CHAPTER 9
SAVING, INVESTMENT, AND INTEREST RATES
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After reading Chapter 9, SAVING, INVESTMENT, AND INTEREST RATES, you should be able to:
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Discuss HOUSEHOLD SAVINGS and the CONSUMPTION FUNCTION.
Discuss the LIFE-CYCLE THEORY OF CONSUMPTION.
Differentiate between the NOMINAL RATE OF INTEREST and the REAL RATE OF
INTEREST.
Explain how interest rates and INVESTMENT are related.
Define CREDIT MARKETS and the MARKET RATE OF INTEREST.
Discuss the structure of interest rates.
CHAPTER OUTLINE
I. CONSUMPTION AND SAVINGS
A.
B.
C.
D.
E.
HOUSEHOLD SAVINGS (or personal savings) is what is left over from our income after paying
our income taxes and buying goods and services.
We can save only by refraining from consumption. When we save, we add to our assets by
increasing funds in savings accounts, by purchasing bonds, stocks, etc.
How much of our income we consume depends on
1. the income we earn after taxes.
2. the interest rate.
The CONSUMPTION FUNCTION shows how much a household wishes to consume at each
level of income and interest rate: C = f (Y, r).
The SAVING FUNCTION shows how much a household wishes to save at each level of income
and interest rate: S = F (Y, r).
II. LIFE-CYCLE CONSUMPTION
A.
B.
C.
According to the LIFE-CYCLE THEORY OF CONSUMPTION, households base their
consumption and saving decisions on the long-term income they expect to earn over their lifetimes.
Typical households start with low income and consume more than their income when they are
“young”; mature households have higher incomes and accumulate savings for their old age; old
households live off their savings.
Through buying on credit or saving, we rearrange our consumption so that it does not vary over the
lifetime as much as our current income.
III. INTEREST RATES AND SAVING
A.
Consumption today is preferable over consumption tomorrow: by consuming our income today, we
get instant satisfaction. The INTEREST RATE constitutes the reward for postponing consumption
into the future. Interest rates determine saving decisions: an increase in the rate of interest, holding
other factors constant, encourages us to save more (to postpone more consumption).
B. There are two types of interest rates:
1. The NOMINAL INTEREST RATE is the contractual interest rate that is observed in credit
markets. It is percentage cost of borrowing, expressed in terms of money.
2. The REAL INTEREST RATE is the nominal rate of interest over some period minus the
expected rate of inflation over the same period.
C. Real interest rate is forward-looking: Lenders make their decisions based on the current nominal rate
minus the expected inflation rate over the period of the loan. Actual inflation can be different; we
can observe the actual real interest rate earned by the savers after the end of the period by deducting
the actual inflation rate from the nominal rate.
D. Changes in the real interest rate affect the terms on which we can exchange current and future
consumption. A higher interest rate implies cheaper future consumption and encourages people to
save more. The relationship between the real interest rate and the amount of saving is positive.
IV. INTEREST RATES AND INVESTMENT
A.
B.
C.
D.
The term INVESTMENT refers to business investment in new plants, equipment, and inventories.
The key determinants of investment are
1. the expectations of the future profits.
2. the costs of borrowing.
Businesses seek profitable investment, which lower production costs and/or increase sales, thus
providing for the greatest rates of return. At the same time, investment is costly: Typically, when a
firm invests, it incurs certain costs since it must purchase new capital goods. The cost of acquiring
additional capital is the prevailing cost of borrowing, or the interest rate. Therefore, firms carry out
additional investments as long as their rate of return exceeds the market rate of interest. The last
investment project should yield a rate of return equal to the market interest rate.
The firm’s INVESTMENT DEMAND CURVE shows the amount of investment desired at
different interest rates. In terms of interest rate and the quantity of investment, the investment
demand curve is negatively sloped: the amount of desired investment increases as the interest rate
falls. The investment demand curve of the economy shows the amount of investment desired at
different interest rates by the economy as a whole.
V. CREDIT MARKETS AND INTEREST RATES
A.
B.
C.
D.
A large portion of the economy’s investment is financed directly by savings of the business firms.
Those projects that cannot be paid for out of the firm’s own saving must be financed by the saving
of others. CREDIT MARKETS bring together businesses that wish to invest (borrowers) with
savers who are prepared to supply their savings for investment projects (lenders) to determine
conditions of exchange such as interest rates and the duration of the loan.
The supply curve of savings and the demand for saving (the demand for investment) determine the
MARKET (or EQUILIBRIUM) RATE OF INTEREST. The equilibrium rate of interest is the
rate that equates the quantity of investment and the quantity of saving.
At an interest rate above the equilibrium rate, savers will want to lend more than investing firms
wish to borrow. Eventually, the interest rate will drop.
In the case where households wish to save more at each rate of interest, that is, they become more
thrifty than before, the interest rate should fall and the volume of investment will become greater.
VI. THE STRUCTURE OF THE INTEREST RATES
A.
B.
There are many types of borrowers in credit markets: businesses who wish to launch new projects,
households who wish to finance home purchase or new cars, governments whose budgets are in
deficit. The interest rate is not the same for all borrowers, and different interest rates are paid on
different financial assets.
