Download Interest Rates

Capital Markets
Savings, Investment, and Interest
Rates
Some Useful Terminology
• Savings: Current income which is deferred for future
consumption (i.e., not spent)
Some Useful Terminology
• Savings: Current income which is deferred for future
consumption (i.e., not spent)
National Income: $8,512.3 B
+ Dividend Payments, Interest, Gov’t Transfers, etc.: $582.5B
- Taxes: $1,077.2 B
= Personal Disposable Income: $8,017.6 B
- Personal Consumption Expenditures: $7,727.2 B
= Personal Savings: $290.4B (3.5% of Personal Income)
Some Useful Terminology
• Savings: Current income which is deferred for future
consumption (i.e., not spent)
National Income: $8,512.3 B
+ Dividend Payments, Interest, Gov’t Transfers, etc.: $582.5B
- Taxes: $1,077.2 B
= Personal Disposable Income: $8,017.6 B
- Personal Consumption Expenditures: $7,727.2 B
= Personal Savings: $290.4B (3.5% of Personal Income)
• Note that there are many ways to save (savings account,
bonds, stocks, etc.)
Some Useful Terminology
• Investment: The purchase of new capital goods.
Some Useful Terminology
• Investment: The purchase of new capital goods.
– Gross Investment: Total purchases of new capital goods
Some Useful Terminology
• Investment: The purchase of new capital goods.
– Gross Investment: Total purchases of new capital goods
• Gross Private Investment: $1,611.2 B
• Gross Public Investment: $355 B
Some Useful Terminology
• Investment: The purchase of new capital goods.
– Gross Investment: Total purchases of new capital goods
• Gross Private Investment: $1,611.2 B
• Gross Public Investment: $355 B
– Net Investment: Gross investment less depreciation of existing
capital (capital consumption)
• Net Private Investment: $500 B
• Net Public Investment: $250 B
NIPA Accounts
• Recall, the accounting identity in the NIPA accounts: GDP
= C + I + G + NX
NIPA Accounts
• Recall, the accounting identity in the NIPA accounts: GDP
= C + I + G + NX
• GDP = Gross Private Savings + Taxes + C
NIPA Accounts
• Recall, the accounting identity in the NIPA accounts: GDP
= C + I + G + NX
• GDP = Gross Private Savings + Taxes + C
Gross Private Savings = I + (G-T) + NX
I (Public + Private) : $1,966 B
+ (G-T): $106B
+ NX: - $559B
Gross Private Savings: $1,513B (16% of GDP)
NIPA Accounts
• Recall, the accounting identity in the NIPA accounts:
GDP = C + I + G + NX
• GDP = Gross Savings + Taxes + C
I + (G-T) + NX = Gross Private Savings
I (Public + Private) : $1,966 B
+ (G-T): $123B
+ NX: - $487B
Gross Private Savings: $1,513B
Personal Savings ($290B) = Gross Private Saving ($1,513B) - Depreciation
Interest Rates
• What is an interest rate?
Interest Rates
• What is an interest rate?
– The interest rate is the relative price of current
spending in terms of foregone future income.
Interest Rates
• What is an interest rate?
– The interest rate is the relative price of current
spending in terms of foregone future income.
– Example: if the interest rate is 5% (Annual),
you must give up $1.05 worth of next year’s
income in order to increase this year’s spending
by $1.
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Interest Rates:1987-2003
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3 Mo. T-Bill
Interest Rates:1987-2003
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3 Mo. T-Bill
10 Year T-Note
The Yield Curve
Yield Curves
• What determines the shape of the yield
curve?
– Segmented Markets Hypothesis
– Expectations Hypothesis
– Preferred Habitat Hypothesis
Interest Rates:1987-2003
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10
8
3 Mo. T-Bill
10 Year T-Note
AAA Corp.
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2
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0
Interest Rates
•
•
•
•
•
•
Treasury Securities (1 - 5%)
Agency Securities (1 - 5%)
Municipal Bonds (3 – 5%)
Corporate Bonds (6 – 11%)
Preferred Stock (5 – 15%)
Asset Backed Securities (4 – 5%)
Interest Rates
•
•
•
•
•
•
Treasury Securities (1 - 5%)
Agency Securities (1 - 5%)
Municipal Bonds (3 – 5%)
Corporate Bonds (6 – 11%)
Preferred Stock (5 – 15%)
Asset Backed Securities (4 – 5%)
• “Risky” Rate = Risk Free Rate + Risk Premium
Real vs. Nominal Interest Rates
• As with any other variable, the nominal interest rate is in
terms of dollars. (the cost of a current dollar in terms of
forgone future dollars). To calculate the real interest rate,
we need to correct for the purchasing power of those
dollars.
