2) Suppose that the individual has income of Y in the first period, and Y2 in the second. The interest rate is denoted by r. Assume that the person's preferences are described by the following utility function In(c) + Bln(c2). The preferences are logarithmic in second period consumption. a) Derive a formula that describes consumption in the first and second period, as function of income, interest rate, and other parameters. b) Suppose that Y = 20, Y = 44, = .5 and r=.10=10%. Find the optimal amount of first and second period consumption, as well as saving. c) Draw this budget constraint on a graph, and denote the endowment point, the optimal consumption point, and the tangency. dS1 dY' d) Calculate formulas for and dS1 dr 3) Suppose that the individual has preferences as described in class which have an extreme amount of curvature, so that the indifference curves are kinked. The kink is such that consumption in the two periods are perfect complements, and C C2. Suppose that Y = 20, Y = 44, B = 1.0 and r.10. Find the optimal amount of first and second period consumption, as well as saving. =