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Capital Markets
Savings, Investment, and Interest Rates
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Some Useful Terminology
• Savings: Current income which is deferred for future consumption (i.e., not spent)
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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)
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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.)
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Some Useful Terminology
• Investment: The purchase of new capital goods.
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Some Useful Terminology
• Investment: The purchase of new capital goods.
– Gross Investment: Total purchases of new capital goods
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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
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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
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NIPA Accounts
• Recall, the accounting identity in the NIPA accounts: GDP = C + I + G + NX
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NIPA Accounts
• Recall, the accounting identity in the NIPA accounts: GDP = C + I + G + NX
• GDP = Gross Private Savings + Taxes + C
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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)
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NIPA Accounts
• Recall, the accounting identity in the NIPA accounts: GDP = C + I + G + NX
• GDP = Gross Savings + Taxes + CI + (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
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Interest Rates
• What is an interest rate?
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Interest Rates
• What is an interest rate?– The interest rate is the relative price of current
spending in terms of foregone future income.
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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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Interest Rates:1987-2003
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The Yield Curve
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Yield Curves
• What determines the shape of the yield curve?– Segmented Markets Hypothesis– Expectations Hypothesis– Preferred Habitat Hypothesis
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Interest Rates:1987-2003
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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%)
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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
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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.
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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)
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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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Real/Nominal Interest Rates
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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?
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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
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Present Value
• With a positive interest rate, income received in the future is less valuable that income received immediately.
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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
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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.
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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
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Income vs. Wealth
• Your wealth is defined and the present value of your lifetime income.
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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)
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Household Savings
• Without an active capital markets, household consumption is restricted to equal current income (that is, C=Y)
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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)
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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%.
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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.
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Consumption Possibilities
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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
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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• However, you must repay your loan next year.
This implies that
C’= $60,000 – (1.05)Loan
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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
• 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
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Consumption Possibilities
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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
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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
• Your maximum allowable loan is $60,000/1.05 = $57,143 (this is associated with zero future consumption)
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Borrowing Limits
• Note that you need to be able to repay your loan next year. Therefore, $60,000 = (1.05)LoanYour 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
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Consumption Possibilities
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Consumption Possibilities
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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.
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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
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Consumption Possibilities
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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
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Consumption Possibilities
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Consumption Possibilities
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Suppose that the interest rate rises to 8%
• Note that if you don’t borrow or lend, you are unaffected.
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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)
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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)
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Consumption Possibilities
Current Consumption (000s)
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Consumption Possibilities
Current Consumption (000s)
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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
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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
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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
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How does rising interest rates influence savings decisions?
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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)
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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)
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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: ????
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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
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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
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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
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Aggregate Savings
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Again, assume that the interest rate is 5%, consider two individuals
Person A• Current income:
$10,000• Anticipated future
income: $50,000
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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
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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
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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
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Consumption vs. Wealth
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Consumption and Wealth
• With capital markets, consumption is not determined by current income, but by wealth (present value of lifetime income)
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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
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Consumption vs. Wealth
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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
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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
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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
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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
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Suppose that economic growth in the US rises. What should happen to aggregate savings?
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Suppose that economic growth in the US rises. What should happen to aggregate savings?
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Technology & Investment Demand
• Recall that an economy has three sources of growth: labor, capital, and technology
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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
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Production (Holding Employment Fixed)
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Production (Holding Employment Fixed)
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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
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Diminishing marginal product implies that as the capital stock rises, the marginal product of
additional capital falls
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Marginal Product and Investment Demand
• Recall that investment refers to the purchase of new capital equipment by the private sector
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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)
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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 costP(k) > PV(MPK)
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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.
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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 …………
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A Numerical example
• What is the present value of this income stream?
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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 + …….
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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)
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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%
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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%
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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)
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Interest rates and Investment
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Investment Demand
• It is assumed that labor and capital are compliments. That is, when employment rises, the productivity of capital increases as well.
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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
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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
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A rise in investment demand
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A rise in investment demand
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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
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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?
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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
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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 0
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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?
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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
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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
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Temporary vs. Permanent Shocks
• Unlike labor markets, the timing and persistence of productivity shock are important
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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
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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
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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 0
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