Real vs. Nominal Interest Rates
• As with any other variable, the nominal interest rate is in
terms of dollars. (the cost of a current dollar in terms of
forgone future dollars). To calculate the real interest rate,
we need to correct for the purchasing power of those
dollars.
• Exact: (1+i ) = (1+ r )*(1 + inflation rate)
Real vs. Nominal Interest Rates
• As with any other variable, the nominal interest rate is in
terms of dollars. (the cost of a current dollar in terms of
forgone future dollars). To calculate the real interest rate,
we need to correct for the purchasing power of those
dollars.
• Exact: (1+i ) = (1+ r )*(1 + inflation rate)
• Approximation: i = r + inflation rate
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01
Real/Nominal Interest Rates
20
15
10
5
0
-5
-10
Inflation
Real
Nominal
Real vs. Nominal Interest Rates
• As with any other variable, the nominal interest rate is in
terms of dollars. (the cost of a current dollar in terms of
forgone future dollars). To calculate the real interest rate,
we need to correct for the purchasing power of those
dollars.
• Exact: (1+i ) = (1+ r )*(1 + inflation rate)
• Approximation: i = r + inflation rate
• How can real interest rates be negative?
Real vs. Nominal Interest Rates
• As with any other variable, the nominal interest rate is in
terms of dollars. (the cost of a current dollar in terms of
forgone future dollars). To calculate the real interest rate,
we need to correct for the purchasing power of those
dollars.
• Exact: (1+i ) = (1+ r )*(1 + inflation rate)
• Approximation: i = r + inflation rate
• How can real interest rates be negative?
– Ex ante vs. ex post
Present Value
• With a positive interest rate, income received in the future
is less valuable that income received immediately.
Present Value
• With a positive interest rate, income received in the future
is less valuable that income received immediately.
• At a 5% annual interest rate, $1.05 to be received in one
year is equivalent to $1 to be received today (because $1
today could be worth $1.05)
$1(1.05) = $1.05
Present Value
• With a positive interest rate, income received in the future
is less valuable that income received immediately.
• At a 5% annual interest rate, $1.05 to be received in one
year is equivalent to $1 to be received today (because $1
today could be worth $1.05)
$1(1.05) = $1.05
• Therefore, the present value of $1.05 to be paid in one year
(if the annual interest rate is 5%) is $1.
Present Value
• With a positive interest rate, income received in the future
is less valuable that income received immediately.
• At a 5% annual interest rate, $1.05 to be received in one
year is equivalent to $1 to be received today (because $1
today could be worth $1.05)
$1(1.05) = $1.05
• Therefore, the present value of $1.05 to be paid in one year
(if the annual interest rate is 5%) is $1.
• In general, the PV of $X to be paid in N years is equal to
PV = $X/(1+i)^N
Income vs. Wealth
• Your wealth is defined and the present value of your
lifetime income.
Income vs. Wealth
• Your wealth is defined and the present value of your
lifetime income.
• For example, suppose you expect your annual income to be
$50,000 per year for the rest of your life. If the annual
interest rate is 3%:
Wealth = $50,000 + $50,000/(1.03) + $50,000/(1.03)^2 + ……
= $50,000/(.03) = $1,666,666 (Approx)
Household Savings
• Without an active capital markets,
household consumption is restricted to
equal current income (that is, C=Y)
Household Savings
• Without an active capital markets,
household consumption is restricted to
equal current income (that is, C=Y)
• With capital markets, the present value of
lifetime consumption must equal the present
value of lifetime income (assuming all debts
are eventually repaid)
A two period example
• Suppose that your current income is equal
to $50,000 and you anticipate next year’s
income to be $60,000. The current interest
rate is 5%.
A two period example
• Suppose that your current income is equal
to $50,000 and you anticipate next year’s
income to be $60,000. The current interest
rate is 5%.
• In the absence of capital markets, your
consumption stream would be $50,000 this
year and $60,000 next year.
