Thanks in advance!

1. Let Yr denote GDP, it total investment and 5: total savings, all in period t. Suppose that savings are proportional to GDP and that investment is proportional to the change in income from period t to period t + 1. Then, for t = 0,1,2, St = \"Yti St+1 = ayc+1 ----- It+1 = (Yr+1 - Yr) St = It; St+1 = It+1 Here, a and B are positive constants and we assume ,3 > a: > 0. (a) Formulate a difference equation determining the path of 1"; given Y0. [4 marks] (b) Find the equilibrium value of Yt. [4 marks] (c) Solve the difference equation for 1'} and comment on its time path. [8 marks]