How to solve the following: In a macroeconomic model, C(t), 1(t) and Y(t) denote respectively the...

Transcribed Image Text:

How to solve the following: In a macroeconomic model, C(t), 1(t) and Y(t) denote respectively the consumption, investment and national income in a country at time t. Assume that for all t: (): C(t) + I(t) = Y(t) (ii) I (t) = kĊ(t) (iii) C(t) = aY (t) +b where a, b and k are positive constants, with a < 1. Y():Y() =--"Y() - ka (a). Derive the following differential equation for (b). Solve the equation when Y (0) = Yo, and the find the corresponding I(t). lim [Y(t)/(t) for Yo #b/(1-a). (C). Compute 100 How to solve the following: In a macroeconomic model, C(t), 1(t) and Y(t) denote respectively the consumption, investment and national income in a country at time t. Assume that for all t: (): C(t) + I(t) = Y(t) (ii) I (t) = kĊ(t) (iii) C(t) = aY (t) +b where a, b and k are positive constants, with a < 1. Y():Y() =--"Y() - ka (a). Derive the following differential equation for (b). Solve the equation when Y (0) = Yo, and the find the corresponding I(t). lim [Y(t)/(t) for Yo #b/(1-a). (C). Compute 100

Answer rating: 100% (QA)

ANSWER To derive the differential equation for Yt we differentiate equation iii with respect to t Ct ... View the full answer