After a long and productive life, Robert Solow, one of  the heroes of macroeconomics, passed away in December 2023 at the age of 99 years.

Solow can be regarded as the father of modern growth theory because he created the model that has become the workhorse for it and has been used by many subsequent researchers, an achievement for which he was awarded the Nobel Prize in Economics in 1987. Earlier, in the tradition of Karl Marx, Evsey Domar and Roy Harrod had developed a growth model with a fixed capital coefficient that suggested the possibility of generating arbitrarily large growth rates by sufficiently increasing the aggregate rate of savings. Solow was fundamentally more pessimistic. He showed that a higher savings rate would only temporarily lead to a higher growth rate, while in the long run it would simply increase the capital coefficient instead. His model has later been extended to describe optimal economic growth patterns such as the Golden Rule and the Modified Golden Rule, as well for deriving the intertemporal general equilibrium model of a competitive market economy.

While his growth model is positive in nature, Solow also made important contributions to normative intertemporal economics. In his book Linear Programming and Economic Analysis, published jointly with Robert Dorfman and Paul Samuelson in 1958, he developed the notion of intertemporal Pareto optimality, showing that the equalization of marginal value products of capital across all investments would not in general be sufficient to create such optimality, but that, instead, the sum of the marginal value product and the respective capital good’s rate of capital gain (which he called “own rate of interest“) had to be equal across all investment opportunities.

Based on this knowledge, in 1974 Solow published a fundamental marginal condition for Pareto-optimality in the exhaustion of a depletable natural resource, also known as the Solow-Stiglitz efficiency condition. According to that condition, the Pareto optimal depletion strategy requires the growth rate of the marginal value product of the resource – the resource  serving as an input to the production process -  to be equal to the marginal product of capital. This condition is similar to the Hotelling rule known from the positive theory of exhaustible natural resources. If it does not hold, it would be possible to increase the living standard of one generation without reducing that of another by reshuffling the composition of society’s wealth portfolio consisting of natural capital below the ground and man-made capital above it. The Solow-Stiglitz efficiency condition is truly fundamental for economics and has gained tremendous importance in a time of increasingly-felt scarcity of depletable natural resources. 

The condition also has strong implications for finding the best strategy for combatting global warming, as it has been possible to extend it to the case of exploiting carbon fuels that involves the accumulation of oxidized carbon in the atmosphere, in addition to depleting the stock of carbon in the ground. Such extension shows that it would be Pareto improving if the stock of carbon were  exhausted more slowly than what market forces themselves bring about. It does not easily lend itself, however, to postulating a carbon budget or a fixed maximum temperature limit.

Robert Solow not only made great contributions to economics, but also was a Johnny Appleseed who made trees of knowledge sprout on both sides of the Atlantic. He helped build institutions for the dissemination of knowledge and economic exchange such as CESifo in Munich, on whose scientific advisory board he actively and regularly participated for many years. The researchers of the CESifo network as well as those employed in the ifo Institute as well as in CES mourn the loss of a great friend and supporter.

Hans-Werner Sinn

December 2023