Saving, Investment and the Real Rate of Interest

Transcription

1 Econ 101H Michael Salemi Saving, Investment and the Real Rate of Interest 1. Introduction a. Define the nominal and real rates of interest b. Data for nominal and real interest rates in the United States c. Intuition: Why the real rate matters for economic decision making. 2. Irving Fisher explained that in the long run the real rate of interest is determined by the patience of people and the productivity of capital a. The patience of people explains their willingness to save. b. The productivity of capital explains why firms borrow funds to build capital c. In equilibrium, the real rate of interest balances saving and investment 3. Saving is the source of funds for investment (capital formation). a. Saving of an economic unit is its income minus its spending on current needs. b. Saving is a flow. Wealth which may be thought of as accumulated saving is a stock. Wealth increases when saving occurs or when the value of assets increases. c. The financial reward to saving is better measured by the real rate of interest than by the nominal rate of interest. A high real interest rate is an incentive to save. d. National saving comprises household saving, firm saving, government saving, and saving by the rest of the world. 4. Investment depends on saved funds for capital formation. a. National saving provides the funds needed for investment. b. Firms acquire new capital only when the expected benefits of that capital exceed the expected costs. c. Cost-benefit analysis for capital building decisions must take into account the fact that the costs and benefits are likely to occur at different times. d. The real rate of interest is a cost of investment. 5. Saving, Investment, and Financial Markets a. Financial markets equalize the supply of funds made available by savers and the demand for funds by firms that want to purchase or construct new capital. b. The demand and supply schedules each depend on the real rate of interest. c. In equilibrium, desired investment must equal desired national saving. d. The demand and supply model helps explain why interest rates change. The Real Rate of Interest Defined Let R t = Nominal rate of interest at time t π t = rate of inflation between time t-1 and t, π* t+1 = optimal forecast of πt+1 r t = real rate of interest at time t Perfect foresight real rate: r t = R t - π t+1 Real Rate: r t = R t - π* t+1

2 The Nominal Rate of Interest and the CPI Inflation Rate Nominal Rate Inflation Rate Jan-60 Jan-62 Jan-64 Jan-66 Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan The nominal rate is the one-year Treasury bond rate. The inflation rate is the year-to-year CPI growth rate. Real Rate of Interest Jan-60 Jan-62 Jan-64 Jan-66 Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan The perfect foresight real rate of interest is computed by assuming that the inflation rate between time t and time t+1 was predicted with perfect accuracy at time t.

3 The Saving Rate in the United States is low relative to that in other nations. Trends in the Components of National Saving The Personal Saving Rate in the US increased during the current recession. U.S. Personal Saving Rate Jan-10

4 A closer look at government saving Federal Government Saving as a Fraction of GDP The rest of the world has allowed the US to invest more than it could given its national saving. Balance of Payments as a Fraction of GDP Jan-60 Jan-62 Jan-64 Jan-66 Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan

5 The real rate of interest is determined by the interaction between the patience of people in an economy and the productivity of capital in that economy. This is essentially a demand and supply story where the real rate of interest is the price and the flow of saving and investment are the quantities supplied and demanded. A decrease in the demand for investment funds will, ceteris paribus, lower the real rate of interest. A decrease in the supply of saving will, ceteris paribus, increase the real rate of interest.