Interest rates vary with the conditions of RISK, LIQUIDITY, and MATURITY associated with a
loan.
1. Lenders must be compensated for the extra risk of lending to borrowers with poor credit
ratings. Low rating means that a borrower may fail to repay a loan. The best credit rating
implies a zero percent risk of default. The lower the credit rating the higher is the interest rate.
The extra interest paid by low-rated borrowers is called risk premium.
2. Financial assets are called liquid if they can be turned into cash quickly or with a small
penalty. Interest rates vary inversely with liquidity.
3. Interest rates vary with the term of maturity, that is, the length of the borrowing period.
REVIEW QUESTIONS
True or False
If the statement is correct, write true in the space provided; if it is wrong, write false. Below the question
give a short statement that supports your answer.
____ 1. The consumption function is the same as the saving function since both are determined by a
household income and interest rate.
____ 2. Given a constant rate of interest, both consumption and saving increase as the income increases.
____ 3. Given an unchanging level of income, consumption falls and saving rises as the rate of interest
increases.
____ 4. The life-cycle theory of consumption states that people base their consumption and saving
decisions on their current level of income.
____ 5. The nominal rate of interest is crucial in making saving decisions since it adjusts for inflation.
____ 6. The real interest rate equals the nominal rate of interest when there is no inflation.
____ 7. The greater the real interest rate, the more people are encouraged to save.
____ 8. Credit markets serve the function of equating personal income and personal savings.
____ 9. Business firms will fund investment projects so long as these projects provide a positive rate of
return.
____ 10.Demand for investment by the entire economy increases as the business expectations become
more optimistic.
Multiple Choice
Circle the letter corresponding to the correct answer.
1. Suppose a $20 million investment project promises to add $1 million to profits each year for an almost
infinite period. What is the rate of return on this investment project?
a. 5 percent
b. 10 percent
c. 19 percent
d. 20 percent
e. 21 percent
2. In any given period, a firm chooses to carry out an additional investment project according to the
following information:
a. the cost of its projects.
b. the state of the firm’s own savings.
c. the market rate of interest.
d. the rate of return on investment.
e. c and d.
3. The market interest rate is the rate of interest that equates
a. the real rate of interest with the rate of return on an investment project.
b. the quantity of investment with the quantity of saving.
c. the amount of savings with consumption expenditures.
d. the real rate of interest with the nominal interest rate.
e. present and future consumption.
4. In the situation when lenders cannot find enough borrowers, the interest rate
a. increases.
b. drops.
c. remains the same until the businesses find profitable projects, and then increases.
d. remains the same until the businesses find profitable projects, and then drops.
e. all of the above is possible.
5. Which of the following is correct? Savings can be made by
a. government.
b. households.
c. businesses.
d. b and c.
e. all of the above.
6. People are able to smooth out fluctuations in their consumption because they can
a. borrow over entire lifetimes.
b. save over entire lifetimes.
c. borrow when they expect their income to rise and save when they expect their income to decline.
d. borrow and/or save depending on the real rate of interest.
e. borrow and/or save depending on the nominal rate of interest.
7. The real interest rate formula includes
a. the nominal rate of interest and the actual rate of inflation.
b. the nominal rate of interest and the anticipated rate of inflation.
c. the market interest rate and the expected demand for investment.
d. the nominal rate of interest and market prices.
e. all of the above.
8. Under which of the following conditions will the interest rate on a loan tend to be the highest?
a. High risk, high liquidity, short term of maturity
b. High risk, low liquidity, long term of maturity
c. Low risk, high liquidity, long term of maturity
d. Low risk, low liquidity, long term of maturity
e. Both a and d
Essay Questions
Write a short essay or otherwise answer each question.
1. Draw a diagram showing life-cycle consumption and income, and explain it. What would the
diagram’s consumption curve look like if people were basing their consumption and saving decisions
on current earnings?
2. What is the investment demand curve of the economy? Why is it downward sloping?
3. Explain how the economy equates investment and saving. How will market equilibrium be affected by
a momentary increase in the interest rate? Draw an appropriate diagram.
4. Explain why an increase in the thrift of households yields a lower interest rate and a greater volume of
investment. Draw an appropriate diagram.
5. A firm is considering three investment projects. Costs of the projects are $5 million, $10 million, and $20
million, respectively. Each project promises to bring profits of $1 million per year for a very long period.
Which of the projects will the firm decide to carry out, if the market interest rate is 9.9%? Assume that
there is no inflation and that the firm can finance the projects only by borrowing in the credit market.
6. In the problem above, assume that the firm is known to have had problems with repaying debts in the
past. How may this affect the firm’s investment decisions? Use the concept of “risk premium” in your
answer.
ANSWERS TO REVIEW QUESTIONS
True or False
False 1. Although both functions have similar form, their meanings are different: the consumption function
shows how much a household wishes to consume at each level of income and interest rate, and the saving
function deals with that portion of income that is left over after consumption.
True 2. If the interest rate holds constant, a household will normally spend and save more as its income
increases.
True 3. The interest rate is the reward for saving. When our income does not change, we usually choose to
save more and spend less as the interest rate increases.
