Notes

Context of the paper:
There may be two-way linkage between Energy and GNP. Therefore, the effect of energy policy on the economy has to be studied.
Before studying the exact effects, it's better to assess the magnitude of the effects. The paper presents a model (not realistic - certain assumptions) to provide an insight into the impacts energy policy has on the Economy.

In 1970, energy was 4% of GNP. Like Elephant-Rabbit stew. If both grow at same rate, energy will continue at 4%. But if energy prices double, and we have the same input mix (energy-other parameters share is the same), the max additional energy share will be 4%, i.e, energy will represent 8% of economy. However, if other input mixes are considered, the share can be decreased.

For the rabbit-elephant theory to be valid, the value share of the energy has to remain constant. This is possible only when the economy responds smoothly to changes in energy demand (which we think implies that the changes in energy demand are slow). However, if energy demand changes quickly, then the value share is no more constant, and if it becomes sufficiently high, then we must look beyond the rabbit-elephant theory.

SUBSTITUTION:
To get the same output, in future, maybe lesser energy is required because the gap has been substituted with something else (other input like investment to create more efficient machines that use this energy to provide output). This flexibility is another important element like the value share. This gives rise to the concept of "elasticity of substitution", which is a measure of ease of substituting one input with another while having same output, and which is a point of disagreement for economists because the exact value is never agreed upon. It can neither be zero nor infinity (both are absurd). However, if we consider this as 1, even if the relative price of energy increases, its value share remains constant (it can be substituted with the same effort it takes to use extra energy). However, we can't consider constant elasticity.

Elasticity of Substitution is virtually the same as Price Elasticity of Demand. However, it is not easy to find the latter. All empirical studies have defects and therefore, the evidence suggest values of the former in between 0.2 and 0.6 (values beyond this range have no significant effect on the impact on the economy).

For constant price, energy grows the same as economy. And if for some reason, we need to decrease energy consumption, this can be done by a redistributable tax. Other measures (like efficiency) can also be incorporated into this and be called Btu tax. For various elasticities, and for various reductions in energy consumption, they've given us the reduction in GNP and the Btu tax that has to be levied. This GNP and Btu tax vary greatly for different values of elasticity (0.2 to 0.6). Some studies show values beyond this too. Any future improved analysis must carefully determine this value and the effectiveness of studies is based on how they characterize this value.

If we assume instead of constant input mix, the change of capital to maintain constant rate of return (??? WTF ???), the GNP decreases further but the Btu tax is lower. The economic impact is either implicitly or explicitly linked to elasticity.