The Economics of Greenhouse Effect: Dynamic General Equilibrium Approach

This paper uses a primitive general equilibrium (GE) model to examine variation in carbon dioxide (CO2) produced by human activity. This model consists of two goods; food and energy. Food is produced using labor and energy, while energy is produced using labor. It is assumed that food output decreases as CO2 increases. The representative household has a utility function with food and energy as variables. The household maximizes utility given an income constraint. If production and utility functions are specified by Cobb-Douglas type, it is easy to compute a short-run GE, given CO2 and population. The energy, produced and consumed in this short-run GE enhances CO2, while CO2 itself decreases in the long run by the sequestration of carbon in wood and the sea. The long-run variation of CO2 is expressed by a differential equation. First, it is assumed that population is constant. Increases of CO2 are a linear function of produced short-run energy, and decreases are constant. The long-run process has either stability in which CO2 converges to zero, or instability in which CO2 expands to infinity. In the case of instability, the policy of taxing energy is effective in the sense that the policy can prevent the divergence. Second, it is assumed that population increases at the fixed rate. Increases of CO2 are an increasing function of produced short-run energy. Decreases are an increasing function of CO2. A variety of simulations are conducted, some of which show the stability of CO2. Finally, following T.R.Malthus it is assumed that population growth decreases as food output decreases, and vice versa. Simulation shows that the model has the final day in which population decreases to zero, while CO2 does not necessarily diverge to infinity. The tax on energy is shown to be effective, in the sense that the final day can be somewhat postponed.