• Animal Spirit (Keynesian) :
Highly volatile investment represents changes
in the mass psychology of investors.
Belief: It could be avoided if investment were
more efficiently coordinated.
They favors the implementation of
government policies to stabilize the business
cycle.
Different Names: Self-fulfilling, Sunspots,
Irrational Exuberance.
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Consumption Smoothing
• Households borrow and lend in the capital
market in an effort to redistribute their
income more evenly over time.
• A convex intertemporal utility function.
• Ex. Robinson Crusoe
• Both Keynesian and Classical economists
agree this reason.
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Borrowing Constraints
• Keynesian economists agree that the capital
market is used by H.H. to smooth income,
but not that the market works well.
• Some economists point out that although
aggregate consumption is smoother than
income, it is not as smooth as it could be.
• RBC model predicts that consumption
should be less volatile than it actual is.
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Borrowing Constraints
• Many people have low incomes early in life
and high incomes later in life.
• We often attempt to borrow more money
than we are able to when young.
• Reason: It is hard for banks to enforce
repayment later on.
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How Does the Borrowing Constraints
Alter the Classical Theory
• Suppose some H.H.s prefer to consume more
than their income and opt to repay their loan
later in life.
• If the credit market is imperfect, they are
constrained.
• The presence of credit constrained individuals
implies that aggregate consumption will
fluctuate more.
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Investment
• How would Robinson make decisions if he
were both a producer and a consumer?
• We illustrate the options available to
Robinson Crusoe with a production
possibility set in which inputs and outputs
occur at different points in time.
• Robinson must decide how to allocate his
produced commodities between
consumption goods and investment goods.
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Intertemporal Production
Possibility Set
• The opportunities of investment is represented
as intertemporal production possibility set.
(Figure 6.2)
• The production possibility set has an upwardslopping frontier because the more present
investment leads to more future income.
• In a modern industrial society, diminishing
returns to investment applies because the stock
of people is fixed.
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The Intertemporal Production
Possibilities Set
Figure 6.2
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The Real Rate And The Nominal
Rate of Interest
r
 i
Real Interest
Rate
 P / P
Nominal Interest
Rate
Inflation Rate
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Investment and the
Production Function
Figure 6.3A
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Maximizing Profits
• The classical theory of production assumes that
markets are competitive.
• Classical theory assumes that firms choose
how much labor to demand in order to
maximize profits, so the same logic is applied
to the decision about how much to invest.
• 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.
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Maximizing Profits
• Theory of the demand for Labor:
marginal product of labor = real wage.
• Theory of the demand for investment goods:
marginal product of investment = real Interest Rate
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Borrowing and the Investment
Schedule
• The classical theory of saving and
investment assumes that firms and H.H.s
can borrow and lend freely at a single rate
of interest, the market rate ( r ).
• Borrowing and lending take place in the
capital market.
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Borrowing and the Investment
Schedule
• Suppose firm can produce output tomorrow
of value Y from an investment of I
resources.


Y

(1  r ) I
• Profit Value of future sales Cost of Borrowing
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Profit Maximization

F.O.C.

Y

 G( I ) 
(1  r ) I
(1  r ) I .
G ' ( I )  (1  r )
marginal product of investment = 1 + real Interest Rate
The investment demand curve slopes downward.
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Investment and the
Production Function
Figure 6.3B
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Deriving the Investment Schedule
• The boundary of the intertemporal production
possibility set:
Y  A I  (1 / 2) I
S
• Max
2
  AI  (1 / 2) I  (1  r ) I
2
• F.O.C.
A I
Marginal Product
of Investment

(1  r ).
Marginal Cost
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Households and the Saving Supply
Curve
• The application of the theory of marginal utility
to the problem of saving is called the
intertemporal utility theory.
• Intertemporal utility theory argues that, given
the choice, families would prefer that
consumption be evenly distributed over time.
• Preferences for consumption at different points
in time are represented by utility.
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The Intertemporal Budget Constraint
• Suppose the household puts its income into the
capital market by lending to another
household or firm.
• In return, the household receives future
resources with interest.
• The rate of interest is the price at which
present consumption can be exchanged for
future consumption.
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Present Value
• When you borrow against future income, the
amount you can borrow is its present value.
• Example:
John will inherit $10000 next year when he
turns 21 years old. He would like to spend his
inheritance on a used car and is impatient and
unable to wait until next year.
If he buy the car right away, bank manager will
lend him:
1
1
(1  r )
Y
1  0.1
10000  9901.
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Borrowing and Lending to Smooth
Consumption
• Y1: present income C1: present consumption
• Y2: future income C2: future consumption
• Intertemporal Budget Constraint places a
bound on the amount of consumption that is
available over a household’s lifetime.
C1
1

