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Unformatted text preview: MRSA = (YA + ) XA and then calculating the marginal rate of substitution for person B MRSB = YB XB Along the contract curve, we have the following Pareto optimal conditions: MRSA = MRSB XA + XB = 1 YA +YB = 1 Applying these conditions to the specific problem at hand (YA + ) = YB XA XB (YA + ) = 1 YA 1 XA XA And we get the following contract curve (convince yourself that this is correct!): YA = 5 XA 4 which is a straight line passing through the horizontal intercept (1/5, 0) instead of the point of origin for person A (convince yourself that this is correct!). 264 YA XB OB Contract Curve OA 1/5 Y B XA What might the Walrasian General Equilibrium solution look like? The following analysis shows the general equilibrium solution for this simple economy where externalities are not corrected for by any form of taxes on the polluter (person B, in this case) or subsidies to the victim (person A, in this case). VICTIM Utility Maximization Max XAYA XB subject to PX XA + PY YA = MA with XB being taken as given. At consumer equilibrium, we have the following conditions (ignoring the externality): YA = PX XA PY PX XA + PY YA = MA Solving these two equations, we have the following consumer demand functions for the victim: 265 At consumer equilibrium, we have the following conditions: YB = PX XB PY PX XB + PY YB = MB Solving these two equations, we get the following consumer demand functions for the polluter: POLLUTER Utility Maximization Max XBYB subject to PX XB + PY YB = MB XA = M A 2PX YA = M A 2PY XB = MB 2PX YB = MB 2PY At the market equilibrium for both goods, we have the following equations: XA + XB = X YA + YB = Y which can be solved for equilibrium prices and quantities PX = PY = 1 XA = XB = YA = YB = YA XB OB General Equilibrium Solution (no externality) Contract curve (with externality) OA 1/5 Y B XA The diagram shows that the uncorrected general equilibrium solution XA = XB = YA = YB = is not on the contract curve derived when accounting for the negative externality. That is, in the presence of externalities, the uncorrected general equilibrium solution is no longer on the contract curve of Pareto Optimal allocations. In other 266 words, there is no relationship between the two inter-twined concepts of Pareto optimality and general equilibrium: in the presence of externalities, the first fundamental theorem of welfare economics breaks down! How do externalities affect the production side? To examine the effects of externalities on the production side, w...
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- Spring '10