Answer to Question #275798 in Macroeconomics for momal

Question #275798

(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

  1. find the equation for the IS curve and explain its economic rationale.
  2. find the equation for the LM curve and explainits economic rationale.
1
Expert's answer
2021-12-06T16:35:07-0500

(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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