A strong implication of our main results is that future economic growth depends either on continued declines in the cost of primary exergy or on an accelerated increase in the output of useful work from a decreasing exergy input, that is, increasing exergy-to-work conversion efficiency. Energy prices have increased significantly in the last few years and are almost certain to increase further, both because of increased demand and because of the need to cut greenhouse gas emissions. If the rate of technological progress in conversion efficiency slows down, we believe that economic growth will necessarily slow down as well. Hence it can no longer be assumed, without question or doubt, that growth along the 'trend' will continue indefinitely and that 'our children and grandchildren will be much richer than we are' as some economists have asserted. Though not discussed here, it is clear that policies that can deliver a 'double dividend'

in the sense of decreasing carbon-based fuel consumption and greenhouse gas emissions, while simultaneously cutting costs, must be sought more intensively than ever before.

There is an obvious case for interpreting our model results as a reflection of the real situation. They are consistent with the observed effect of energy (oil) price spikes on economic growth. They are also consistent with the fact that big firms frequently find ways to cut large numbers of jobs to increase profits without cutting output. Typically, such a move is welcomed by the stock market. The implication is that the real economy has been distorted in a number of ways to create or preserve unnecessary and unproductive 'paper shuffling' jobs. The fact that redundant employees usually find other work, sooner or later, is a fortunate consequence of economic growth.

On the other hand, there is also a case for regarding our results as an artifact of the model. The use of a production function of capital, labor and useful work implies that these factors are perfectly substitutable, which is clearly not the case, except in the very long run, as we have noted repeatedly. It is true that consumers can be flexible about their use of auto transportation, heating, air-conditioning and so on. Similarly, workers using hand tools can replace power tools and machines in some applications, especially construction and local goods transportation. But invested capital in most industrial sectors is not flexible, either in regard to labor requirements or exergy requirements. While new investment (for example, in systems optimization) can reduce the need for both labor and useful work per unit of output, this happens only in the intermediate or long run.

Hence labor and capital are not truly substitutes, except at the margin. Workers in the existing economy require power tools, machines and places to work. The relationship between useful work and capital is ambiguous. The two factors are evidently complementary, at least in the short run. Machines require energy (useful work) inputs to perform their functions. This fact, together with the complementarity of labor and capital, also in the short run, casts doubt on the appropriateness of a production function that implies perfect substitutability, as does the Cobb-Douglas function.

The LINEX function also implies substitutability between factors, to be sure. But it implies substitutability between ratios of the factors (in the exponent) while it also allows for some degree of complementarity insofar as both numerator and denominator can increase or decrease together. In mathematical terms, factor substitutability should be near zero for large values of either variable but should be finite, and maximum, near the optimal combination, that is, as the function approaches the limiting case, which is the Leontief (zero substitution) production function (for example,

Diewart 1974). However, we confess that it is not yet clear whether the cost-share proof in Appendix A applies to a function of ratios.

If we had used a Cobb-Douglas model with no third factor, the calculated elasticity of labor would be automatically equal to the cost share, subject to all the other assumptions needed for the proof in Appendix A. Of course, in the Cobb-Douglas model, output elasticity is a constant. It is a generally accepted 'stylized fact' of economics that the capital-labor ratio remains constant, or nearly so, over time. Similarly, the ratio of the capital and labor shares of payments in the national accounts tends to remain rather constant over time. Our model results should be consistent with these stylized facts. We can only say that consistency is possible, but not guaranteed, by the results obtained up to now.

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