Answer these questions please

Problem 3 - Using MRS to represent preferences (12 points) Consider an individual named Bo. Bo has preferences over 2-dimensional consumption bundles x = (x1, x2) where consumption is constrained to be non-negative, so a E R. . Bo's preferences are strictly monotone and belong to the class of perfect substitutes preferences. Bo's marginal rate of substitution is 2 (where I am implicitly talking about MRS as describing the value of good 1 stated in terms of good 2, same as in lectures). 1. Consider two bundles a = (17, 8) and b = (12, 14). Which one does Bo prefer? 2. Has the problem provided enough information to describe Bo's preferences over any two bun- dles x, y E R2. Argue your answer. (Hint: Use that you know that the utility function that represents these preferences has a linearly additive form, u(x) = ax1 + bx2.) 3. Let's expand this example to an economy with 3 goods. So a consumption bundle is defined as x = (X1, X2, 23) and all quantities are constrained to be non-negative, so x E RS . Now, we have to expand how we think about substitution between goods. Specifically, define MRSi, (x) = MUi(x)/MUj (x) for i, j E {1, 2, 3}. That is MRSij states how valuable Bo thinks good i is in terms of units of good j. Maintain that Bo's preferences are monotone and belong to the perfect substitutes class. Furthermore, it is the case that MRS12 = 2. Also, MRS13 = 6. (a) Do you have enough information to determine MRS23? If so, what is it? (b) Consider the two bundles a = (13, 10, 24) and b = (10, 20, 18). Which one does Bo prefer