Let aggregate national income be given by Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by Investment is given by Y₁ = C₁ + 1₂ +G₁ C₁ = mY₁ 1₁=1+ a(Yt-1-Yt-2) And government expenditure declines over time according to G=Go(1-8), 0<8 <1 (1) (ii) Where & is the exogenous rate of decline of government expenditure Derive the linear second order difference equation. Solve the difference equation.
Let aggregate national income be given by Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by Investment is given by Y₁ = C₁ + 1₂ +G₁ C₁ = mY₁ 1₁=1+ a(Yt-1-Yt-2) And government expenditure declines over time according to G=Go(1-8), 0<8 <1 (1) (ii) Where & is the exogenous rate of decline of government expenditure Derive the linear second order difference equation. Solve the difference equation.
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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Transcribed Image Text:b) Let aggregate national income be given by
Y, = C; + l4 + G
Where C, I and G are consumption, investment and government expenditure. Assume
that consumption is given by
C = mY,
Investment is given by
Ik = 1 + a(Yc-1 – Ye-2)
And government expenditure declines over time according to
G = Go(1 – 8)', 0 < 8 <1
Where 8 is the exogenous rate of decline of government expenditure
Derive the linear second order difference equation.
(i)
Solve the difference equation.
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