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Unformatted text preview: tisfy MRSA = MRSB, so... __YA__ = __YB__ (1-) XA (1-) XB and we want our contract curve coordinates in terms of consumer A so we can convert consumer B's demands into: YB = Y YA XB = X XA 162 So... ___ YA__ = __ Y YA __ (1-) XA (1-) X XA YA__ = __(1-) XA (1-) Let Z = (1-) (1-) YA (X XA) = Z (Y YA ) XA YA X YA XA + Z YA XA = Z Y YA [X (1 Z) XA] = Z Y YA = _____Z Y________ X (1 Z) XA Now the "bow" is either the second derivative of this mess above or we can compare on the main diagonal to estimate the shape of the contract curve. How do we do that? We compare the ______ and the ______ terms. (1 ) (1 ) Suppose that the ______ > ______ then the indifference curve for A is steeper than (1 ) (1 ) the indifference curve for B on the main diagonal, this leads to the slopes being equal below the main diagonal. In the reverse case, the opposite is true. Y YA __ X XA 163 YA XB OB ICA ICB OA YB XA We can draw the utility levels of the contract curve. By definition, the contract curve is a collection of all of the possible Pareto Optimal allocations in the economy. Each point on the contract curve is a Pareto optimal allocation from which we can calculate the corresponding utility levels UA and UB. If we plot these pairs of Pareto optimal utility levels, we have the utility possibility frontier for the economy (UPF).
B UPF UA The difference between the contract curve and the UPF is that while both refer to Pareto optimal allocations, they use different units of measurement. 164  A contract curve yields allocations (XA, XB, YA, YB) in terms of goods.  A UPF yields allocations (UA, UB) in terms of utility levels. HOMEWORK  Draw the Edgeworth Box representations of your homework solutions to the pure exchange questions in Lecture #8.  Find the contract curve and draw it for the following two consumers in a pure exchange economy: UA = XA + YA1/2 Don't forget... Homework #3: How do we know that the Consumption / Leisure choice is, in fact, the one which maximized Robinson's utility? (Use L = 5.4 and L = 5.3 in your higher/lower calculations). SEE PAGE 154 . UB = XB + YB 165 ECON 301 LECTURE #10 PARETO OPTIMAL THEORY P...
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- Spring '10