Bond guru Bill Gross created a firestorm when he recently asserted the “cult of equity is dying.” In the August 2012 PIMCO Investment Outlook, Gross observed that since 1912 stocks have earned an average annual real rate of return of 6.6 percent. According to Gross, this rate of return cannot be maintained in an economy whose growth rate in real GDP averages only 3.5 percent. Gross argues that if the historical trend were to continue another 100 years, it would result in stockholders owning “nearly all of the money in the world!”

On CNBC Wharton Professor Jeremy Siegel disputed the conclusion reached by Gross, arguing that the mistake Gross made was in equating “return” with “growth.” Siegel pointed out that a stock’s return in part comes from dividends, and it is entirely possible for stocks to grow with GDP at a low rate of 3.5 percent while, because of dividends, the total return to stocks is higher.

Who is correct? In a way they both are. As explained in the framework of Robert Solow’s neoclassical growth model, a stable equilibrium occurs when the growth rate in capital is equal to the growth rate in real GDP. There are an infinite number of stable equilibriums, each associated with a different saving rate. If the saving rate is low, then the economy’s equilibrium capital-to-labor ratio will be low. A high saving rate corresponds to a high equilibrium capital-to-labor ratio.

As revealed by the Solow model, in general Siegel’s analysis is correct. The return to capital, which is capital’s marginal product, does not have to be equal to the overall growth rate in the economy. A low savings rate results in a low capital-to-labor ratio, and thus capital’s marginal product—which is the return to capital—can be very high. Most importantly, the high return to capital can be an equilibrium outcome that lasts into perpetuity. The high returns are simply a consequence of scarcity.

Neurosurgeons have also historically experienced a return far exceeding that of the average of all other occupations. They likely enjoy a rate of return to their human capital investment that far exceeds the average growth rate of the economy. Why do they not end up owning the entire economy? Simply because there aren’t very many of these fortunate individuals.

However, Gross was not entirely off the mark. There is an optimal equilibrium occurring in the Solow model, where the amount of capital is “just right” in the sense that per-capita consumption is maximized. This equilibrium is referred to as the “golden rule path.” When an economy reaches the “golden rule” equilibrium, the rate of return to capital is EXACTLY equal to the economy’s growth rate in real GDP.

Stock return data from the past 100 years suggest capital has been relatively scarce, and the golden-rule path has not been reached. Going forward, should the economy accumulate sufficient capital to attain the golden-rule path, we will then have reached the point where Gross’ expectation of real returns to capital averaging 3.5 percent per year will be realized.