Exact Analytical Solutions of Selected Behaviourist Economic Growth Models with Exogenous Climate Damages - Kovalevsky, Dmitry V. (Discontinuity, Nonlinearity, and Complexity, 2026)
Capital dynamics are calculated for (i) the AK model with output reduced by climate damages, (ii) the AK model with climate-dependent depreciation rate, and (iii) the Solow–Swan model with output given either by the Cobb–Douglas production function or by the constant elasticity of substitution (CES) production function and reduced by climate damages. The climate projections used as model inputs are exogenous. Simple analytical parametrisations for temperature dynamics are assumed (either linear or exponential temperature growth). The quadratic and the Nordhaus climate damage functions are considered. Exact analytical solutions for capital dynamics are derived in closed form (with the exception of the Solow–Swan model with CES production function). Numerical examples are provided for illustrative purposes. As the unabated climate change with unlimited temperature growth is assumed, the long-runmodel dynamics are dramatic: the capital converges to zero at infinite time, and the economy collapses.