My Microeconomic Notes—Indirect Utility Function

Direct utility function :

U = f (q₁,q₂)

At the equilibrium  q₁* = q₁ (p₁,p₂,y)    q₂* = q₂ (p₁,p₂,y)

→U* = f [q₁*（p₁,p₂,y）,q₂*(p₁,p₂,y) ] = g(p₁,p₂,y) …… This is an indirect utility function

The indirect utility function is convenient to examine the effect of changes in prices and income on utility.

Suppose in the base year , we have U⁰ = g(p₁⁰,p₂⁰,y⁰) …… （1）

Suppose prices change to p₁`,p<sub>2</sub>`

Then by setting U⁰ = g(p₁`,p<sub>2</sub>`,y) ……(2) and equating (1) and (2) ,we can compute the value of y such that the utility level is unchanged under two sets of prices.