In: Math
Consider the following macroeconomic model: C(t) + I(t) = Y (t) I(t) = 0.8 dC(t) dt C(t) = 0.4Y (t) + 1 where C(t), I(t), Y (t) denote respectively the consumption, investment and national income at time t. Write the differential equation in terms of C(t), find the solution for the differential equation, and draw the phase diagram and comment on the stability.