Applied Mathematics for Business and Economics

Lecture Note Function of Two Variables

commodity is given by the Cobb-Douglas utility functionUxy xy( , )= αβ, where

0 <<α 1 and α+=β 1. Show that utility will be maximized when

and

kk

xy

ab

α β

==. GtifiCnmñak;man k duløasRmab;cMNayeTAelIrbs;eRbIR)as;BIrRbePT.

RbePTTI1 éfø aduløakñúg1Ékta nigRbePTTI2éfø bduløakñúg1Ékta. ]bmafa

GtßRbeyaCn_Edl)anmkBIrbs;eRbIR)as;RbePTTI1cMnYnxÉkta nigBIrbs;eRbIR)as;RbePTTI2cMnYny

ÉktakMNt;edayGnuKmn_ Uxy xy(), = αβEdl 0 <α<+=1 and α β 1. cUrbgðajfa

GnuKmn_GtßRbeyaCn_Qandl;GtibrmaebI and

kk

xy

ab

α β

==.