The Neoclassical Model

The "neoclassical" theory of economic growth grew out of a criticism of Roy Harrod's thinking. According to the critics, Harrod had overlooked the principle of diminishing returns. This principle applies just as much to capital as it does to labor, according to the neoclassical view. And this (they said) is what Harrod had missed.

Neoclassical economic theorists stress that the marginal productivity of capital diminishes. That means Harrod's two limits on economic growth are not independent after all. If capital grows faster than the labor force, its marginal productivity will drop, so the profitability of investment will drop, and that will slow down its growth until capital grows no faster than the labor force. This is illustrated by the following figure.

The Neoclassical Model

On the horizontal axis we measure the ratio of invested capital per worker. The invested capital could consist of equipment, machinery, training and technological knowledge, so the more investment per worker, the more output per worker. On the vertical axis we have the interest rate, a measure of the productivity of one more dollar of investment, that is, the "marginal productivity of capital." Because of diminishing returns, the marginal productivity of capital decreases as capital per worker increases. In effect, the neoclassical approach reverses Malthus' approach, treating labor as the fixed input and capital (per worker) as the variable input.

Here is the point: if capital grows faster than labor (the "warranted rate" is greater than the "natural rate") then the ratio of capital to labor increases, so the profitability of investment decreases, and investment slows down. This continues until an equilibrium is reached. In the figure, the horizontal gray line shows the interest rate that agrees with the time preference of the investing public. If the interest rate falls below the time preference rate, then (on the average, anyway) investors would no longer be willing to invest. Once the marginal productivity of capital has dropped down to the rate of time preference, capital per worker will no longer increase. The equilibrium ratio of capital to labor is k.

In equilibrium, the warranted rate of growth and the natural rate of growth are the same -- that is, the capital stock and the labor force grow at the same rate, and labor productivity does not grow at all.