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In: Economics

Following the conventional notation, consider a representative consumer with the utility function ?(?,?)=??+? and the budget...

Following the conventional notation, consider a representative consumer with the utility function
?(?,?)=??+?
and the budget constraint ???+???≤?. Assume throughout that all prices and quantities are positive and infinitely divisible.

Derive the consumer’s indirect utility function ?(∙). Assuming initially that ??=??=1 and ?=10, calculate the change in the consumer’s utility if the price of good ? doubles, all else equal.

Solutions

Expert Solution

THE STEP BY STEP WORKING IS AS FOLLOWS-

FIRST WE DIFFERENTIATED THE U WITH RESPECT TO X AND Y AND THEN USING MRS WE FOUND A RELATION BETWEEN X AND Y

THEN WE SUBSTITUTED IT IN BUDGET CONSTRAINT AND FOUND OUR OPTIMAL X* Y* AND THEN WE DERIVED OUR INDIRECT UTILITY FUNCTION USING THEM AS MARKED IN THE BOXES.

THEN WITH THE VALUES GIVEN WE FOUND V1 AND V2 AND SUBTRACTED THEM FOR FINDING THE CHANGE .

HOPE IT WAS HELPFUL FOR YOU. PLEASE GIVE IT A LIKE. THANKYOU!

Rahul Sunny answered 2 years ago
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