7. A model by J.R. Hicks uses the following difference equation: Yi+2 - (b+k) Yi+itkle = a(1+g), t = 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.8. Consider the model C. = 0.75Y It = 4(14 -Y-1) Y = E-1 where C = consumption, Y = income, E = total expenditure, / = investment. (a) Show that this results in a second order difference equation for income. (b) Solve this equation.9. For the following equation (a) Determine the intervals of a over which (real) fixed points exist. (b) Determine the intervals of a for which they are stable or unstable.10. Consider the price-adjustment demand and supply model: = 2-3p Q = -3+P dp it = 2(Q* - Q') (a) Derive the first-order linear differential equation for price p = p(t). (b) Solve the differential equation from (a).11. The following differential equation is k = 0.2k3 - 0.1k is a version of the Solow growth model. This is a Bernoulli differential equation. Solve it