Future Consumption (000s)
Consumption Possibilities
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0
0
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Current Consumption (000s)
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Borrowing to increase current consumption
• To increase your current consumption, you
could take out a loan. Your current
consumption would now be
C = $50,000 + Loan
Borrowing to increase current consumption
• To increase your current consumption, you could
take out a loan. Your current consumption would
now be
C = $50,000 + Loan
• However, you must repay your loan next year.
This implies that
C’= $60,000 – (1.05)Loan
Borrowing to increase current consumption
• To increase your current consumption, you could take out a
loan. Your current consumption would now be
C = $50,000 + Loan
• However, you repay your loan next year. This implies that
C’= $60,000 – (1.05)Loan
• For example, if you take out a $10,000 loan, your current
consumption would be $60,000, while your future income
would be $60,000 - $10,000(1.05) = $49,500
Futuer Consumption (000s)
Consumption Possibilities
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Current Consumption (000s)
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Borrowing Limits
Note that you need to be able to repay your
loan next year. Therefore,
$60,000 > (1.05)Loan
Borrowing Limits
• Note that you need to be able to repay your
loan next year. Therefore,
$60,000 = (1.05)Loan
• Your maximum allowable loan is
$60,000/1.05 = $57,143 (this is associated
with zero future consumption)
Borrowing Limits
• Note that you need to be able to repay your
loan next year. Therefore,
$60,000 = (1.05)Loan
Your maximum allowable loan is
$60,000/1.05 = $57,143 (this is associated
with zero future consumption)
Therefore, your maximum current
consumption is $107,143
Consumption Possibilities
Futuer Consumption (000s)
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100
80
60
40
20
0
0
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20
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40
50
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80
Current Consumption (000s)
90 100 110 120
Consumption Possibilities
Futuer Consumption (000s)
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80
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40
20
0
0
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20
30
40
50
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Current Consumption (000s)
90 100 110 120
Saving to increase future consumption
• You could increase future consumption by saving some of
your income (i.e. a negative loan). Suppose you put
$20,000 in the bank, your current consumption is now
$30,000.
Saving to increase future consumption
• You could increase future consumption by saving some of
your income (i.e. a negative loan). Suppose you put
$20,000 in the bank, your current consumption is now
$30,000.
• Next year, your bank account will be worth $20,000(1.05)
= $21,000. Therefore, your future consumption will be
$81,000
Consumption Possibilities
Futuer Consumption (000s)
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80
60
40
20
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Current Consumption (000s)
90 100 110 120
Maximizing future consumption
• Suppose you save your entire income. Your
current consumption will be zero, but your
future consumption will be
C’ = $60,000 + $50,000(1.05) = $112,500
Consumption Possibilities
Futuer Consumption (000s)
120
100
80
60
40
20
0
0
10
20
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40
50
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80
Current Consumption (000s)
90 100 110 120
Consumption Possibilities
Futuer Consumption (000s)
120
100
80
60
40
20
0
0
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20
30
40
50
60
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80
Current Consumption (000s)
90 100 110 120
Suppose that the interest rate rises to 8%
• Note that if you don’t borrow or lend, you
are unaffected.
Suppose that the interest rate rises to 8%
• Note that if you don’t borrow or lend, you are
unaffected.
• At higher interest rates, your borrowing limit falls:
Loan = $60,000/1.08 = $55,556 (higher interest
rates are bad for borrowers)
Suppose that the interest rate rises to 8%
• Note that if you don’t borrow or lend, you
are unaffected.
• At higher interest rates, your borrowing
limit falls: Loan = $60,000/1.08 = $55,556
(higher interest rates are bad for borrowers)
• However, if you are saving, you receive
more interest: $50,000(1.08) = $54,000
(higher interest rates are good for savers)
Futuer Consumption (000s)
Consumption Possibilities
Current Consumption (000s)
Future Consumption (000s)
Consumption Possibilities
Current Consumption (000s)
The interest rate is the relative price of current consumption
in terms of future consumption
• When any relative price changes, there are
two distinct effects that impact consumer
behavior
The interest rate is the relative price of current consumption
in terms of future consumption
• When any relative price changes, there are two distinct
effects that impact consumer behavior
– The substitution effect: as relative prices change, consumer
typically alter purchases to favor the good that has become cheaper
The interest rate is the relative price of current consumption
in terms of future consumption
• When any relative price changes, there are two distinct
effects that impact consumer behavior
– The substitution effect: as relative prices change, consumer
typically alter purchases to favor the good that has become cheaper
– Income Effect: Changing prices alter one’s purchasing power.
