1. Let Xt represent the value of some variable X during period t. For example, Yt and It represent national income and investment spending at time t. Let gX represent the rate at which X changes between period t and period t +1. For example, gX = 0.05 represents a 5% rate of growth, therefore Xt+1 (1+ gX)Xt = (1.05) Xt. For each of the following three scenarios, show what happens to the ratio of investment to income as time increases. What happens as to this ratio as time goes to infinity? Separately, illustrate your conclusions in a diagram with time on the horizontal axis and the ratio of investment to income on the vertical axis. Three cases: (a) gI < gY; (b) gl = gY; (c) gl > gY