mathematics economics revision prob:

7. A model by J.R. Hicks uses the following difference equation: Y+42 - (b +k) Yi+ +ky = a(1+g). 1 = 0, 1, ... where a, b, g. k are positive constants. (a) Find a particular solution Y"* of the equation assuming that (1+9)?-(b+k)(1+g) +k # 0. (b) Give conditions for the characteristic equation to have two complex roots. (c) Find the growth factor r of the oscillations when the conditions obtained in part (b) are satisfied, and determine when the oscillations are damped.6. Let us consider the second order non-homogeneous difference equation which is a mathematical representation of a version of the Samuelson model Y- c(1+)+wY-a=1 0