Problem 5 Optimal consumption choice, Bert (25 points) This question lets you study a consumer's optimal consumption choice in both interior and corner solutions. Refer to the example of Bert in the lecture slides. Let Bert's preference be given by the quasilinear utility function 115(3) : $1 + 3%. Let prices be given by p : (2, 1). Let Bert's income be m = 36. 1. Determine Bert's optimal consumption choice. [Hint2 Use the condition for an optimal interior demand choice, M RS (3*) : p1 / p2, together with the equation for the budget line 1927* 2 m. Check that your solution satises non-negativity constraints. If they are not, consider which corner solution is preferred] 2. Now, suppose the price of good 1 increases from 131 = 2 to p1 = 5. What is Bert's optimal consumption choice, now? [Hint Proceed as before] 3. Given p2 : 1, What is the highest price of good 1 such that the optimal consumption choice satises M RS (33*) : p1 / p2? Or in other words, what is the highest good 1 price, such that the optimal consumption choice is interior. (There is a language subtlety here: The optimal consumption choice can be in a corner, but not be constrained by the corner). 4. Draw the income~consumption curve for Bert for income levels m E [0, 50] and p 2 (4,1)