Question: A consumer has a utility function u(x 1 , x 2 )= 3(x 1 2 + x 2 2 ) and the budget constraint is

A consumer has a utility function u(x1, x2)= 3(x12+ x22) and the budget constraint is

p1x1+ p2x2=I , p1 , p2 , I> 0 . Check the Roy's identity i(p, I)= -{v(p, I)/ pi} {v(p, I)/ I }

for i=1, 2. ( p,I) is the Marshallian demand function, v =v( p,I) is the indirect utility function.

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