Need your help with this problem. thank you

5. Hillary's preferences are represented by the utility function u(x₁, x₂) = x₁ x₂ . Suppose p₂= 1 throughout. Let her original optimal choice be the bundle (x₁, x₂) = (1, 1).

(a) Can you write the equation for her standard demand curve for good 1 (implied by the income she has in that original choice)?

(b) Can you write the equation for her compensated demand curve for good 1 (fixing the utility level she obtained at that original optimal choice)?

(c) Can you comment on yourfindings in connection with the total effect, substitution effect, and income effect?

(d) Can you confirm this using the Slutsky equation, evaluated at that point?