Transcription of Lecture Notes on Constant Elasticity Functions
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Lecture Notes on Constant Elasticity Functions
Lecture Notes on Constant Elasticity FunctionsThomas F. RutherfordUniversity of ColoradoNovember, 20021 CES UtilityIn many economic textbooks the Constant - Elasticity -of-substitution (CES) utility function isdefined as:U(x, y) = ( x + (1 )y )1/ It is a tedious but straight-forward application of Lagrangian calculus to demonstrate that theassociated demand Functions are:x(px, py, M) =( px) M p1 x+ (1 ) p1 yandy(px, py, M) =(1 py) M p1 x+ (1 ) p1 corresponding indirect utility function has is:V(px, py, M) =M( p1 x+ (1 ) p1 y)1 1 Note thatU(x, y) is linearly homogeneous:U( x, y) = U(x, y)This is a convenient cardinalization of utility, because percentage changes inUareequivalent to percentage Hicksian equivalent variations in income.
Thomas F. Rutherford University of Colorado November, 2002 1 CES Utility In many economic textbooks the constant-elasticity-of-substitution (CES) utility function is defined as: U(x,y) = (αxρ +(1−α)yρ)1/ρ It is a tedious but straight-forward application of Lagrangian calculus to demonstrate that the associated demand functions are: x(p ...
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