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Unformatted text preview: lution incorporates all institutional constraints directly in the welfare maximization problem. It thus maximizes the welfare function subject to the constraint given by the PPF plus the additional institutional constraint. Maximize U(X, Y) = XY Subject to X + Y = 1 Y=X At the point of maximum welfare (see point 2 in the diagram below), the welfare contour must intersect both the PPF and the institutional constraint line X+Y=1 Y=X Solving for the second best solution X = 2/3 = 0.66667 Y = 1/3 = 0.33333 U = 2/3 = 0.4714
Y 1/3 1 2 Constraint PPF 2/3 X It is clear that the second best solution results in a lower welfare level (U = 0.47) compared to the first best solution (U = 0.5). In the diagram, point 2 (the second best solution) is on a lower social welfare contour than point 1 (the first best solution). 278  PIECEMEAL SOLUTION In addition to the first best and second best solutions, let's consider what is often called the "piecemeal" solution (see point 3 in the diagram below). This applies the institutional constraint to the first best solution. This approach is half-hearted since it attempts to satisfy the institutional constraint without incorporating it into the welfare maximization problem (as in the second best solution). Taking the first best solution for X X= and satisfying the institutional constrant Y=X gives us the "piecemeal" solution (which is somewhat ridiculous, don't you think?) X= Y= U = 1/8 = 0.3536
Y PPF 1/3 1 2 Constraint 3 X 2/3 The diagram shows that the "piecemeal" solution results in the lowest welfare level (U = 0.35) compared to the second best solution (U = 0.47) and compared to the first best solution (U = 0.5). So, the message that the theory of Second Best is trying to deliver is that with the presence of institutional constraints it may not be possible to satisfy the Pareto efficiency conditions in practice. The theory of Second Best has an important policy implication, that is 279 If the full set of Pareto optimality conditions cannot be satisfied, then any subset of these Pareto optimality conditions will not do an...
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- Spring '10