The Greenhouse Effect and Carbon Accumulation Dynamics: A General Equilibrium Simulation

A dynamic process on carbon dioxide in the atmosphere, Y, is constructed under the general equilibrium framework to examine the property of stationary points of the dynamic process. In this primitive economic model there are two production sectors: agriculture sector and energy sector; and one (aggregate) household. Y is externality on food production of agriculture sector. At each time, production and consumption are conducted with Y given. The dynamic system of Y is subject to two countervailing factors. One is Y-raising (negative) factor through the production and consumption of energy by three economic agents at each time. The other is a set of Y-reducing (positive) factors through the photosynthetic function of the trees and farm outputs and the repository working of the sea at each time. The externality function of Y on the food production, E(Y), is single-peaked, such as the normal distribution function. The simulation on the dynamic process shows, first, that the stationary points of the process: Y*; consist of at most 3 points, depending on the positive factor coefficient, which indicates the effect of the photosynthesis on the reduction of Y. Second, it shows that there is at least one discontinuous point of the coefficient, whose small deviation creates discontinuous movement of Y*. It confirms that the environmental tax on the consumption of energy to reduce Y* might be harmful to the household, depending on the derivative of E(Y) at Y*: when Y is external economy to food production. Finally, the optimum rate of tax is derived.