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**Unformatted text preview: **For the expenditure function we just replace the compensated demands we have found into E = p x X + p Y Y . E = P X exp(U-(1-β )ln((1-β )P X / β P Y )) + P Y exp(U-β ln( β P Y /(1-β )P X )) E = [ ] [ ]---+-Px Py U Py Py Px U Px ) 1 /( ) exp( / ) 1 ( ) exp( 1---= 1 1 ) 1 ( ) exp( Py Px U E b) From E* we can solve directly for the utility level U ---= 1 1 ) 1 ( ) exp( Py Px I U -=--1 1 ) 1 ( Py Px I Ln U c) Solution for X: From the compensated demand: [ ]--=--= 1 / ) 1 ( ) exp( )) / ) 1 ln(( ) 1 exp(( ) exp( Py Px U X Py Px U X Plugging back the Indirect Utility function we get: X= β I/Px The same process for Y yields: Y=(1-β )I/Py...

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- Winter '08
- cunningham
- Economics, Utility, Hicksian demand function, Marshallian demands, Px / Py, Ln Px Py