Question

Consider the consumption of a consumer in two different dates, time 0 andt. Sup-pose that at timetprice vector ispt= (pt1,pt2) and the consumption bundle isxt= (xt1,xt2). Attime 0 the price vector and the consumption bundle arep0= (p01,p02),x0= (x01,x02), respectively.ThePaasche quantity indexcomputes the change in quantity using time 0 prices as weight:Pq=p0·xtp0·x0=p01xt1+p02xt2p01x01+p02x02.And theLaspeyres quantity indexcomputes the change in quantity using timetprices as weight:Lq=pt·xtpt·x0=pt1xt1+pt2xt2pt1x01+pt2x02Finally, define an index of the change in total expenditure by:M=pt·xtp0·x0=pt1xt1+pt2xt2p01x01+p02x02Show that:1. IfPq>1, the consumer has a revealed preference forxtoverxt.2. IfLq<1, the consumer has a revealed preference forx0overxt.3. No revealed preference is implied by eitherM >1 orM <1.

Answer 1

Answer:

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Explanation:

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