Let aggregate national income be given by Yt = Ct + It + Gt Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by Investment is given by Ct = myt It = 1 + α(Yt-1 - Yt-2) And government expenditure declines over time according to Gt = Go (1 - 8)t, 0<8 <1 Where is the exogenous rate of decline of government expenditure Derive the linear second order difference equation. Solve the difference equation. (i) (ii)

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Let aggregate national income be given by
Y; = Ct + It + Gt
Where C, I and G are consumption, investment and government expenditure. Assume
that consumption is given by
C = mY;
Investment is given by
I = i + a(Yt-1- Yt-2)
And government expenditure declines over time according to
G = Go(1 – 8)*,
0 < 8 < 1
Where d is the exogenous rate of decline of government expenditure
(i)
Derive the linear second order difference equation.
(ii)
Solve the difference equation.
Transcribed Image Text:Let aggregate national income be given by Y; = Ct + It + Gt Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by C = mY; Investment is given by I = i + a(Yt-1- Yt-2) And government expenditure declines over time according to G = Go(1 – 8)*, 0 < 8 < 1 Where d is the exogenous rate of decline of government expenditure (i) Derive the linear second order difference equation. (ii) Solve the difference equation.
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