When purchasing power falls/rises, purchases fall/rise
How does rising interest rates influence savings
decisions?
How does rising interest rates influence savings
decisions?
• The substitution effect is unambiguous: as interest
rates rise, current consumption becomes more
expensive. Therefore, consumers spend less (i.e.
save more)
How does rising interest rates influence savings
decisions?
• The substitution effect is unambiguous: as interest
rates rise, current consumption becomes more
expensive. Therefore, consumers spend less (i.e.
save more)
• The income effect depends on your current
situation: borrowers experience a negative income
effect and therefore would spend less (save more)
while savers experience a positive income effect
and therefore would spend more (save less)
Impact of rising interest rates
Borrowers
• Substitution effect:
spend less (save more)
• Income effect: Spend
less (save
more)___________
Net effect: Save More
Savers
• Substitution effect:
spend less (save more)
• Income effect: spend
more (save
less)___________
Net effect: ????
Aggregate Savings
• At the individual level, we would need to consider income
and substitution effects to determine the precise impact of
rising/falling interest rates on savings behavior
Aggregate Savings
• At the individual level, we would need to consider income
and substitution effects to determine the precise impact of
rising/falling interest rates on savings behavior
• At the aggregate level, new savings is very close to zero
(i.e., there are approximately the same number of
borrowers as there are lenders
Aggregate Savings
• At the individual level, we would need to consider
income and substitution effects to determine the
precise impact of rising/falling interest rates on
savings behavior
• At the aggregate level, new savings is very close
to zero (i.e., there are approximately the same
number of borrowers as there are lenders
• Therefore, the income effects cancel out and
higher interest rates have an unambiguous positive
effect on savings
Interest Rate (%)
Aggregate Savings
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0
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Savings ($)
40
50
Again, assume that the interest rate is 5%, consider
two individuals
Person A
• Current income:
$10,000
• Anticipated future
income: $50,000
Again, assume that the interest rate is 5%, consider
two individuals
Person A
• Current income:
$10,000
• Anticipated future
income: $50,000
Person B
• Current Income:
$50,000
• Anticipated Future
income: $8,000
Again, assume that the interest rate is 5%, consider
two individuals
Person A
• Current income:
$10,000
• Anticipated future
income: $50,000
Wealth: $57,619
Person B
• Current Income:
$50,000
• Anticipated Future
income: $8,000
Again, assume that the interest rate is 5%, consider
two individuals
Person A
• Current income:
$10,000
• Anticipated future
income: $50,000
Wealth: $57,619
Person B
• Current Income:
$50,000
• Anticipated Future
income: $8,000
Wealth: $57,619
Consumption vs. Wealth
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0
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50
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40
30
20
10
50
0
0
10
20
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40
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57.6
60
70
Consumption and Wealth
• With capital markets, consumption is not
determined by current income, but by wealth
(present value of lifetime income)
Consumption and Wealth
• With capital markets, consumption is not
determined by current income, but by wealth
(present value of lifetime income)
• These two individuals, having the same wealth,
should choose the same consumption
Consumption vs. Wealth
70
0
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50
10
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20
10
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0
0
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20
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57.6
60
70
Again, assume that the interest rate is 5%, consider
two individuals
• Person A
• Current income: $10,000
• Anticipated future
income: $50,000
Wealth: $57,619
Current Spending:
$30,000
Person B
• Current Income: $50,000
• Anticipated Future
income: $8,000
Wealth: $57,619
Current Spending:
$30,000
Again, assume that the interest rate is 5%, consider
two individuals
• Person A
• Current income: $10,000
• Anticipated future
income: $50,000
Wealth: $57,619
Current Spending:
$30,000
Savings: -$20,000
Person B
• Current Income: $50,000
• Anticipated Future
income: $8,000
Wealth: $57,619
Current Spending:
$30,000
Savings: $20,000
Again, assume that the interest rate is 5%, consider
two individuals
• Person A
• Current income: $10,000
• Anticipated future
income: $50,000
Wealth: $57,619
Current Spending:
$30,000
Savings: -$20,000
Future Spending: $29,000
Person B
• Current Income: $50,000
• Anticipated Future
income: $8,000
Wealth: $57,619
Current Spending:
$30,000
Savings: $20,000
Future Spending: $29,000
Consumption and Wealth
• With capital markets, consumption is not
determined by current income, but by wealth
(present value of lifetime income)
• These two individuals, having the same wealth,
should choose the same consumption.
