(a) show the slope of IS curve depends on interest elasticity of investment demand and marginal prosperity of consume and save.
(b) consider the following numerical version of IS-LM model:
C=500+0.75Y^d
T=20%
I=400-2000r
Ms=500
Md=0.5Y-8000r
G=600
(a)
If the marginal propensity to consume is high, then a given change in investment demand causes a big increase in national income and product. Hence the IS curve is flat. If investment demand is independent of the interest rate, then the IS curve is vertical.
The IS curve derives from the property that it represents that desired investment equals desired saving.
Let t denote taxes:
"i(r)=[y-t-c(y)]+(t-g)"
"i(r)" represents desired investment.
The right hand side represents desired saving.
"y-t-c(y)" is household savings given by disposable income less consumption demand.
"t-g" is government saving.
(b)
1.
IS relation:
AD= consumption+investment+government expenditure.
"Y=C+I+G"
"Y=500+0.75Y^d+400-2000r+600"
"Y=500+0.75(Y-T)+400-2000r+600"
"T=0.20\\times G"
"\\implies0.25Y=700-0.75(0.20\\times 600)-2000r"
"Y=2320-2000r"
2.
LM relation:.
"M_s=M_d"
"500=0.5Y-8000r"
"r=0.0000625Y-0.0625"
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