Dynamic Capital Interactions, Externalities and Trade

The motivation for this paper is to introduce trade in a dynamic model with capital interactions and to evaluate the consequences of trading on capital accumulation and market clearing prices. We consider a dynamic two-country, two-commodity model in which each country specializes in the production of one commodity and trades with the other country to consume both. The amount of capital used for production in one country generates externalities in the production of the good in the other country. This is one element of interdependence between nations. Another source of interdependence comes from the market clearing prices, since the equilibrium price depends upon supply decisions while consumption decisions are affected by these prices. We have a dynamic duopoly model to capture the strategic dynamic interaction between the countries. We work with a linear-logarithmic example and find a closed loop Cournot-Nash equilibrium. We derive the equilibrium evolution of stocks and prices over time and show that the noncooperative equilibrium is efficient either when there is no production externality or when the marginal rate of substitution between the commodities is same within the country and for the world economy. We also compare our result to the equilibrium that occurs each country, in autarky, produces both goods for its own consumption. We show that both countries are strictly worse off in the latter case.