False 4. The life-cycle theory of consumption predicts that people tend to smooth out fluctuations in
consumption over time by anticipating future changes in their incomes. Young people borrow, expecting
future rises in their incomes, while mature people consume less and save more, expecting their income to
shrink as they become old.
False 5. It is the real interest rate that anticipates inflation and affects saving decisions.
True 6. The real interest rate is defined as the nominal rate of interest minus anticipated inflation.
True 7. Changes in the real interest rate affect the terms on which we can exchange current and future
consumption. Thus, a higher interest rate translates into cheaper future consumption.
False 8. Credit markets bring together businesses that wish to invest with savers who supply their savings.
False 9. Business firms will fund investment projects until the rate of return on the last project is equal to
the market interest rate.
False 10. Demand for investment by the entire economy increases as the interest rate declines.
Multiple Choice
1.
a. The rate of return on a $20 million investment project is 5 percent--the annual addition to profit
divided by the cost of the project.
2.
e. Firms carry out additional investment projects as long as their rate of return exceeds the market rate
of interest.
3.
b. The credit market is in equilibrium at an interest rate that equates the desired amount of investment
with the desired amount of saving.
4.
b. If the amount of desired investment exceeds the amount of desired saving, and lenders cannot find
enough borrowers, the interest rate drops until the credit market reaches an equilibrium.
5.
e. Not all saving in the economy is the personal saving. Businesses save by retaining profits that are not
distributed to owners as dividends and by setting aside funds to replace capital that is depreciating.
Also the government saves by spending less than it collects in taxes.
6.
c. According to the life-cycle theory of consumption, in order to avoid swings in consumption, people
borrow when they are young, expecting that their incomes will eventually rise; and people save as they
become mature, expecting that their incomes will fall when they are old.
7.
b. The real interest rate is the nominal rate minus anticipated inflation. This formula does not claim that
we correctly anticipate inflation. Actual inflation can be different from expected. After the fact,
however, we can look back and observe the actual interest rate earned by savers by deducting the actual
inflation rate from the nominal rate.
8. b. Interest rates vary with the conditions of risk, liquidity, and maturity associated with a loan. Higher
risk, lower liquidity, and longer term of maturity make the loans less profitable for the lenders. To
compensate, lenders will charge higher interest rates on loans if one or more of these conditions are met.
Essay Questions
1.
See Figure 9.2 in the textbook.
People base their consumption and saving decisions on the long-term income they expect to earn over
their lifetimes. For this reason, the consumption curve is smoother than the income curve. Young
households start with low income; in the anticipation of growing income in the future, they borrow and
consume more than they earn. Mature households have higher incomes and save for their old age; their
consumption is less than their current income. Old households live off their savings, consuming again
in excess of their income. If people were basing their consumption and saving decisions on current
earnings only, the consumption curve would run close to the income curve: there would be no reason
for the households to borrow or save much, if they did not anticipate significant changes in their
future income.
2.
The investment demand curve of the economy shows the amount of investment desired at different
interest rates by the economy as a whole. A downward slope of the curve means that the firms in the
economy are willing to undertake a greater number of new investments as the interest rate falls, and
vice versa. This happens because the interest rate is the cost of acquiring capital for the firms. The
lower these costs, the greater number of investment projects that become profitable, and the more firms
are willing to make new investments.
3.
The saving function shows how much a household wishes to save at each level of income and interest
rate. The investment demand curve shows the amount of investment desired at different interest rates.
The saving function is positively sloped: a higher interest rate brings forth more saving. The investment
demand curve is negatively sloped: a lower interest rate encourages investment. At the point where the
saving and investment demand functions intersect the quantity of investment is equal to the quantity of
saving. The vertical coordinate of this point is the equilibrium rate of interest. A momentary increase
in the interest rate will result in a disequilibrium in the credit market: the desired amount of saving
exceeds the desired amount of investment; some lenders are unable to find borrowers for their
savings.
See Figure 9.5 in the textbook.
4.
The increase in household thrift causes the saving function to shift to the right: households are willing
to save more under the same interest rate. The point where the saving function and the investment
demand curve intersect will move downward and to the right, which means a lower interest rate and a
greater volume of investment in the new equilibrium.
See Figure 9.6 in the textbook.
5.
The firm will carry out those projects that promise returns exceeding the costs of acquiring the capital,
or, in other words, when the rate of return exceeds the market interest rate. The projects’ rates of return
are: 20% (=1/5), 10% (=1/10), and 5% (=1/20), respectively. The first two numbers exceed the market
interest rate, while the last one falls short of it. Hence, the firm should reject the third project.
6.
If the firm had problems with repaying debts in the past, it can be expected to fail to repay a loan again.
This firm has a poor credit rating; that is, lending to it is risky. Lenders must be compensated for the
risk of lending to borrowers with poor credit rating. This compensation comes in the form of a higher
interest rate, paid by low-rated borrowers. This extra interest is called risk premium. It is quite likely
that the firm in this problem will have to pay an interest rate exceeding 10% (market interest rate of
9.9% plus some risk premium). Then, only the first project, yielding a 20% rate of return, will be
profitable.