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Unformatted text preview: x 2 and less x 1 . Technical aside. Many students tried to use the rst order conditions MRS = p 1 p 2 to nd the optimal bundle. What they failed to realize was that the preferences were not convex. To nd the original optimal bundle, we integrate over the marginal utilities of both goods, separately. U ( x 1 ,x 2 ) = Z MU 1 dx 1 = Z 2 x 1 dx 1 = x 2 1 + c 1 U ( x 1 ,x 2 ) = Z MU 2 dx 2 = Z 3 x 2 dx 2 = 3 2 x 2 2 + c 2 So, we conclude that: U ( x 1 ,x 2 ) = x 2 1 + 3 2 x 2 2 + c Where c , c 1 , c 2 are arbitrary constants. The indierence curves of this utility function are elliptical, centered around the origin. It is clear then that preferences are not convex, so the rst order conditions MRS = p 1 p 2 cannot be used. (Nonconvex preferences imply that points of tangencies are local minima, not maxima.) 2...
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This note was uploaded on 01/22/2009 for the course ECON 100A taught by Professor Staff during the Fall '08 term at UCSD.
 Fall '08
 staff
 Microeconomics

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