# 304 Reading: Interest Rates and Capital

## The Demand for Capital

The quantity of capital that firms employ in their production of goods and services has enormously important implications for economic activity and for the standard of living people in the economy enjoy. Increases in capital increase the marginal product of labor and boost wages at the same time they boost total output. An increase in the stock of capital therefore tends to raise incomes and improve the standard of living in the economy.

Capital is often a fixed factor of production in the short run. A firm cannot quickly retool an assembly line or add a new office building. Determining the quantity of capital a firm will use is likely to involve long-run choices.

A firm uses additional units of a factor until marginal revenue product equals marginal factor cost. Capital is no different from other factors of production, save for the fact that the revenues and costs it generates are distributed over time. As the first step in assessing a firm’s demand for capital, we determine the present value of marginal revenue products and marginal factor costs.

## Capital and Net Present Value

Suppose Carol Stein is considering the purchase of a new \$95,000 tractor for her farm. Ms. Stein expects to use the tractor for five years and then sell it; she expects that it will sell for \$22,000 at the end of the five-year period. She has the \$95,000 on hand now; her alternative to purchasing the tractor could be to put \$95,000 in a bond account earning 7% annual interest.

Ms. Stein expects that the tractor will bring in additional annual revenue of \$50,000 but will cost \$30,000 per year to operate, for net revenue of \$20,000 annually. For simplicity, we shall suppose that this net revenue accrues at the end of each year.

Should she buy the tractor? We can answer this question by computing the tractor’s net present value (NPV), which is equal to the present value of all the revenues expected from an asset minus the present value of all the costs associated with it. We thus measure the difference between the present value of marginal revenue products and the present value of marginal factor costs. If NPV is greater than zero, purchase of the asset will increase the profitability of the firm. A negative NPV implies that the funds for the asset would yield a higher return if used to purchase an interest-bearing asset. A firm will maximize profits by acquiring additional capital up to the point that the present value of capital’s marginal revenue product equals the present value of marginal factor cost.

If the revenues generated by an asset in period n equal Rn and the costs in period n equal Cn, then the net present value NPV0 of an asset expected to last for n years is:

To purchase the tractor, Ms. Stein pays \$95,000. She will receive additional revenues of \$50,000 per year from increased planting and more efficient harvesting, less the operating cost per year of \$30,000, plus the \$22,000 she expects to get by selling the tractor at the end of five years. The net present value of the tractor, NPV0 is thus given by:

Given the cost of the tractor, the net returns Ms. Stein projects, and an interest rate of 7%, Ms. Stein will increase her profits by purchasing the tractor. The tractor will yield a return whose present value is \$2,690 greater than the return that could be obtained by the alternative of putting the \$95,000 in a bond account yielding 7%.

Ms. Stein’s acquisition of the tractor is called investment. Economists define investment as an addition to capital stock. Any acquisition of new capital goods therefore qualifies as investment.

## The Demand Curve for Capital

Our analysis of Carol Stein’s decision regarding the purchase of a new tractor suggests the forces at work in determining the economy’s demand for capital. In deciding to purchase the tractor, Ms. Stein considered the price she would have to pay to obtain the tractor, the costs of operating it, the marginal revenue product she would receive by owning it, and the price she could get by selling the tractor when she expects to be done with it. Notice that with the exception of the purchase price of the tractor, all those figures were projections. Her decision to purchase the tractor depends almost entirely on the costs and benefits she expects will be associated with its use.

Finally, Ms. Stein converted all those figures to a net present value based on the interest rate prevailing at the time she made her choice. A positive NPV means that her profits will be increased by purchasing the tractor. That result, of course, depends on the prevailing interest rate. At an interest rate of 7%, the NPV is positive. At an interest rate of 8%, the NPV would be negative. At that interest rate, Ms. Stein would do better to put her funds elsewhere.

