17.2: Reading- Loanable Funds
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The Market for Loanable Funds
When a firm decides to expand its capital stock, it can finance its purchase of capital in several ways. It might already have the funds on hand. It can also raise funds by selling shares of stock, as we discussed in a previous module. When a firm sells stock, it is selling shares of ownership of the firm. It can borrow the funds for the capital from a bank. Another option is to issue and sell its own bonds. A bond is a promise to pay back a certain amount at a certain time. When a firm borrows from a bank or sells bonds, of course, it accepts a liability—it must make interest payments to the bank or the owners of its bonds as they come due.
Regardless of the method of financing chosen, a critical factor in the firm’s decision on whether to acquire and hold capital and on how to finance the capital is the interest rate. The role of the interest rate is obvious when the firm issues its own bonds or borrows from a bank. But even when the firm uses its own funds to purchase the capital, it is forgoing the option of lending those funds directly to other firms by buying their bonds or indirectly by putting the funds in bank accounts, thereby allowing the banks to lend the funds. The interest rate gives the opportunity cost of using funds to acquire capital rather than putting the funds to the best alternative use available to the firm.
The interest rate is determined in a market in the same way that the price of potatoes is determined in a market: by the forces of demand and supply. The market in which borrowers (demanders of funds) and lenders (suppliers of funds) meet is the loanable funds market.
We will simplify our model of the role that the interest rate plays in the demand for capital by ignoring differences in actual interest rates that specific consumers and firms face in the economy. For example, the interest rate on credit cards is higher than the mortgage rate of interest, and large, established companies can borrow funds or issue bonds at lower interest rates than new, start-up companies can. Interest rates that firms face depend on a variety of factors, such as riskiness of the loan, the duration of the loan, and the costs of administering the loan. However, since we will focus on general tendencies that cause interest rates to rise or fall and since the various interest rates in the economy tend to move up and down together, the conclusions we reach about the market for loanable funds and how firms and consumers respond to interest rate changes will still be valid.
The Demand for Loanable Funds
In the previous section we learned that a firm’s decision to acquire and keep capital depends on the net present value of the capital in question, which in turn depends on the interest rate. The lower the interest rate, the greater the amount of capital that firms will want to acquire and hold, since lower interest rates translate into more capital with positive net present values. The desire for more capital means, in turn, a desire for more loanable funds. Similarly, at higher interest rates, less capital will be demanded, because more of the capital in question will have negative net present values. Higher interest rates therefore mean less funding demanded.
Thus the demand for loanable funds is downward-sloping, like the demand for virtually everything else, as shown in Figure 13.2. The lower the interest rate, the more capital firms will demand. The more capital that firms demand, the greater the funding that is required to finance it.
The Supply of Loanable Funds
Lenders are consumers or firms that decide that they are willing to forgo some current use of their funds in order to have more available in the future. Lenders supply funds to the loanable funds market. In general, higher interest rates make the lending option more attractive.
For consumers, however, the decision is a bit more complicated than it is for firms. In examining consumption choices across time, economists think of consumers as having an expected stream of income over their lifetimes. It is that expected income that defines their consumption possibilities. The problem for consumers is to determine when to consume this income. They can spend less of their projected income now and thus have more available in the future. Alternatively, they can boost their current spending by borrowing against their future income.
Saving is income not spent on consumption. (We shall ignore taxes in this analysis.) Dissaving occurs when consumption exceeds income during a period. Dissaving means that the individual’s saving is negative. Dissaving can be financed either by borrowing or by using past savings. Many people, for example, save in preparation for retirement and then dissave during their retirement years.
Saving adds to a household’s wealth. Dissaving reduces it. Indeed, a household’s wealth is the sum of the value of all past saving less all past dissaving.
We can think of saving as a choice to postpone consumption. Because interest rates are a payment paid to people who postpone their use of wealth, interest rates are a kind of reward paid to savers. Will higher interest rates encourage the behavior they reward? The answer is a resounding “maybe.” Just as higher wages might not increase the quantity of labor supplied, higher interest rates might not increase the quantity of saving. The problem, once again, lies in the fact that the income and substitution effects of a change in interest rates will pull in opposite directions.
