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Unformatted text preview: the PPF from equation (5).
Private Good Y PPF F (X, Y) = 0 Public Good X  Then we draw an indifference curve for consumer A which corresponds to the given utility level A as in equation (2).
Private Good Y ICA = A PPF Public Good X 240  Since good X is a public good, the amount of the good X produced by the PPF must be the same as the amount consumed by EACH person... XA = XB = X On the other hand, since good Y is a private good, the amount of good Y produced by the PPF must be allocated BETWEEN both consumers... YA + YB = Y For each level of good X on the horizontal axis, the total amount of good Y produced must first be allocated to YA required by consumer A so that his welfare level is unchanged (as required by the constraint). Whatever amount of good Y is left over is then allocated to person B. YB = Y YA In other words, the vertical difference between the PPF and the indifference curve of A represents all the options available to B in order to maintain the same welfare level for person A. [Options Available to B Without Hurting A] = PPF ICA Private Good Y ICA = A
Options Available to B PPF Public Good X  With the choice set of all options available to B (without hurting A) being fully described, the remaining task is to pick the point on that option curve which corresponds to the highest indifference curve for B. This amounts to choosing the highest indifference curve ICB which is tangent to the option curve (point S in the diagram below). 241 Private Good Y S ICB PPF ICA = A Public Good X  At point S of the optimal solution to the constrained welfare maximization problem, the curve of options available to B must be tangent to the indifference curve of B. In other words, these two curves must have the same slope at the point of tangency, point S. [Slope of Options Curve for B] = [Slope of PPF] MRT So... MRSA + MRSB = MRT [Slope of ICA] MRSA = = [Slope of ICB] [Slope of ICB] MRSB So, we can see the difference between Samuelson's theory and the regular Pareto optimal allocation rules... Recall that the usual Pareto optimal allocation rules equate all individual marginal rates of substitution with the common margina...
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- Spring '10