Consider an individual that must decide how much to consume in a two-period model. Suppose that her preferences for present consumption (c) and future consumption (c) can be characterized by the following utility function: u(c, c) = C +20/ Assume that her income in the present period is M, her income in the future period is M, and the nominal interest rate is i. Further, assume that the price index in the present period (p) is 1 and the price index in the future period (p2) is P2 = (1 + d)p1 where d is the rate of inflation. (a) [6 marks] Derive this individual's marginal rate of time preference (MRTP). What does her MRTP say about her willingness to sacrifice future consumption for more present consumption? Use an appropriate diagram with c on the horizontal axis to ex- plain. (b) [9 marks] Solve for this individual's optimal choice of c and c respectively. Is c an increasing or decreasing function of d? What about c? What does the relationship between c and d say about the substitutability of c and c? Explain. (c) [5 marks] For what values of d will this individual be a saver? Explain.