Problem 7 Optimal consumption choice, Bert (27 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 quasi-linear utility function u(z) = x1 + 3,/2. Let prices be given by p = (2,1). Let Bert's income be m = 36. 1. Determine Bert's optimal consumption choice. [Hint: Use the condition for an optimal interior demand choice, M RS(z*) = p1/p2, together with the equation for the budget line pz* = m. Check that your solution satisfies non-negativity constraints. If they are not, consider which corner solution is preferred.| 2. Now, suppose the price of good 1 increases from p; = 2 to p; = 5. What is Bert's optimal consumption choice, now? [Hint: Proceed as before.] 3. Given py = 1, what is the highest price of good 1 such that the optimal consumption choice satisfies M RS(z*) = 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 [0,50] and p = (4,1)