Exercise 3. Calculation with the IS curve and the multiplier.Show how to derive an IS curve that includes the consumption multiplier. That is, assumeinvestment is described byand consumption is described byIt = āƒŸt — b(R₁ – ñ)īt,-Ct =ācīt + x Ỹt Yt.The other categories of expenditures follow the same rules as in class.a) Show how to get the expression of the IS curve for this case.b) Why do we say that there is a multiplier? What is the magnitude of the multiplier?Explain the intuition behind the multiplier.= 0.02, b = 0.5, x = 0.4, and that there are no short-term demand shocks ā = 0.Assumec) How does output respond when the real interest rate increases by 0.01.d) Draw a graph of the baseline IS-curve and the IS-curve with the multiplier. You shouldplot the "short-term fluctuation" (X-axis) vs the real interest rate in the (Y-axis), for eachcase. Which curve is flatter, and why?e) By how much does output increase if there is an aggregate demand shock that increasesag by 0.01.

Given information Investment functionIt=aIYt-b(Rt-r)YtConsumption functionCt=aCYt+xYt~Yt

Answered: Show how to derive an IS curve that…

Show how to derive an IS curve that includes the consumption multiplier. That is, assume investment is described by and consumption is described by It = āƒŸt — b(Rt — F)īt, 7

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

Exercise 3. Calculation with the IS curve and the multiplier.
Show how to derive an IS curve that includes the consumption multiplier. That is, assume
investment is described by
and consumption is described by
It = āƒŸt — b(R₁ – ñ)īt,
-
Ct =ācīt + x Ỹt Yt.
The other categories of expenditures follow the same rules as in class.
a) Show how to get the expression of the IS curve for this case.
b) Why do we say that there is a multiplier? What is the magnitude of the multiplier?
Explain the intuition behind the multiplier.
= 0.02, b = 0.5, x = 0.4, and that there are no short-term demand shocks ā = 0.
Assume
c) How does output respond when the real interest rate increases by 0.01.
d) Draw a graph of the baseline IS-curve and the IS-curve with the multiplier. You should
plot the "short-term fluctuation" (X-axis) vs the real interest rate in the (Y-axis), for each
case. Which curve is flatter, and why?
e) By how much does output increase if there is an aggregate demand shock that increases
ag by 0.01.

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