2. Suppose John has an intertemporal consumption decision. His preferences over consumption in two periods is represented by the following utility function: U(C1, C2) = C1/2 + 802 His intertemporal budget constraint takes the form: C2 m2 C1 + = mit 1+r 1+r MU1 a) Derive John's MU1, MU2, and MRS12 = MU2 b) Find John's optimal consumption choices ci and cz (you can use any approach you want - substitution or Langrangian)c) Ifm1 = 100,m2 = 150,;r = 0.05, and 6 = 0.075, what are John's optimal consumption choices? Is John a borrower or saver? d) If r decreases to 0.01, what are John's new optimal consumption choices? Is John a borrower or saver? e) Sketch the results of c) and d) in two graphs. One graph for the change in the optimal cl and the other for the change in the optimal C2. In both these graphs, show the substitution, income, and total effects of the change in r