The consumer has an incom Mand a utility function of the form u (x1; x2) = aInx1 + (1 - a)Inx2 If the prices of the two goods are given by p1 and p2, derive the Hicksian demand functions for a given utility level U: Derive the expenditure function. Using the concept of duality, derive the indirect utility function.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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The consumer has an incom Mand a utility function of the form

u (x1; x2) = aInx1 + (1 - a)Inx2

  1. If the prices of the two goods are given by p1 and p2, derive the Hicksian demand functions for a given utility level U:
  1. Derive the expenditure function.
  2. Using the concept of duality, derive the indirect utility function.
Expert Solution
Step 1

Utility Function : U = aInx1 + (1 - a)Inx2

Price of x1 = p1 

Price of x2 = p2 

Hicksian demand functions are the compensated demand function which show the relationship between price and quantity demanded remaining isolated with the change in purchasing power arising out of the price changes .

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