4. Consider a stationary monetary equilibrium in which consumption of the young and old, real money balances, mm = M# and the ination rate are constant over F\" time. Assume that the utility function takes the form u{c] = , D s: o: a: 1 so that u'{c] = c'\". Ellc: 11:: {a} Show.r that in a stationary equilibrium, money market clearing requires g = (1 %} m1. {5 Marl-ts] (b) Derive an expression for the inflation rate in a stationary equilibrium. (5 Marks (c) Using the above result, show that in a stationary equilibrium, mi = (5 1+zo Marks) (d) Suppose o > 0 and that money growth is pushed towards infinity, that is, z - co. What happens to mi, a and c2 in this limiting case? Provide some intuition with reference to the individual's optimal intertemporal consumption trade-off condition