A consumer buys two goods, x₁ and x₂, in order to achieve the utility given by: u (x₁, x₂) = 2 ln x₁ + 3 ln x₂. She is required to spend exactly her income of I dollars on x₁ and x₂, which have prices equal to p₁ > 0 and p₂ > 0, respectively. 1. Write down the constrained optimization problem that captures the consumer's decision.

2. Solve for the consumption bundle (x₁,x₂) that maximizes her utility. Note that these should be functions of the parameters I, p₁, p₂.

3. Show that the optimal bundle x*₁ is decreasing in p₁ and increasing in I. (Hint: Use partial derivatives).