Question

For Each of the following situations,

i) Write the Indirect Utility Function

ii) Write the Expenditure Function

iii) Calculate the Compensating Variation

iv) Calculate the Equivalent Variation

U(X,Y) = MIN (X, 3Y). M = $40. Initially, PX = 1 and PY = 1. Then the Price of X changes to PX = 3.

i) Indirect Utility Function: __________________________

ii) Expenditure Function: ____________________________

iii) CV = ________________

iv) EV = ________________

Answer 1

THE STEP BY STEP WORKING IS AS FOLLOWS

FIRST WE MAXIMIZE THE UTILITY AND PUT X=3Y IN BL AND GET X* Y*

AFTER GETTING X* Y* WE SOLVED FOR THE UTILITY AND DERIVED OUR INDIRECT UTILITY FUNCTION

FOR EXPENDITURE FUNCTION WE REARRANGED THE INDIRECT UTILITY FUNCTION IN TERMS OF M

THEN FOR THE CV WE USED THE NEW PX X₀ Y₀ AND FOUND THE M'

CV=M-M'

FOR EV WE USED THE ORIGINAL PX PY AND Y₁ X₁ TO CALCULATE M''

EV = M-M''

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