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Peak Wealth? Sustainability and Substitutability in a Solvable Growth Model with Irreversible Climate Change

Author: Martin F. Quaas

Date: July 2014

Abstract

The paper develops an analytically solvable growth model in discrete time with stocks of consumable capital, human capital, a non-renewable resource, and irreversibly accumulated greenhouse gases. The model allows for analyzing different elasticities of substitution between reproducible and non-reproducible production factors. I present a full analytical characterization of the transition dynamics for the case of less favorable substitution possibilities, showing that the optimal consumption growth rate is monotonically decreasing over time, and eventually turns negative, i.e. consumption and wealth peak after finite time. The growth rate of the optimal carbon tax is larger than the consumption growth rate and always positive. I further show that results generalize to the case of stochastic capital and resource dynamics.

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