• For a given level of wealth, those with high rates
of income growth would be expected to be
borrowers
Interest Rate (%)
Suppose that economic growth in the US rises. What
should happen to aggregate savings?
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6
5
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3
2
1
0
0
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20
30
Savings ($)
40
50
Suppose that economic growth in the US rises. What
should happen to aggregate savings?
12
Interest Rate (%)
10
8
6
4
2
0
0
10
20
30
Savings ($)
40
50
Technology & Investment
Demand
• Recall that an economy has three sources of
growth: labor, capital, and technology
Production Technology
• Recall that an economy has three sources of
growth: labor, capital, and technology
• The production function describes the
relationship between output and the three
Production (Holding Employment Fixed)
Output
Production (Holding Employment Fixed)
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Capital
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10
Marginal Product of Capital
• The marginal product of capital is defined as
the additional output produced by each
additional unit of capital purchased.
• In the previous slide, the first unit of capital
generated 25 units of output while the second
unit of capital raised total output from 20 to 45
• Therefore, the MPK of the first unit of capital
is 25 while the MPK of the second unit of
capital is 20
Output
Diminishing marginal product implies that as the
capital stock rises, the marginal product of
additional capital falls
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25
20
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Capital
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10
Marginal Product and Investment Demand
• Recall that investment refers to the purchase
of new capital equipment by the private
sector
Marginal Product and Investment Demand
• Recall that investment refers to the purchase
of new capital equipment by the private
sector
• Firms are profit maximizers and, hence,
only take actions that increase firm value
(present value of lifetime earnings)
Marginal Product and Investment Demand
• Recall that investment refers to the purchase of
new capital equipment by the private sector
• Firms are profit maximizers and, hence, only take
actions that increase firm value (present value of
lifetime earnings)
• Therefore a firm will only buy a new piece of
capital when the contribution of that capital to
firm value is greater that its cost
P(k) > PV(MPK)
A Numerical example
• Suppose that the current interest rate is 5% and that the
cost of a unit of machinery is $100. Capital is assumed to
depreciate at a rate of 10% per year.
A Numerical example
• Suppose that the current interest rate is 5% and that the
cost of a unit of machinery is $100.
• Given the technology from the previous slide, the marginal
product of the first unit of capital is $25/yr. Income stream
will this capital generate?
• Year 1: $25
Year 2: $25(1-.10) = $22.50
Year 3: $25(1-.10)(1-.10) = $20.25
Year 3: $25(1-.10)(1-.10)(1-.10) = $18.23 …………
A Numerical example
• What is the present value of this income stream?
A Numerical example
• What is the present value of this income stream?
PV = $25/(1.05) + $22.50/(1.05)^2 + $20.25/(1.05)^3 + …….
A Numerical example
• What is the present value of this income stream?
PV = $25/(1.05) + $22.50/(1.05)^2 + $20.25/(1.05)^3 + …….
PV = $25/( i + depreciation ) = $25/(.15) = $167
• Is this a positive NPV project? Yes ( $167 > $100)
A Numerical example
• What is the present value of this income stream?
PV = $25/(1.05) + $22.50/(1.05)^2 + $20.25/(1.05)^3 + …….
PV = $25/( i + depreciation ) = $25/(.15) = $167
• Is this a positive NPV project? Yes ( $167 > $100)
• In fact, solving the above expression tells us that this is a positive NPV
project for any interest rate under
i = (MPK/Pk) – depreciation = ($25/$100) - .10 = .15 = 15%
Interest rates and Investment
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Interest rates and investment
• Note that once the first unit of capital has
been purchased, the second unit of capital
only has a marginal product of 20.
• Therefore, for this unit of capital to be a
positive PV project, the interest rate must be
lower than 20/100 - .10 = .1 = 10%
Interest rates and Investment
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Interest rates and Investment
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Interest rates and investment
• Diminishing marginal product of Capital
guarantees that the demand for investment
is downward sloping (increasing rates of
investment require lower interest rates)
• To get the total demand for loans, multiply
the investment curve by the price of capital)
Interest rates and Investment
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200
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500
Investment Demand
• It is assumed that labor and capital are
compliments. That is, when employment
rises, the productivity of capital increases as
well.
