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Unformatted text preview: ws: P = MC where = 1 (without any institutional constraints) 1 (when institutional constraints exist) The theory of Second Best is aptly named because it deals with the welfare analysis of an economy in the presence of unavoidable institutional constraints. The First Best refers to the idealistic scenario in the absence of any institutional constraints (i.e. perfect competition). 275 FIRST BEST Optimal solution to the welfare maximization max. in the absence of institutional constraints. For example, given the PPF equation F (X, Y) = 0 SECOND BEST Optimal solution to the welfare in the presence of institutional constraints. For example, given the PPF equation F (X, Y) = 0 and the institutional constraint P = MC the first best solution solves the welfare maximization problem Maximize U(X, Y) Subject to F (X, Y) = 0 We need only one constraint in the welfare maximization problem, namely, the PPF which represents the structure of the economy. the second best solution solves the welfare maximization problem Maximize U(X, Y) Subject to F (X, Y) = 0 PX = MCX We need two constraints in the welfare max. problem, namely, the PPF which represents the structure of the economy and the added constraint for other institutional features. Note that all added institutional constraints must be fully incorporated into the welfare maximization problem. EXAMPLE For example, consider the following simple welfare maximization problem of a two sector economy with a square root welfare (utility) function: U = XY and a linear production possibility frontier X+Y=1 276 We can compare three potential methods of finding a welfare maximizing solution:  FIRST BEST SOLUTION The first best solution maximizes the welfare function subject to the constraint given by the production possibility frontier Maximize U(X, Y) = XY Subject to X + Y = 1 At the point of maximum welfare (see point 1 in the diagram below), the welfare contour is tangent to the PPF, and hence, MRS = MRT Y=1 X X+Y=1 Solving for the first best solution X= Y= U= Y 1 PPF X 277  SECOND BEST SOLUTION The second best so...
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- Spring '10