By Geoffrey Alexander Jehle Philip J. Reny
This rigorous, up to date textual content on smooth microeconomic idea offers the entire middle arithmetic, neoclassical thought, video game thought, and knowledge economics had to entry the trendy specialist literature. complicated conception is patiently and punctiliously constructed, then essentially defined and illustrated simply because even well-prepared scholars make the most of extra math aid. cautious motives, effective theorem-proof association, and plenty of examples and workouts make this a uniquely powerful textual content for complex classes. scholars will relish the transparent writing and available type.
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Extra info for Advanced Microeconomic Theory
X U. 3. asins and unbounded above in u. 4. asing in p. 5. Homogeruous ofdegru 1 in p. 6. Concave in p. If, itt addition. 11(·) is strictly quasiconcave, we have 7. SMphard's lemma; e(p. ttliablt in p al (p0 , u0) with p0 » 0, ae(JJO • 110) ap, h(pO = x, 0) · " . and i = I, . . · "· Proof: To prove property I, noee that the lowest value in U is u(O) because u( · ) is strictly in creasing on IR!. Consequently, e(p. u(O)) = 0 because x = 0 attains utility u(O) and requires an expenditure of p · 0 = 0.
P�. u) and x�(p: , p¥. u). As before, if we fix price p� and we plot the own-price of good 1 in Pig. 1 . 1 6(b) against the corresponding hypothetical quantities of good I the consumer would "buy" if constrained to utility level u, we would trace out a ''demand· curve-like" locus as depicted. This construction is the Hicksian demand curve for good 1 , given utility level u . � for different levels of utility-for different indifference curves. The shape and position of each of them, however, will always be determined by the underlying preferences.
By the relative price of some good. we mean the number of urtits of some other good that must be forgone to acquire I unit of lhe good in question. If p1 is the money price of good i, it wiU be measured in units of dollars per unit of good i. The money price of good j will have units of dollars per unit of good j . The relative price of good i in terms of good j measures lhe units of good j forgone per unit of good i acquired. This will be given by tbe price ratio pd Pi because p; Pi = Sjunit j = unit i $junit i units of j S- = uuit of i · unit j S · - By rul IDcome, we mean the muimum number of units of some commodity the consumer could acquire if he spent �is entire money income.
Advanced Microeconomic Theory by Geoffrey Alexander Jehle Philip J. Reny