Advanced Microeconomic Theory by Geoffrey Alexander Jehle Philip J. Reny

By Geoffrey Alexander Jehle Philip J. Reny

This rigorous, up to date textual content on sleek microeconomic thought provides the entire center arithmetic, neoclassical concept, video game idea, and knowledge economics had to entry the trendy expert literature. complicated idea is patiently and thoroughly built, then sincerely defined and illustrated simply because even well-prepared scholars reap the benefits of extra math aid. cautious motives, effective theorem-proof association, and lots of examples and routines make this a uniquely powerful textual content for complicated classes. scholars will delight in the transparent writing and obtainable kind.

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11(p, y)). 2. x�(p, u) = x1{p, t(p. w)). ian demand at prices p and income y is equal to the Hiclcsian demand at prices p and the utility level that is the maximum that achieved at prices p and income y. haUiao demand at those prices and an income level equal to the mini mum expenditure necess uy at those prices to achieve that utility can be level. 9 says that solutions to ( 1 . 14), and vice versa. More precisely, if x" solves ( 1 . 1 2) at (p, y), the theorem says that x• solves (1. 14) at (p, w), where u = u(ll").

L)e(p2, u) :<0 t(p', u ) as we intended to show. C(x•, A •) aPI • � = XI ;;: xl (p, u), as required. Because x�(p. u ) ::: 0. this also proves propeny 4. 36 for a proof of 7 that does not require any additional assumptions. ; p < I. We want to derive the corresponding expenditure func­ tion in this case. Because preferences are monotonic, we can formulate tbe expenditure minimization problem ( 1 . t. u - (x1p + x2p) l/p = 0, and its lagrangian, (E. oods, th e first-order conditions for a minimum CONSUMER THEORY 39 subject to lhe constraint ensure lhat the solution values ar.

Y ) is quasiconvell i n (p, y). It will suffice. then, to show that our supposi tion on the budget sets is correct. We want lo show that if x e B', then x e 81 or x e 81 for ali t e (0. 1 ]. If we choose ei ther extreme value for 1. 8' coincides with either 81 or 81 , so the relations hold trivially. II remains to sbow that they hold for ali i e (0, I). Suppose it were not true. Then we could find some 1 e (0, I ) and some x ·e 8' such that x j! 8 1 and x

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