Consumption C(t), investment I(t) and national income Y(t) at time t satisfy the equations: C(t) + I(t) = Y(t) I(t) = kC(t) C(t) = aY(t) + b Where a, b, k E R^(+) with a < 1. Show that Y (t) satisfies the equation: Y(t) = ((1-a)/ka)Y - (b/ka) Solve for Y(0) = Y_0 > b/(1-a). Then find the function I(t) and calculate Lim_(t tends to infinity) of (Y(t)/I(t))
Consumption C(t), investment I(t) and national income Y(t) at time t satisfy the equations: C(t) + I(t) = Y(t) I(t) = kC(t) C(t) = aY(t) + b Where a, b, k E R^(+) with a < 1. Show that Y (t) satisfies the equation: Y(t) = ((1-a)/ka)Y - (b/ka) Solve for Y(0) = Y_0 > b/(1-a). Then find the function I(t) and calculate Lim_(t tends to infinity) of (Y(t)/I(t))
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consumption C(t), investment I(t) and national income Y(t) at time t satisfy the equations:
C(t) + I(t) = Y(t)
I(t) = kC(t)
C(t) = aY(t) + b
Where a, b, k E R^(+) with a < 1. Show that Y (t) satisfies the equation:
Y(t) = ((1-a)/ka)Y - (b/ka)
Solve for Y(0) = Y_0 > b/(1-a). Then find the function I(t) and calculate
Lim_(t tends to infinity) of (Y(t)/I(t))
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