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Structural change in a two-sector model of the climate and the economy

Gustav Engström. 2012.


This paper introduces issues concerning substitution possibilities among goods into a two-sector macroeconomic growth model where emissions from fossil fuels give rise to a climate externality. Substitution possibilities are modeled using a constant elasticity of substitution (CES) production function where the intermediate inputs differ only in their technologies and the way they are affected by the climate externality. By solving the social planners problem and characterizing the competitive equilibrium I am able to derive a simple formula for optimal taxes and resource allocation over time. The impact of different assumptions regarding the elasticity of substitution on taxes turns out to be a simple function of the size or relative magnitude of the distribution parameter of the CES function, technology and the impact of the climate externality. In particular, it is shown that a higher (lower) elasticity of substitution will result in a higher (lower) optimal unit tax rate if and only if the distribution parameter of the most productive sector, multiplied by its total factor productivity and climate damage function, is smaller (larger) than the corresponding term of the other sector. I also present some numerical simulations for a calibrated model based on the U.S. and Indian economy. The results show that the assumptions regarding substitution possibilities plays a much bigger role for optimal fossil fuel consumption in the agriculturally intense Indian economy.

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