The Productivity

Against the theory that finds interest in the mind, there has always stood one that finds it in the world: interest exists, on this account, not because we are impatient but because capital is productive. A tool, a machine, a roundabout method of making things yields more than it costs; the rate of interest is simply the rate of that yield — the marginal product of capital, the extra output the last increment of capital brings forth.

This is the productivity theory, and it is the natural extension to capital of the same marginal principle the founding volume found applied to labor. Just as a competitive employer hires workers until the value of the last worker's product equals the wage, so a competitive firm adds capital until the value of the last unit's product equals its cost — and that cost, the return the unit must earn, is the rate of interest. Capital, like labor, is paid its marginal product; and interest is the name of capital's. The rate is thus a technical fact about production: the yield the economy's stock of capital actually throws off at the margin, out there in the machines and structures, owing nothing to anyone's psychology.¹

The appeal of this is considerable, and it is the appeal of objectivity. Where time preference grounds the rate in something internal and contestable — impatience, a weakness of the imagination — the productivity theory grounds it in something external and seemingly measurable: the return on real investment, the fact that a dollar's worth of machinery can produce more than a dollar's worth of output over its life. It fits the businessman's intuition that the rate must, in the end, answer to the real opportunities for productive investment, and it supplies the "opportunity" blade of Fisher's scissors with a concrete edge. The rate, on this view, is simply what the world's capital can earn.²

The trouble is the one the founding volume already met, and it is fatal in the same way. To speak of "the marginal product of capital" one must measure the quantity of capital — and capital, unlike hours of labor, is not a homogeneous thing that can be counted in natural units. It is a heterogeneous heap of machines, buildings, and inventories, addable only by value. And the value of a capital good is the stream of earnings it is expected to yield, discounted to the present — discounted, that is, at the rate of interest. So the quantity of capital depends on the rate, while the rate is supposed to be determined by the marginal product of the quantity of capital. The reasoning closes in a circle. The Cambridge capital controversy made the circle vivid with the phenomenon of reswitching: a single method of production can be the most profitable one at both a low and a high rate of interest, yet not at the rates between, so that there is no orderly, downward-sloping relation between the rate and the quantity of capital employed. The demand curve for capital need not slope down; "more capital" need not mean "a lower return"; and the proposition that the rate equals the marginal product of capital cannot be sustained as a general foundation.³

It is important to say precisely what this does and does not show. It does not show that capital is unproductive — capital is plainly productive, and machines plainly help to make things. What it shows is that "the rate of interest equals the marginal product of capital" cannot be a foundational, technically-given fact, because the quantity whose marginal product is invoked cannot be defined without already knowing the rate. The productivity theory, like its twin for wages, survives as a description of behavior within a given equilibrium — firms do push investment to the point where its return matches the going rate — but it fails as a foundation: it cannot tell us what the rate is, because it presupposes the rate in the very act of measuring the capital whose productivity is supposed to set it.⁴

Two of the great theories of interest, then, turn out to be the two blades of a single pair of scissors — impatience and productivity, Fisher's time preference and Fisher's opportunity — and one of the blades cannot be ground without already possessing the rate. Interest is not simply read off the productivity of capital, because the productivity of capital is not a number that exists prior to, and independent of, the rate. Something else must pin the rate down before the productivity of capital can so much as be reckoned. Keynes's answer — that the rate is pinned not in the world of goods and machines at all, but in the market for money, by the demand to hold it — is the subject of the next plate, and it moves the determination of the rate from the factory to the bank.⁵

The productivity theory promised to find the rate in the machines — an objective fact of technique, the yield the world's capital throws off. The capital controversy showed that the machines cannot tell us the rate without first being valued at the rate, so that the objective theory of interest is, at its foundation, circular. The search for what sets the rate therefore turns, with Keynes, away from the real economy of goods and toward the monetary economy of money and expectation — and there it finds a rate that is not the reward for waiting at all.