Consider a hypothetical consumer, Tom Smith. Let us simplify the analysis of Mr. Smith’s choices concerning the timing of consumption by assuming that there are only two periods: the present period is period 0, and the next is period 1. Suppose the interest rate is 8% and his income in both periods is expected to be $30,000.
Mr. Smith could, of course, spend $30,000 in period 0 and $30,000 in period 1. In that case, his saving equals zero in both periods. But he has alternatives. He could, for example, spend more than $30,000 in period 0 by borrowing against his income for period 1. Alternatively, he could spend less than $30,000 in period 0 and use his saving—and the interest he earns on that saving—to boost his consumption in period 1. If, for example, he spends $20,000 in period 0, his saving in period 0 equals $10,000. He will earn $800 interest on that saving, so he will have $40,800 to spend in the next period.
Suppose the interest rate rises to 10%. The increase in the interest rate has boosted the price of current consumption. Now for every $1 he spends in period 0 he gives up $1.10 in consumption in period 1, instead of $1.08, which was the amount that would have been given up in consumption in period 1 when the interest rate was 8%. A higher price produces a substitution effect that reduces an activity—Mr. Smith will spend less in the current period due to the substitution effect. The substitution effect of a higher interest rate thus boosts saving. But the higher interest rate also means that he earns more income on his saving. Consumption in the current period is a normal good, so an increase in income can be expected to increase current consumption. But an increase in current consumption implies a reduction in saving. The income effect of a higher interest rate thus tends to reduce saving. Whether Mr. Smith’s savings will rise or fall in response to a higher interest rate depends on the relative strengths of the substitution and income effects.
To see how an increase in interest rates might reduce saving, imagine that Mr. Smith has decided that his goal is to have $40,800 to spend in period 1. At an interest rate of 10%, he can reduce his saving below $10,000 and still achieve his goal of having $40,800 to spend in the next period. The income effect of the increase in the interest rate has reduced his saving, and consequently his desire to supply funds to the loanable funds market.
Because changes in interest rates produce substitution and income effects that pull saving in opposite directions, we cannot be sure what will happen to saving if interest rates change. The combined effect of all consumers’ and firms’ decisions, however, generally leads to an upward-sloping supply curve for loanable funds, as shown in Figure 13.2. That is, the substitution effect usually dominates the income effect.
The equilibrium interest rate is determined by the intersection of the demand and supply curves in the market for loanable funds.
Capital and the Loanable Funds Market
If the quantity of capital demanded varies inversely with the interest rate, and if the interest rate is determined in the loanable funds market, then it follows that the demand for capital and the loanable funds market are interrelated. Because the acquisition of new capital is generally financed in the loanable funds market, a change in the demand for capital leads to a change in the demand for loanable funds—and that affects the interest rate. A change in the interest rate, in turn, affects the quantity of capital demanded on any demand curve.
The relationship between the demand for capital and the loanable funds market thus goes both ways. Changes in the demand for capital affect the loanable funds market, and changes in the loanable funds market can affect the quantity of capital demanded.
Changes in the Demand for Capital and the Loanable Funds Market
Figure 13.3 suggests how an increased demand for capital by firms will affect the loanable funds market, and thus the quantity of capital firms will demand. In Panel (a) the initial interest rate is r1. At r1 in Panel (b) K1units of capital are demanded (on curve D1). Now suppose an improvement in technology increases the marginal product of capital, shifting the demand curve for capital in Panel (b) to the right to D2. Firms can be expected to finance the increased acquisition of capital by demanding more loanable funds, shifting the demand curve for loanable funds to D2 in Panel (a). The interest rate thus rises to r2. Consequently, in the market for capital the demand for capital is greater and the interest rate is higher. The new quantity of capital demanded is K2on demand curve D2.
Changes in the Loanable Funds Market and the Demand for Capital
Events in the loanable funds market can also affect the quantity of capital firms will hold. Suppose, for example, that consumers decide to increase current consumption and thus to supply fewer funds to the loanable funds market at any interest rate. This change in consumer preferences shifts the supply curve for loanable funds in Panel (a) of Figure 13.4 from S1 to S2 and raises the interest rate to r2. If there is no change in the demand for capital D1, the quantity of capital firms demand falls to K2 in Panel (b).
Our model of the relationship between the demand for capital and the loanable funds market thus assumes that the interest rate is determined in the market for loanable funds. Given the demand curve for capital, that interest rate then determines the quantity of capital firms demand.