At any one time, millions of choices like that of Ms. Stein concerning the acquisition of capital will be under consideration. Each decision will hinge on the price of a particular piece of capital, the expected cost of its use, its expected marginal revenue product, its expected scrap value, and the interest rate. Not only will firms be considering the acquisition of new capital, they will be considering retaining existing capital as well. Ms. Stein, for example, may have other tractors. Should she continue to use them, or should she sell them? If she keeps them, she will experience a stream of revenues and costs over the next several periods; if she sells them, she will have funds now that she could use for something else. To decide whether a firm should keep the capital it already has, we need an estimate of the NPV of each unit of capital. Such decisions are always affected by the interest rate. At higher rates of interest, it makes sense to sell some capital rather than hold it. At lower rates of interest, the NPV of holding capital will rise.

Because firms’ choices to acquire new capital and to hold existing capital depend on the interest rate, the demand curve for capital in Figure 13.1, which shows the quantity of capital firms intend to hold at each interest rate, is downward-sloping. At point A, we see that at an interest rate of 10%, \$8 trillion worth of capital is demanded in the economy. At point B, a reduction in the interest rate to 7% increases the quantity of capital demanded to \$9 trillion. At point C, at an interest rate of 4%, the quantity of capital demanded is \$10 trillion. A reduction in the interest rate increases the quantity of capital demanded. Figure 13.1. The Demand Curve for Capital. The quantity of capital firms will want to hold depends on the interest rate. The higher the interest rate, the less capital firms will want to hold.

The demand curve for capital for the economy is found by summing the demand curves of all holders of capital. Ms. Stein’s demand curve, for example, might show that at an interest rate of 8%, she will demand the capital she already has—suppose it is \$600,000 worth of equipment. If the interest rate drops to 7%, she will add the tractor; the quantity of capital she demands rises to \$695,000. At interest rates greater than 8%, she might decide to reduce her maintenance efforts for some of the capital she already has; the quantity of capital she demands would fall below \$600,000. As with the demand for capital in the economy, we can expect individual firms to demand a smaller quantity of capital when the interest rate is higher.

## Shifts in the Demand for Capital

Why might the demand for capital change? Because the demand for capital reflects the marginal revenue product of capital, anything that changes the marginal revenue product of capital will shift the demand for capital. Our search for demand shifters must thus focus on factors that change the marginal product of capital, the prices of the goods capital produces, and the costs of acquiring and holding capital. Let us discuss some factors that could affect these variables and thus shift the demand for capital.

### Changes in Expectations

Choices concerning capital are always based on expectations. Net present value is computed from the expected revenues and costs over the expected life of an asset. If firms’ expectations change, their demand for capital will change. If something causes firms to revise their sales expectations upward (such as stronger than expected sales in the recent past), it is likely to increase their demand for capital. Similarly, an event that dampens firms’ expectations (such as recent weak sales) is likely to reduce their demand for capital.

### Technological Change

Technological changes can increase the marginal product of capital and thus boost the demand for capital. The discovery of new ways to integrate computers into production processes, for example, has dramatically increased the demand for capital in the last few years. Many universities are adding new classroom buildings or renovating old ones so they can better use computers in instruction, and businesses use computers in nearly every facet of operations.

### Changing Demand for Goods and Services

Ultimately, the source of demand for factors of production is the demand for the goods and services produced by those factors. Economists say that the demand for a factor is a “derived” demand—derived, that is, from the demand for what the factor produces. As population and incomes expand, we can expect greater demand for goods and services, a change that will increase the demand for capital.

### Changes in Relative Factor Prices

Firms achieve the greatest possible output for a given total cost by operating where the ratios of marginal product to factor price are equal for all factors of production. For a firm that uses labor (L) and capital (K), for example, this requires that MPL/PL=MPK/PK, where MPLand MPK are the marginal products of labor and capital, respectively, and PL and PK are the prices of labor and capital, respectively. Suppose these equalities hold and the price of labor rises. The ratio of the marginal product of labor to its price goes down, and the firm substitutes capital for labor. Similarly, an increase in the price of capital, all other things unchanged, would cause firms to substitute other factors of production for capital. The demand for capital, therefore, would fall.

### Changes in Tax Policy

Government can indirectly affect the price of capital through changes in tax policy. For example, suppose the government enacts an investment tax credit for businesses, that is, a deduction of a certain percentage of their spending on capital from their profits before paying taxes. Such a policy would effectively lower the price of capital, causing firms to substitute capital for other factors of production and increasing the demand for capital. The repeal of an investment tax credit would lead to a decrease in the demand for capital. 