Consider an economic agent who has preferences over the bundles (x1, x2), which is represented by the following utility function: u(x1, x2) = ln(x1) + 2ln(x2)

(a) Formulate the consumer's utility maximization problem for this agent for given prices p1, p2 and income level I and derive the uncompensated demand functions for good 1 and good 2 by solving this problem.

(b) From your answer for (a), give an expression for the indirect utility function V (p1, p2, I).

(c) Find the expenditure function E(p1, p2, U) of this agent by using your answer to part (b) and duality between utility maximization and expenditure minimization.

(d) Derive the compensated demand functions for good 1 and good 2 from (c) by using the Shepard's Lemma.

(e) Depict the compensated and uncompensated demand curves of good 1 on the same graph. Which one is steeper?

(f) Find income effect and substitution effect as a function of p1, p2, U and I.