Cobb-Douglas Preferences

Cobb-Douglas Preferences - Economics 21 Intermediate...

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Economics 21: Intermediate Microeconomics Topic 2: Consumer Theory – Cobb-Douglas Preferences 1 Economics 21: Intermediate Microeconomics Topic 2: Consumer Theory Cobb-Douglas Preferences Reference: Varian, p.93 Outline: I. Introduction II. Cobb-Douglass Preferences III. Positive Monotonic Transformations IV. Marginal Rate of Substitution I. Introduction Cobb-Douglass preferences are one of the simplest algebraic representations of well-behaved preferences. II. Cobb-Douglas Preferences Assume the consumer’s utility function is given by: u x 1 , x 2 ( ) = x 1 c x 1 d (1) We will maximise this utility function subject to the following budget constraint: p 1 x 1 + p 2 x 2 = m (2) Thus, setting up the Lagrange multiplier: 1 max x 1 , x 2 , ! L = x 1 c x 2 d + m " p 1 x 1 " p 2 x 2 ( ) (3) ! L ! x 1 = cx 1 c " 1 x 2 d " # p 1 = 0 (4) ! L ! x 2 = dx 1 c x 2 d " 1 " p 2 = 0 (5) ! L ! " = m # p 1 x 1 # p 2 x 2 = 0 (6) Dividing (4) by (5): 1 See the Appendix to Chapter 4 of Varian for details.
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Cobb-Douglas Preferences - Economics 21 Intermediate...

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