1. A consumer has preferences represented by the utility function U(x) E- ,In(x) 'i = 1 where x; denotes the quantity consumed of good i and n> 3. (a) Assuming that the consumer has fixed income y and...

Extracted text: 1. A consumer has preferences represented by the utility function U(x) E- ,In(x) 'i = 1 where x; denotes the quantity consumed of good i and n> 3. (a) Assuming that the consumer has fixed income y and can buy good i at price p; , find the ordinary and compensated demand elasticities for good 1 with respect to p; , j = 1, .. , n. (b) Suppose that the consumer is legally obligated to purchase an amount A, of good n (e.g. heating oil) where p„An < y.="" if="" there="" are="" no="" constraints="" on="" the="" choices="" of="" the="" other="" n-1="" goods,="" then="" find="" the="" ordinary="" and="" compensated="" demand="" elasticities="" for="" good="" 1="" with="" respect="" to="" p;,="" j="1," ...="" ,="" n.="" compare="" your="" answers="" to="" part="" (a)="" above.="" (c)="" now="" suppose="" that="" the="" consumer="" is="" legally="" obligated="" to="" purchase="" an="" amount="" ak="" of="" good="" k="" where="" k="n-r," n="" and="" 0=""><>< n-2="" and="" ep,ak="">< y.="" use="" the="" arguments="" in="" parts="" (a)="" and="" (b)="" %3d="" above="" to="" explain="" what="" will="" happen="" to="" the="" elasticity="" of="" good="" 1="" with="" respect="" to="" p;="" as="" r="" increases="" (i.e.="" as="" the="" number="" of="" constraints="" increases)="" and="" comment="" on="" the="">