C2
(1  r )

Y1

1
Y2
(1  r )
present
present value of
current
present value of
consumption future consumption resources future resources
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Borrowing and Lending to Smooth
Consumption
1
1
C1 
C2

Y1

Y2
(1  r )
(1  r )
Left Side:
Sum of the values of present and future consumption.
Right Side:
Sum of the values of present and future income.
The price of future consumption is 1/(1+r) , where r is the
interest rate.
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The Saving Supply Curve
•
Households maximize utility lead to a
relationship between the real interest rate
and the quantity of saving, called saving
supply curve.
Two Effects when r varies:
1. Substitution Effect
2. Wealth Effect
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The Saving Supply Curve
• Substitution Effect (S.E.):
As r goes up, current consumption becomes
relatively more expensive, and makes the
household want to substitute consumption
today for consumption tomorrow.
• Wealth Effect (W.E.):
An increase in r makes the household
wealthier.
Neoclassical theory assumes the supply of
saving slopes upward, i.e. S.E.>W.E. .
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Saving and the Real Interest Rate
Figure 6.4
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Deriving the Saving Supply Curve
• Utility function

2  C1 

2
U
 C2
2
• In current period, H.H. saves S from its income Y and
consumes C1:
S  Y  C1
• In the second period (old age), H.H. consumes the
principal and interest on its saving (1+r)S. We assume
that H.H. has no income in old age.
C2  (1  r )S
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Deriving the Saving Supply Curve
• Max

2 Y  S

2
U
2
 (1  r ) S
• F.O.C.
 ( 2  Y  S )  (1  r )  0.
• Saving Function:
S  Y  1  r.
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Saving and Investment in a Closed
Economy
• Figure 6.5 shows how the interest rate, saving
and investment are simultaneously determined.
• The saving supply curve represents the funds
that are flowing into the capital market from
H.H.
• The investment curve represents the funds
flowing out of the market to firms that borrow
the money to build new factories and machines.
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Saving and Investment in a Closed
Economy
• At r1, H.H.s supply S1 and firms want to
borrow I1 to finance investment projects;
I > S.
• At r2, H.H.s supply S2 and firms want to
borrow I2 to finance investment projects;
I < S.
• Only when r = rE does saving equal
investment. Then the capital market is in
equilibrium and I = S = IE.
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Capital Market Equilibrium
Figure 6.5
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Equilibrium in the Capital Market
• Investment demand curve:
A  I  (1  r ).
• Saving supply curve
S  Y  1  r.
• I = S,
 AY 
r

2 

(Y  A)
SI 
 1.
2
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Productivity and the Investment
Demand Curve
• Classical view of business cycle:
Technology Shocks.
• Example: The invention of the personal
computer in the 1970s.
• The new invention raise the productivity
and the firm demands more investment for
any given rate of interest.
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Productivity and the Investment
Demand Curve
Figure 6.6A
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Productivity and the Investment
Demand Curve
Figure 6.6B
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Animal Spirits and the Investment
Demand Curve
• Because investment and production do not take
place at the same time, investors may make
mistakes.
• Keynes thought that irrational swings of
optimism and pessimism might be more
important driving forces in the stock market
than fundamentals.
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Animal Spirits and the Investment
Demand Curve
• A new technology is unproven and
investments that are made on the basis
of mistaken belief about future
productivity have the same effect on
the capital market as investments that
later turn out to be profitable.
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Animal Spirits and the Investment
Demand Curve
• Is the market overvalued today?
1. We are entering a new era in which the
economy will witness unprecedented
growth.
2. The information age has made markets
more efficient, narrowing the gap between
debt and equity as more households begin
to invest in the market on a daily basis.
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Animal Spirits and the Investment
Demand Curve
• Robert Shiller argues that:
1. The high value of the current market
represents a “bubble” that is not justified by
fundamentals.
2. He cautions that an overvalued market is, by
historical standards, inherently precarious.
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Saving and Investment in an Open
Economy
• The difference between the open economy
and the closed economy models is that:
In the open economy, domestic saving does
not equal domestic investment;
The deficit is made up by net borrowing
from abroad.
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Saving and Investment in
an Open Economy
Figure 6.7A
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Saving and Investment in
an Open Economy
Figure 6.7B
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Homework
Question 1, 4, 7, 12
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