6 Exercises 1. Corey has a mountain bike worth $300, a credit card debt of $150, $200 in cash, a Sandy Koufax baseball card worth $400, $1,200 in a checking account, and an electric bill due for $250. a. Construct Corey s balance sheet and calculate his net worth. For each remaining part, explain how the event affects Corey s assets, liabilities, and wealth. b. Corey goes to a baseball card convention and finds out that his baseball card is a worthless forgery. c. Corey uses $150 from his paycheck to pay off his credit card balance. The remainder of his earnings is spent. d. Corey writes a $150 check on his checking account to pay off his credit card balance. Of the events in the previous three parts, which, if any, corresponds to saving on Corey s part? 2. Ellie and Vince are a married couple, both with college degrees and jobs. How would you expect each of the following events to affect the amount they save each month? Explain your answers in terms of the basic motivations for saving. a. Ellie learns she is pregnant. b. Vince reads in the paper about possible layoffs in his industry. c. Vince had hoped that his parents would lend financial assistance toward the couple s planned purchase of a house, but he learns that they can t afford it. d. Ellie announces that she would like to go to law school in the next few years. e. A boom in the stock market greatly increases the value of the couple s retirement funds. f. Vince and Ellie agree that they would like to leave a substantial amount to local charities in their wills. 3. Individual retirement accounts, or IRAs, were established by the U.S. government to encourage saving. An individual who deposits part of current earnings in an IRA does not have to pay income taxes on the earnings deposited, nor are any income taxes charged on the interest earned by the funds in the IRA. However, when the funds are withdrawn from the IRA, the full amount withdrawn is treated as income and is taxed at the individual s current income tax rate. In contrast, as individual depositing in a non-ira account has to pay income taxes on the funds deposited and on interest earned in each year but does not have to pay taxes on withdrawals from the account. Another feature of IRAs that is different form a standard saving account is that funds deposited in an IRA cannot be withdrawn prior to retirement, except upon payment of a substantial penalty. a. Greg, who is five years from retirement, receives a $10,000 bonus at work. He is trying to decide whether to save this extra income in an IRA account or in a regular savings account. Both accounts earn 5 percent nominal interest, and Greg is in the 30 percent tax bracket in every year (including his retirement year). Compare the amounts that Greg will have in five years under each of the two savings strategies, net of all taxes. Is the IRA a good deal for Greg? b. Would you expect the availability of IRAs to increase the amount that households save? Discuss in light of (1) the response of saving to changes in the real interest rate and (2) psychological theories of saving.

7 4. Ellie and Vince are trying to decide whether to purchase a new home. The house they want is priced at $200,000. Annual expenses such as maintenance, taxes, and insurance equal 4 percent of the home s value. If properly maintained, the house s real value is not expected to change. The real interest rate in the economy is 6 percent, and Ellie and Vince can qualify to borrow the full amount of the purchase price (for simplicity, assume no down payment) at that rate. Ignore the fact that mortgage interest payments are tax-deductible in the United States. a. Ellie and Vince would be willing to pay $1,500 monthly rent to live in a house of the same quality as the one they are thinking about purchasing. Should they buy the house? b. Does the answer to part a change if they are willing to pay $2,000 monthly rent? c. Does the answer to part a change if the real interest rate is 4 percent instead of 6 percent? d. Does the answer to part a change if the developer offers to sell Ellie and Vince the house for $150,000? e. Why do home-building companies dislike high interest rates? 5. The builder of a new movie theater complex is trying to decide how may screens she wants. Below are her estimates of the number of patrons the complex will attract each year depending on the number of screens available. Number of Screens Total number of patrons 1 40, , , , ,000 After paying the movie distributors and meeting all other non-interest expenses, the owner expects to net $2.00 per ticket sold. Construction costs are $1,000,000 per screen. a. Make a table showing the value of marginal product for each screen from the first through the fifth. What property is illustrated by the behavior of marginal products? b. How many screens will be built if the real interest rate is 5.5 percent? c. If the real interest rate is 7.5 percent? d. If the real interest rate is 10 percent? e. If the real interest rate is 5.5 percent, how far would construction costs have to fall before the builder would be willing to build a five-screen complex? 6. For each of the following scenarios, use supply and demand analysis to predict the resulting changes in the real interest rate, national saving, and investment. Show all your diagrams. a. The legislature passes a 10 percent investment tax credit. Under this program, for every $100 that a firm spends on new capital equipment, it receives an extra $10 in tax refunds from the government. b. A reduction in military spending moves the government s budget from deficit into surplus. c. A new generation of computer-controlled machines becomes available. These machines produce manufactured goods much more quickly and with fewer defects. d. The government raises its tax on corporate profits. Other tax changes also are made, such that the government s deficit remains unchanged.