National income Y varies over time t according to the following model: dY/dt = 0.6(C + I
Question:
National income Y varies over time t according to the following model:
dY/dt = 0.6(C + I - Y)
C = 0.8Y + 600
I = 800
where C is consumption and I is planned investment. Initially, Y = 2000.
(a) Find an expression for Y(t) and deduce that the system is stable.
(b) Sketch a graph of Y against t.
(c) Find the time taken for national income to rise to 90% of its equilibrium value. Round your answer to one decimal place.
(d) Find an expression for C(t).
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d dt Hence 0608Y600800Y CF de For a particular solution try yt D 0012D840 D70...View the full answer
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