倫敦經(jīng)濟學(xué)院高微講義-消費者理論(3)-展示頁
2024-10-28 10:47本頁面
【正文】 st decreases mean welfare increases. CV and EV... Compensating Variation as D(cost) CV(p ? p39。, M) the utility level at new prices p39。 = V(p, M + EV) u39。. ? But now, if the price fall had not happened, what hypothetical change in ine would have brought the person to the new utility level? Here39。 In this version of the story we get the Compensating Variation Note CV is positive for price fall In this version the original utility level is the reference point x 2 x 1 x** x* new prices original prices u { CV But all this is based on the assumption that the right thing to do is to use the original utility level as a reference point. There are alternative assumptions we might reasonably make. For instance... The pensating variation measuredin terms of good 2 ? Again suppose p is the original price vector and p39。s story number 1 u = V(p39。, M) p ?p39。. ? But what hypothetical change in ine would bring the person back to the starting point? ? (and is this the right question to ask...?) u = V(p, M) u39。 u some distance function Utility ratios Utility differences 3 things that are not much use: ?Use ine not utility as a measuring rod ?To do the transformation we can use the V function ?We could do this in (at least) two ways... Idea...!! ? Suppose p is the original price vector and p39。 / u depends on the cardinal isation of the U function d(u39。 ? x** ...obviously the person is better off... and allow a price to fall... x2 u … ut how much better off? How do we quantify this gap? If we take the consumer39。s surplus Utility and Ine Consumer 39。? x2 x1 ? x* u x2 x1 ? x* subject to U(x) ? u min n S pixi i=1 subject to max n S pixi ? M i=1 U(x) Because the solutions to the primal and dual problems must match... M = C(p, u) minimised cost in the dual constraint ine in the primal … we know that the underlying solution can be written this way... maximised utility in the primal co
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