Investment Demand
• It is assumed that labor and capital are
compliments. That is, when employment
rises, the productivity of capital increases as
well.
• Therefore, as a rise in employment should
increase the demand for capital and, hence,
the demand for loans
Investment Demand
• It is assumed that labor and capital are
compliments. That is, when employment rises, the
productivity of capital increases as well.
• Therefore, as a rise in employment should increase
the demand for capital and, hence, the demand for
loans
• Further, any technological improvement should
also raise the demand for investment
A rise in investment demand
16
14
12
10
8
6
4
2
0
0
100
200
300
400
500
A rise in investment demand
25
20
15
10
5
0
0
100
200
300
400
500
Capital Market Equilibrium
• For now, assume that there is no
government and the US is a
closed economy
• Add up individual firm’s hiring
decisions to get aggregate
investment
• Add up individual household
decisions to get aggregate
savings
• A capital market equilibrium is
an interest rate that clears the
market (i.e.,savings equals
investment)
• Here, i*= 10%, S* = I*= 300
20
16
12
8
4
0
0
100
200
300
400
500
Example: Post-war Germany
• It is estimated that 20-25% of
Germany’s capital stock was
destroyed during WWII. How
would the German capital
market respond to this?
20
16
12
8
4
0
0
100
200
300
400
500
Example: Post-war Germany
• It is estimated that 20-25% of
Germany’s capital stock was
destroyed during WWII. How
would the German capital
market respond to this?
• A lower capital stock decreases
increases the productivity of
new investment and, thus
increases investment demand
24
20
16
12
8
4
0
0
100
200
300
400
500
Example: Post-war Germany
• It is estimated that 20-25% of
Germany’s capital stock was
destroyed during WWII. How
would the German capital
market respond to this?
• A lower capital stock decreases
increases the productivity of
new investment and, thus
increases investment demand
• The resulting higher
equilibrium has a higher
interest rate, higher savings and
investment
24
20
16
12
8
4
0
0
100
200
300
400
500
Example:The Bubonic Plague
• The Bubonic Plague, or “Black
Death” ravaged Europe in the
1300’s. From 1347-1352,
approximately 30% of the
population in Europe was killed
(25 million). What impact will
this have on capital markets?
20
16
12
8
4
0
0
100
200
300
400
500
Example:The Bubonic Plague
• The Bubonic Plague, or “Black
Death” ravaged Europe in the
1300’s. From 1347-1352,
approximately 30% of the
population in Europe was killed
(25 million). What impact will
this have on capital markets?
• A decrease in employment
lowers the productivity of
investment (labor and capital
are complements) and, hence,
investment demand
20
16
12
8
4
0
0
100
200
300
400
500
Example:The Bubonic Plague
• The Bubonic Plague, or “Black
Death” ravaged Europe in the
1300’s. From 1347-1352,
approximately 30% of the
population in Europe was killed
(25 million). What impact will
this have on capital markets?
• A decrease in employment
lowers the productivity of
investment (labor and capital
are complements) and, hence,
investment demand
• The result: lower interest rates,
savings, and investment
20
16
12
8
4
0
0
100
200
300
400
500
Temporary vs. Permanent Shocks
• Unlike labor markets, the
timing and persistence of
productivity shock are
important
20
16
12
8
4
0
0
100
200
300
400
500
Temporary vs. Permanent Shocks
• Unlike labor markets, the
timing and persistence of
productivity shock are
important
• New capital takes time to
install. Therefore, productivity
improvements must be long
lasting to effect investment
demand
20
16
12
8
4
0
0
100
200
300
400
500
Temporary vs. Permanent Shocks
• Unlike labor markets, the
timing and persistence of
productivity shock are
important
• New capital takes time to
install. Therefore, productivity
improvements must be long
lasting to effect investment
demand
• A temporary improvement in
productivity will increase
savings (as consumers smooth
this extra income), but have no
impact on investment
20
16
12
8
4
0
0
100
200
300
400
500
Temporary vs. Permanent Shocks
• Unlike labor markets, the
timing and persistence of
productivity shock are
important
• New capital takes time to
install. Therefore, productivity
improvements must be long
lasting to effect investment
demand
• On the other hand, a permanent
technological improvement will
increase investment, but have
little impact on savings
24
20
16
12
8
4
0
0
100
200
300
400
500