Suppose that a preference relation is represented by the CES(Constant Elasticity of Substitution) utility function:

U( x₁ ,x₂) =(X^p₁ + X^p₂)^1/p where p <0 and p equal or not 0

And the prices of x₁ and x₂ are p₁ and p_2, and the wealth is w.

a)Solve the UMP to derive the Marshallian demand function..

b)Find the indirect utility function

c)Write downRoy's identity , and verify it for x₁

d)Write down the expenditure minimization problem. Find the Hicksian demand function.

e)Find the expenditure function.

f)Write down Shephard's lemma, and verify it for h₂

g)Define equivalent variation (EV) and compensated variation (CV),