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Unformatted text preview: e consider the following simple example of an economy with and without externalities. Labour is the only factor in the economy consisting of a fixed aggregate endowment of L=8 WITHOUT EXTERNALITIES Given production functions X = 2.5 LX Y = 50 LY WITH EXTERNALITIES Given production functions X = 2.5 LX Y = (50 2.5X) LY Note that in this externality case, the production of good X has a detrimental effect on the production of good Y. To derive the PPF for this simple economy, we substitute the production functions into the factor allocation condition LX + LY = L _X_ + _Y_ = 8 2.5 50 Solving for X and Y, we have Y + 20X = 400 This is a linear equation which means that the PPF is a straight line. To derive the PPF for this economy, we substitute production functions into the factor allocation condition LX + LY = L _X_ + ____Y____ = 8 2.5 (50 2.5X) Solving for X and Y, we have Y + 40X X2 = 400 This is a quadratic equation which means that the PPF is a parabolic curve which we refer to as a non-convex PPF. 267 Y 400 Y 400 X 20 20 X So, how does this non-convex PPF compare to the usual PPF? The key difference is the direction of the curvature as shown below (this will have consequences for our maximization problems).
Y 400 Y 400 Normal PPF Non-convex PPF X 20 20 X A normal PPF does not go below the straight line. Okay. A non-convex PPF does not go above the straight line. So what's wrong with a non-convex PPF? The main issue with a non-convex PPF is that it does not give us a correct solution to the welfare maximization process. For example, when we use the concept of a social welfare function (SWF) to break the indeterminacy of the Pareto optimal solution, a non-convex PPF can produce more than one point of tangency (see the diagrams below). 268 Y 400
SWF Contour Non-convex PPF 20 X or we might get the point of tangency at a minimum instead of a maximum welfare solution! Y 400
Non-convex PPF Minimum Welfare 20
INSTITUTIONAL CONSTRAINTS X We have been considering some sources of economic...
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- Spring '10