The question of interest is, how do we choose an allocation among all the feasible ones? The key concept to evaluate this choice is the concept of efficiency.

A feasible allocation is Pareto efficient if there does not exist another feasible allocation that could make one individual better off without making anyone else worse off.

As a corollary, this identifies inefficiency as situations where there exist other feasible allocations that can make some individual better off without making anyone worse off. Intuitively, it means that in efficient allocations are undesirable. This motivates the focus of economic analysis on efficient allocations. But how do we know that a particular allocation is efficient (or inefficient)? Making such an evaluation can be difficult empirically.

The Pareto efficiency criterion involves a welfare evaluation of the n individuals affected by the decision-making process for z ^e. This requires measuring the benefits received by the n individuals. Measuring individual benefits can be using a reference bundle of private goods. It will be convenient to choose money as the reference bundle. For our purpose, we identify the m-th private commodity as money . We denote one unit of money by g = (0, 0, 1). And we denote one unit of sure money by g ^e = ( g( e ₁), g( e _s)) = ( g, , g). Although we allow for transaction costs for the first (