Economic growth, the social cost of carbon: additive versus multiplicative damages

In a calibrated integrated assessment model of Ramsey growth and climate change in the global economy we investigate the differential impact of additive and multiplicative global warming damages for both a socially optimal and business-as-usual scenario. Fossil fuel is available at a cost which rises as reserves diminish and a carbon-free backstop is supplied at decreasing cost. If damages are not proportional to aggregate production and the economy is along a development path, the optimal carbon tax is smaller than with multiplicative damages. The economy switches later from fossil fuel to the carbon-free backstop and leaves less fossil fuel in situ. By adjusting climate policy in this way there is very little difference on the paths for global consumption, output and capital, and thus very little difference for social welfare despite the higher temperatures. For all specifications the optimal carbon tax is not a fixed proportion of world GDP but must follow a hump shape.