Question

A. A consumer with Cobb-Douglas utility function U(x₁, x₂) =sqrt(x₁x₂)has Marshallian demand x₁(p, I) = I/2p₁ , x₂(p, I) =I/2p₂ and Hicksian Demand h₁(p, u) = u * sqrt(p₂/p₁) and h₂(p,u) = u* sqrt(p₁/p₂).

Initially the consumer has a budget I= 100 and prices are p₁=p₂= 4. Then the price of good 1 increses to p₁^'= 8.

(a) What is the the compensating variation associated with this price increase?

(b) What is the equivalent variation?

B. A consumer has utility functionU(x₁, x₂) =√x₁+√x₂.

(a) Compute his indirect utility function and Marshallian demand function.

(b) From the indirect utility function, deduce his expenditure function.

(c) Use Shephard’s lemma to obtain his Hicksian demand function.