By Prof. Pablo Coto-Millán (auth.)
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Extra resources for Utility and Production: Theory and Applications
Example text
11 ) 2 Main Forms of Utility Functions 28 Besides. , the Hessian of the matrix must be strictly negative definite: & --Pl a. l = -p~ < 0; -Pl 0 which is satisfied for any positive price. <1. 3 The Indirect Utility Function Once the demanded amounts of the different goods, which solve the maximisation problem. 8), we will know the maximmn level of utility. which can possibly be reached at given prices and income. This information is given by the indirect utility function, V (p,y); txf V(p, y) = max u(x) = max x~·a }so that px = y.
Norton & Company, Inc. 1990 Gravelle. : Microeconomics. 2nd ed. London: Longman Group, Ltd. 1995 Henderson. M .. : Microeconomic Theory. A Mathematical Approach. 3 rd ed. New York: Mc Graw-Hill Book Company, Inc. 1985 Madden. : Concavity and Optimisation in Microeconomics. Basil Blackwell, Ltd. K. 1986 Sher, N .. : Microeconomic Theory. Elsevier, North Holland Inc. 1980 Silberberg. : The Structure of Economics. A Mathematical Analysis, 2nd ed. Singapore: Mc Graw-Hill Publishing Company 1991 Varian.
To: P, . X , + PJ . XJ = Y where the prices P= (P , P , .... P ) and P= (Pk , ... ' 12k J +1 n the user's level of Income. First-order conditions allow us to obtain the following typical consumer Marshallian demands: Xi= Xi (Pi. Pj. 1) particularly interesting since it corresponds to passenger transport service. 1) still presents some problems. Firstly, functions such as this one should be valid for any income distribution among the different economic agents. 1) would provide as many values as income Y distributions among the users were possible and, therefore, such a function would not exist.