Suppose you have the following indirect utility function: V (Px» Py, I) = In PxPy %3D What are marshallian demands for x and y? O(8x, 8y) = (: %3D 2px 2py 1 O(gx, 8y) = (In 2py 2px O(gx, gy) = (exp(2p.Py -), exp(2p.Py O(gx»8y) = (; 2p, +P, Px+2py What is the expenditure function for the associated expenditure minimization problem? OE(Px, Py, U) = (px + Py) In(U) OE(Px, Py, U) = Vexp(U)PxPy %3D OE(Px, Py, U) = (pi + p3) In(U) OE(P. Py U) = exp(U)p.Py

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter5: Income And Substitution Effects
Section: Chapter Questions
Problem 5.5P
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Suppose you have the following indirect utility function:
V(px, Py, I) = In (
PxPy
What are marshallian demands for x and y?
O(gx, gy) = (2p, 2p,
2px' 2py
O(8x, 8y) = (In
, In )
2px
2py
I
O(gx, gy) = (exp(2p.Py
), exp( 2p.P,
))
2pxPy
%D
O(8x» 8y) = (
%3D
2p, +P,' Px+2p,
What is the expenditure function for the associated expenditure minimization problem?
OE(px, Py, U) = (px + Py) In(U)
%3D
OE(px, Py, U) = Vexp(U)PxPy
%3D
OE(Px, Py, U) = (p + p3) In(U)
%3D
OE(Px, Py, U) = exp(U) PxPy
%3D
Transcribed Image Text:Suppose you have the following indirect utility function: V(px, Py, I) = In ( PxPy What are marshallian demands for x and y? O(gx, gy) = (2p, 2p, 2px' 2py O(8x, 8y) = (In , In ) 2px 2py I O(gx, gy) = (exp(2p.Py ), exp( 2p.P, )) 2pxPy %D O(8x» 8y) = ( %3D 2p, +P,' Px+2p, What is the expenditure function for the associated expenditure minimization problem? OE(px, Py, U) = (px + Py) In(U) %3D OE(px, Py, U) = Vexp(U)PxPy %3D OE(Px, Py, U) = (p + p3) In(U) %3D OE(Px, Py, U) = exp(U) PxPy %3D
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NICHOLSON
Publisher:
Cengage