14. For the following differential equation 1 = 2VC - 0.253, =>0 (a) Find all steady-state(s) (equilibria, fixed points). (b) Using linear approximation describe local asymptotic stability of the steady-state(s).13. In a macroeconomic model C(t), I(t), and Y () denote respectively the consumption, invest- ment, and national product in a country at time f. Assume that, for all f : Y(0) = C(O) + 1(t ) 1(t) = 20(1) C(t ) = = (1)+6 where b is a positive constant. (a) Derive the following differential equation for Y(!) : Y(!) = Y(t) - b. (b) Solve this equation when Y(0) = Yo, > 0 and then find the corresponding I(t).12. For the following differential equation 1=x'to'- 4(x+1) (a) Find all steady-state(s) (equilibria, fixed points). (b) Using linear approximation describe local asymptotic stability of the steady-state(s).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.10. Consider the price-adjustment demand and supply model: = 2-3p Q' = -3+p dp = 2(0* - Q') (a) Derive the first-order linear differential equation for price p = p(t). (b) Solve the differential equation from (a).9. For the following equation (a) Determine the intervals of a over which (real) fixed points exist. (b) Determine the intervals of / for which they are stable or unstable.8. Consider the model Ct = 0.75Y It = 4(Y -Y-1) Et = C+h 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