Consider an individual that must decide how much to consume in a two-period model. Suppose that her preferences for present consumption (c1) and future consumption (C2) can be characterized by the following utility function: M01. 02) = :31 + ZINC2 Assume that her income in the present period is M1, her income in the future period is M2, and the nominal interest rate is 1'. Further? assume that the price index in the present period (p1) is 1 and the price index in the future period (p2) is s2=(1+d)P1 where d is the rate of ination. (a) [6 marks] Derive this individual's marginal rate of time preference (MRTP). What does her M RTP say about her willingness to sacrice future consumption for more present consumption? Use an appropriate diagram with .21 on the horizontal axis to ex- plain. (b) [9 marks] Solve for this individual's optimal choice of c1 and C2 respectively. Is c1 an increasing or decreasing function of d? What about C22? What does the relationship between .21 and of say about the substitutability of c1 and c2? Explain. (c) [5 marks] For what values of of will this individual be a saver? Explain