A paper shows that the failure to describe modern economies adequately is not due to the introduction of calculus into economic theory by the so-called ‘marginal revolution’ during the second half of the 19th century, when the mathematical formalism of physics decisively influenced economic theory. Rather, the culprit is the disregard of the first two laws of thermodynamics and of technological constraints in the theory of production and growth of industrial economies.
Energy is ten times more important than its cost
If one foregoes cost-share weighting and determines the output elasticities of capital, labor, energy, and creativity econometrically, one gets for energy economic weights that exceed energyʼs cost share by up to an order of magnitude, and the Solow residual disappears. The production factor energy accounts for most, and creativity for the rest of the growth that neoclassical economics attributes to ‘technological progress’.
According to the cost-share theorem, reductions of energy inputs by up to 7%, observed during the first energy crisis 1973–1975, could have only caused output reductions of 0.35%, whereas the observed reductions of output in industrial economies were up to an order of magnitude larger. Thus, from this perspective the recessions of the energy crises are hard to understand. In addition, cost-share weighting of production factors has the problem of the Solow residual. The Solow residual accounts for that part of output growth that cannot be explained by the input growth rates weighted by the factor cost shares. It amounts to more than 50% of total growth in many countries. Standard neoclassical economics attributes the discrepancy between empirical and theoretical growth to what is being called ‘technological progress’ or, sometimes, ‘Manna from Heaven.’ The dominating role of technological progress ‘has lead to a criticism of the neoclassical model: it is a theory of growth that leaves the main factor in economic growth unexplained’, as the founder of neoclassical growth theory, Robert A Solow, stated himself.
Growth in Germany, Japan, and the USA
The reproduction of economic growth in Germany, Japan, and the USA during the second half of the 20th century. Their left parts exhibit the empirical growth (squares) and the theoretical growth (circles) of the dimensionless output , and the right parts present the empirical time series of the dimensionless factors capital , labor , and energy . The base year t0 is 1960 for Germany and the USA, and 1965 for Japan. Note the variations of inputs and outputs in conjunction with the oil price explosions. The price of a barrel of crude oil in inflation-corrected was driven by the OPEC boycott in response to the Yom-Kippur war from 15$ in 1973 to 53$ in 1975, and by the war between Iraq and Iran from 48$ in 1979 to 100$ in 1981. Then the oil price plummeted to 30$ in 1986 (with dramatic consequences for the Soviet Union). Between 1997 and 2011 it has risen again, from 18$ to 110$.
(Left) Economic growth and (right) contributions of the three main production factors to economic growth in Germany in the late 20th century. Credit: R. Kümmel. The Second Law of Economics: Energy, Entropy, and the Origins of Wealth. Growth in the total economy of the Federal Republic of Germany (FRG) between the years 1960 and 2000. The five coefficients, shown below the output graph, model the time dependence of the LinEx–function parameters a and c. They reproduce the drastic structural break at German reunification in 1990.
Growth in the total US economy between 1960 and 1996.
Summary and outlook
Energy-dependent production functions, with output elasticities that are for energy much larger and for labor much smaller than the cost shares of these factors, reproduce economic growth in Germany, Japan, and the USA with small residuals and good statistical quality measures—even during the downturns and upswings in the wake of the first and the second oil-price explosion. This does not contradict the usual behavioral assumptions that entrepreneurs maximize profit or that society maximizes overall welfare, because real-world economic actors are aware of the technological and the related ‘virtually binding’ constraints on the combinations of capital, labor, and energy. ‘Soft’ constraints from legal and social obligations may also matter. The barriers from the constraints on capacity utilization and automation prevent modern industrial economies from reaching the neoclassical optimum of mainstream economics, where output elasticities would be equal to factor cost shares.
Since in industrially advanced countries cheap energy is economically much more powerful than expensive labor, there has been the long-time trend toward increasing automation, which replaces expensive labor by cheap energy-capital combinations. In the G7 countries, this trend has drastically reduced the number of people employed in the sectors agriculture and industries during the last four decades, and the contribution of these sectors to GDP as well. Now, in the service sector, electricity-powered computers with appropriate software kill more and more jobs, too. The resulting danger of unemployment in the less qualified part of the labor force is enhanced by the trend toward globalization, where goods and services produced in low-wage countries can be delivered at small cost to high-wage countries thanks to cheap energy and increasingly sophisticated, highly computerized transportation systems.
The nearly unanimous social and political response to this danger is the call for strategies to stimulate economic growth. But these strategies face obstacles from entropy production, which is coupled to energy conversion and its pivotal role in economic growth:
(1) there are thermodynamic limits to the improvement of energy efficiency at unchanged energy services, because entropy production destroys exergy;
(2) emissions associated with entropy production, especially the ones of carbon dioxide from the combustion of fossil fuels, threaten climate stability.
The question is, whether society will be willing and able to finance the huge investments that are necessary for the transition to a highly efficient production system powered by non-fossil fuels.