Question

Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain. 3) Graph the income consumption curve for good 2 as a function of income for given prices > 1. Verify Roy's identity 4) Find the consumer's indirect utility function when P2

Answer 1

0 4(x,x) = lnt, tų ( income Now at eg MRs 62 = Pile2 - MRS = Mu, Muz=% So at equt x = P, / P2 => Pq = P, XP, | X= P/P) . Ang From . B.C -> Pixtp x2= I DƏ :. : *2=T-PI (B/) *2 = (I-pe) P2 = 1/82-1 with-2); .5/>1 80, demeand fine? 4 4 is winchepoudant 4 cilave devel, which simplies that i is a nececely. Yes Both Goods are nišimal was dixitaiso. No, Dantes are not homethetics, Bwx für Homotholicitay , the IC cu radial .expusion of each other along a soy About the high Pout here for quasi lemeid sef, (Refrances), le are radial expansion - along a ray through the digin Pout here for quai linear Pref, (Preferences) inc. are radial expansion along either horisontal & vertical line te

2, now I/P2 <1, then X2 X=0 & x* = I/P, . A entire income is spent on good it only , Conor 80 ln exert 8, 9 ce for Good 2 till Ick, then *z*=0, - after I k, then xq î linealy with income an i | 4, u(x - x) = a . . +, -1 số Ray isilly se lepas seme ce (alpi) x ² 20/8e,= (10) Penge = 20/25 = YP2 -> ICC. *, --24/2. Income CP2 PAVA dular then. -20/21, +P₂. R. b. roved 2010I RC

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