Problem 3 Using MRS to represent preferences (12 points) Consider an individual named Bo. Bo has preferences over 2-dimensional consumption bundles x = (x1,x9) where consumption is constrained to be non-negative, so = Rf_. 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 z,y R2. Argue your answer. (Hint: Use that you know that the utility function that represents these preferences has a linearly additive form, u(x) = azq + bxs.) 3. Let's expand this example to an economy with 3 goods. So a consumption bundle is defined as x = (x1,x2,x3) and all quantities are constrained to be non-negative, so x R_3|_. Now, we have to expand how we think about substitution between goods. Specifically, define M RS;;(x) = MU;(xz)/MU;(x) for i,j {1,2,3}. That is M RS,; states how valuable Bo thinks good 7 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 M RS2 = 2. Also, M RS3 = 6. (a) Do you have enough information to determine M RS53? If so, what is it? (b) Consider the two bundles a = (13,10, 24) and b = (10, 20, 18). Which one does Bo prefer