Question is below:

3) Consider a consumer who has preferences given by U(:.-:1, 2:2) = 9:2 +2'/1 (quasilinear utility), with Mum = E' Mus = 1, where M U21 and M U32 are the marginal utility of 2:1 and $2, respectively. Normalizing the price of good 2 to 1, the budget constraint is given by y = 101131 + $2- a) What is the marginal rate of substitution in this case? b) What is the next step that we need to do to solve this problem? c) Given your answer to b) solve for :1 and 2:2. d) What are the (unrealistic) implications of quasilinear utility? 6) Suppose y = 10 and p1 = {1, 2, 3}, what is the value of your utility in each case? f) Plot your indifference curves for each value labeling the graph, including each axis, correctly. How do the indifference curves shift with changes in the utility functions? Does the consumer ever not consume good 1? How about good 2? What assumptions on income are required to ensure an interior solution (i.e. both goods are consumed)