Abstract
What is the relationship between Pareto Optimum and Competitive Balance?
Very briefly, the relationship between Pareto optimality and competitive equilibrium is an implication relation: z is a competitive equilibrium => z is Pareto optimal (note that the relation of implication does not apply in both directions).
This result is easy to show, since the condition for a Pareto optimum is only the tangency between the indifference curves of the two individuals (that is to say TMSA = TMSB), while a competitive equilibrium requires in addition, for each individual TMS is equal to the ratio of prices (ie, it must TMSA = TME = TMSB).
The contract curve is the set of points Pareto-optimal (in an Edgeworth box). Two things must be verified to Pareto-optimal point: first, this should be feasible (=> for each property, the sum of the amounts held by each individual = quantity of the good available in the economy). Secondo, the indifference curves of the two individuals must be tangent (=> their TMS must be equal). All this gives several equations that must be satisfied simultaneously for a Pareto-optimal point. The equation of the contract curve is the 'solution' to this system of equations.
