By Geoffrey Alexander Jehle Philip J. Reny
This rigorous, up to date textual content on smooth microeconomic idea offers all the middle arithmetic, neoclassical thought, online game concept, and data economics had to entry the fashionable expert literature. complicated thought is patiently and thoroughly built, then essentially defined and illustrated simply because even well-prepared scholars make the most of extra math support. cautious factors, effective theorem-proof association, and lots of examples and routines make this a uniquely potent textual content for complex classes. scholars will take pleasure in the transparent writing and available variety.
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Extra info for Advanced Microeconomic Theory
1. 19) CHAPTER 1 42 Equations ( 1 . 18) and ( 1 . 19) illustrate again lhe close relationship between utility the same coin. Malhematically, both the indirect utility function and the ellpenditure function are simply lhe appropriately chosen invenu of each olhe:r. maximization and expenditure minimization. A We can illustrate these procedures by drawing on findings from lhe previous examples. 2, we found that tbe CES direct utility function gives the indirect utility function, II (p, y) = y (P,I + Pi' )- "' (E.
X R •. By ( 1 . 16), t( p, 11(p, y)) S. y. We'd like to sbow in fact thatequality must bold. So suppose not, that is, suppose e(p, u) < y, where u = 11(p, y). Note that by definition of u(· ), u e U, so that w < ii. 7, we may therefore cboose t > O small enough so that u + t
R+ -+ R defined as follows: v(p, y) = xEr. t . p . X :S y. ( 1 . 1 2) The fu ncti on u(p, y) is called the lndlred utility function. It is the maximum-value function correspondi ng to the consumer's uti lity maximization problem. When u(x) is continuous, v(p, y) is well-defined f01r all p » 0 and y � 0 because a solution to the maxi· mizalion problem ( 1 . 1 2) is guaranteed to exist. If, in addition, u(x) is strictly quasiconcave, then the sol11tion is unique and we write it as x(p. y), the consumer's demand function .
Advanced Microeconomic Theory by Geoffrey Alexander Jehle Philip J. Reny
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