倫敦經(jīng)濟(jì)學(xué)院高微講義-消費(fèi)者理論(5)-資料下載頁
2025-10-09 11:17本頁面
【正文】 (p , M) ?Roy39。s Identity (All of these can be established using the known properties of the cost function) The Indirect Utility Function has some familiar properties... u = V(p, M) (...use the definition of the optimum) = V(p, C(p,u)) 0 = Vi(p, C(p,u)) + VM(p, C(p,u)) Ci(p,u) Differ ntiating) 0 = Vi(p, M) + VM(p, M) xi* sing Shephard39。s Lemma) ? ?? ?? ?x D MV MV Mii iM*,= = ?pppand so... The ordinary demand function for modity i Roy39。s Identity...??? V(p,M) ...solution response: ? ? ? ?? ?x D MV MV Mii iM*,= = ?pppProblem... max U(x) subject to Si=1 pi xi ? M n Utility maximisation: summary C(p,u) ...solution Problem... min ( )xxp x U ui iin=??1subje c t toresponse: xi* = Hi(p,u) Costminimisation: the consumer A long(ish) summary ? A lot of the basic results of the consumer theory can be found without too much hard work. ? We need two “tricks” ? 1. A simple relabelling exercise: cost minimisation is reinterpreted from output targets to utility targets. ? 2. The insight that utility maximisation subject to budget is equivalent to cost minimisation subject to utility. ? THE FIRM ? min cost of inputs ? subject to output target ? Solution is of the form C(w,Q) ? THE CONSUMER ? min budget ? subject to utility target ? Solution is of the form C(p,u) 1. Cost minimisation: two applications ? PRIMAL ? max utility ? subject to budget constraint ? Solution is a function of (p,M) ? DUAL ? min budget ? subject to utility constraint ? Solution is a function of (p,u) 2. The consumer: two equivalent approaches Hi(p,u) Di(p,M) V(p,M) pensated demand for good i indirect utility ordinary demand for input i C(p,u) cost (expenditure) H is also known as Hicksian demand. Basic functional relations
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