Significant carbon reductions imply availability of energy (or energy services) at a much higher cost, defined in the limit by the price of non-carbon energy. Assuming that the original mix was approximately optimal, this will result in a decline in output, because the changed factor mix will be less productive. In addition, there is a reduction in welfare associated with a shift to a less desired composition of products, though of course this will be balanced by the benefits of preventing climate change. Macroeconometric models give the losses in GNP due to a constraint on carbon emissions, but this only measures the decline in production. General equilibrium models often calculate estimates of the Hicksian equivalent variation (the increase in income that would be required to leave consumer welfare unchanged), which is a better measure because it includes the loss in welfare to the consumer from reduced use of energy.
Carbon reductions through intra-fossil fuel substitution (IFFS) and non-fossil fuel substitution (NFFS) do not reduce energy availability directly, but reduce the carbon intensity of the energy used. Indirectly, a shift to these more expensive sources of low carbon or non-carbon energy will reduce total energy use, the magnitude of this depending on the price elasticity of energy demand. Higher price of non-fossil energy technologies implies a drop in production as resources have been diverted into the energy sector and away from producing direct consumption goods.
The total impact on output, or the economic cost, associated with a carbon constraint in optimisation models is measured as the difference in output/welfare in the constrained scenario (with a limit on carbon emissions) and the scenario with no restrictions on carbon emissions. In production function models, the loss is measured in terms of reduced output; in models without an explicit production sector, the output impact can be inferred (Cline 1992). In this case, changes in carbon emission levels and energy consumption, in response to a carbon tax, reflect the opportunity cost of energy. It is therefore possible to integrate across marginal taxes to infer the production cost of the carbon constraint as this cannot exceed the amount of money saved by switching to low carbon technologies (i.e. price of carbon*the amount saved), if consumers and producers are acting rationally, and there are no other production externalities from energy use.
The economic costs of imposing a carbon tax can be overstated if the efficiency gains resulting from the recycling of carbon tax revenue (by replacing the most inefficient taxes on other factors of production) are not considered. The optimal mix of public revenue raising occurs when the welfare gain from increasing carbon taxes, and recycling revenues, equals that from decreasing taxation on any other factor of production/consumption. If the optimal level of energy taxation, not taking into account climate change externalities, is less than the Pigouvian environmental tax (i.e. direct marginal damage cost of CO2), then the optimal tax, including the externality costs, will be below the Pigouvian level. This is because taxing energy involves a loss in income as well as a gain in environmental quality. The tax would only be set at the Pigouvian level if reducing energy use imposed a pure welfare cost, rather than a production externality. These issues are addressed in a few models such as the OECD-GREEN model and the Whalley and Wigle (1991) study.
The lower the substitutability between energy and other factors of production, the more steeply taxes will have to rise in order to stabilise emissions. Even with an elasticity of substitution equal to unity, the tax curve is non-linear, and taxes increase more than proportionately with the target cutback in carbon. If a model uses a discrete backstop technology then, in the long run, all energy will be produced by this technology (heterogeneity of end use, i.e. transport or heating, is usually not modelled for backstop technologies). As a carbon tax increases, the differential between non-carbon and carbon backstop technologies is neutralised and the tax rate settles at the difference in cost between the carbon free backstop and the carbon backstop. Thus availability of backstop technologies breaks down the monotonic relationship between required tax and the target reduction. Essentially the technical divorce between carbon reductions and energy usage produces much smaller economic costs than if there were no backstop technology.
In long run studies (100-200 years) the trend parameters of CO2 and GDP growth, combined with the price and timing of the backstop technology, will completely dominate the results; making the sophistication of the remaining model structure rather redundant in its influence on policy prescriptions.
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