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Unformatted text preview: welfare change in CV by moving from E1 to E2. This is, however, a contradiction since both E1 and E2 are on the same contract curve and, as such, are both Pareto Optimal equilibrium points (i.e. no potential Pareto improvement exists). So Boadway's Paradox shows us that there are no potential Pareto improvements in moving from E1 to E2 and yet, we found a net aggregate welfare effect where CVsum < 0. The lesson is that aggregate welfare calculations could be misleading if we are not careful about possible (re)distributional issues. Okay. Let's take an example...Consider a simple exchange economy with two goods with unit aggregate endowments X=Y=1 Consumer A has a square root utility function while Consumer B has a CobbDouglas utility function with = 2/3 and = 1/3. MRSA = YA XA MRSB = 2YB XB Without any loss of generality, we choose good Y as the numeraire so that PY = 1.  We first construct the contract curve from the Pareto Optimal conditions MRSA = MRSB XA + XB = X YA + YB = Y Applying these general equations to the specific problem at hand YA = 2YB XB XA XA + XB = 1 YA + YB = 1 217 Solving for the contract curve, we get YA = 2XA 1 + XA  Now we can select two points E1 and E2 on the same contract curve (defined above). Suppose that we choose E1 at XA = 0.25 and E2 at XA = 0.50. Substitute these values into the equation of the contract curve and we get... XA = 0.25 XA = 0.50 YA = 0.40 YA = 2/3 (at point E1) (at point E2) From these values, we can calculate various variables such as MRS, PX, incomes and utility levels that are needed for the welfare calculations. The results of the calculations are: Consumer A XA YA MRSA PX PY (numeraire) MA UA CVA Consumer B XB YB MRSB PX PY (numeraire) MB UB CVB Point E1 0.25 0.40 1.60 1.60 1.00 0.80 0.316228 Point E1 0.75 0.60 1.60 1.60 1.00 1.80 0.696238 Point E2 0.50 0.666667 1.333333 1.333333 1.00 1.333333 0.577350 -0.603037 Point E2 0.50 0.333333 1.333333 1.333333 1.00 1.00 0.436790 0.593988 218 The calculation shows that A gains and B loses during...
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- Spring '10