1 Linear model UN3213 - Problem Set 1 (Math-Econ Review) E milienGouin-Bonenfant January 26, 2024 Consider the following linear model, which predicts that output {Yt}t=0 is given by Yt 1 = Yt whereY0 isgivenand>0,0<<1. (a) Compute the steady-state Yt = Y and illustrate. (b) Illustrate graphically (i.e., plot Yt 1 as a function of Yt, as well as the 45 degree line). (c) Obtain an expression for Yt by iterating Equation (1.1) forward starting from Y0. (1.1) (d) Suppose that the economy starts with a level of output above its steady-state value (i.e., Y0 > Y). Show that the next period's output will be lower than today's (i.e., Y1 < Y0). You can do this mathematically (a proof) or just give the explanation why in words. 2 Nonlinear Model Consider the following nonlinear model, which predicts that output {Yt}t=0 is given by Yt 1 = eYt whereY0 isgiven,and>0,0<<1. (a) Compute the steady-state Yt = Y. (2.1) (b) Use equation (2.1) to show that yt 1 = yt, where you will use the notation yt = logYt,y = logY. (c) In class, we mentioned that log differences are approximately equal to growth rates. Com- pute the growth rate yt