Table 13.2 shows that a change in the quantity of capital that firms demand can begin with a change in the demand for capital or with a change in the demand for or supply of loanable funds. A change in the demand for capital affects the demand for loanable funds and hence the interest rate in the loanable funds market. The change in the interest rate leads to a change in the quantity of capital demanded. Alternatively, a change in the loanable funds market, which leads to a change in the interest rate, causes a change in quantity of capital demanded.
| Table 13.2 Two Routes to Changes in the Quantity of Capital Demanded | |
| A change originating in the capital market | A change originating in the loanable funds market |
| 1. A change in the demand for capital leads to… | 1. A change in the demand for or supply of loanable funds leads to … |
| 2.…a change in the demand for loanable funds, which leads to… | 2.…a change in the interest rate, which leads to… |
| 3.…a change in the interest rate, which leads to… | 3.…a change in the quantity of capital demanded. |
| 4.…a change in the quantity of capital demanded. |
A change in the quantity of capital that firms demand can begin with a change in the demand for capital or with a change in the demand or supply of loanable funds.
KEY TAKEAWAYS
- The net present value (NPV) of an investment project is equal to the present value of its expected revenues minus the present value of its expected costs. Firms will want to undertake those investments for which the NPV is greater than or equal to zero.
- The demand curve for capital shows that firms demand a greater quantity of capital at lower interest rates. Among the forces that can shift the demand curve for capital are changes in expectations, changes in technology, changes in the demands for goods and services, changes in relative factor prices, and changes in tax policy.
- The interest rate is determined in the market for loanable funds. The demand curve for loanable funds has a negative slope; the supply curve has a positive slope.
- Changes in the demand for capital affect the loanable funds market, and changes in the loanable funds market affect the quantity of capital demanded.
Case in Point: The Net Present Value of an MBA
An investment in human capital differs little from an investment in capital—one acquires an asset that will produce additional income over the life of the asset. One’s education produces—or it can be expected to produce—additional income over one’s working career.
Ronald Yeaple, a professor at the University of Rochester business school, has estimated the net present value (NPV) of an MBA obtained from each of 20 top business schools. The costs of attending each school included tuition and forgone income. To estimate the marginal revenue product of a degree, Mr. Yeaple started with survey data showing what graduates of each school were earning five years after obtaining their MBAs. He then estimated what students with the ability to attend those schools would have been earning without an MBA. The estimated marginal revenue product for each year is the difference between the salaries students earned with a degree versus what they would have earned without it. The NPV is then computed using
The estimates given here show the NPV of an MBA over the first seven years of work after receiving the degree. They suggest that an MBA from 15 of the schools ranked is a good investment—but that a degree at the other schools might not be. Mr. Yeaple says that extending income projections beyond seven years would not significantly affect the analysis, because present values of projected income differentials with and without an MBA become very small.
While the Yeaple study is somewhat dated, a 2002 study by Stanford University Graduate School of Business professor Jeffrey Pfeffer and Stanford Ph.D. candidate Christina T. Fong reviewed 40 years of research on this topic and reached the conclusion that, “For the most part, there is scant evidence that the MBA credential, particularly from non-elite schools…are related to either salary or the attainment of higher level positions in organizations.”
Of course, these studies only include financial aspects of the investment and did not cover any psychic benefits that MBA recipients may incur from more interesting work or prestige.
| School | Net present value, first 7 years of work | School | Net present value, first 7 years of work |
| Harvard | $148,378 | Virginia | $30,046 |
| Chicago | 106,847 | Dartmouth | 22,509 |
| Stanford | 97,462 | Michigan | 21,502 |
| MIT | 85,736 | Carnegie-Mellon | 18,679 |
| Yale | 83,775 | Texas | 17,459 |
| Wharton | 59,486 | Rochester | −307 |
| UCLA | 55,088 | Indiana | −3,315 |
| Berkeley | 54,101 | NYU | −3,749 |
| Northwestern | 53,562 | South Carolina | −4,565 |
| Cornell | 30,874 | Duke | −17,631 |
- Principles of Microeconomics Section 13.2 . Authored by: Anonymous. Located at: http://2012books.lardbucket.org/books/microeconomics-principles-v1.0/s16-02-interest-rates-and-capital.html. License: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike