Pareto Optimality and Social Optimum
In the previous chapter, we showed, as Proposition 2, that the market equilibrium obtained under the uniform carbon tax scheme is a social optimum in the sense that a set of positive weights exists for the utilities of individual countries (α1., …, α n.), [αν > 0] such that the world utility
is maximized among all feasible patterns of allocation (c1, …, c n., x1., …, xn., a1., …, an., a).
The converse of this proposition does not hold. The pattern of allocation at a social optimum exhibits all the conditions necessary for market equilibrium under the universal carbon tax scheme except for the balance-of-payments conditions. One of the primary functions of the institutions of markets for tradable emission permits is the arrangement of the initial allotment of tradable emission permits among individual countries so that the balance-of-payments conditions are satisfied at the social optimum corresponding to the uniform carbon tax regime.
The new era of economic thinking was ushered in by Arrow and Debreu (1954), and many contributions since have been made concerning the existence and stability of general equilibrium systems involving both private and public goods. They are all noted for the precision and