iii. just need the answer Consider the following dynamic IS-LM model.C(t) = 20+ 0.8Y(t-1)(iv)Ya(t) = Y(t) - Tx(t)Tx(t) = 5 +0.25Y(t)I(t) = 20 2r(t)G = 50E (t) = C(t) + I (t) + GAY(t+1)= 0.05 [E(t) - Y(t)]0.5r(t)Ma(t) 10+ 0.25Y(t)M,(t) = 55Ar(t+1)=0.8 [Ma(t) – M,(t)](i) What is the equilibrium level of Y and r?(ii) Show that dynamic IS and LM equations are the recursive equations for Y(+1) andr(t+1). That is,=this policy change?Y(t+1) = 86a + (1 − a)Y(t) + 0.6aY(t - 1) - 2ar(t)r(t + 1) = -45ß +0.25ßY(t) + (1 - 0.5B)r(t)where a = 0.05 is the speed of good market adjustment and ß = 0.8 is the speed ofmoney market adjustment. [Hint: Substitute all the relationships in each of theadjustment equations in turn. The algebra can be somewhat tedious but notintellectually difficult.]Suppose the Reserve Bank reduces the money supply (Ms) to 53.6 in period 2, given Y and rare at their equilibrium values in periods 0 and 1.(iii)calculate the new equilibriumoutput and interest rate. [Hint: The LM curve shifts left so you need to re-calculate thedynamic LM curve]plot the trajectory of the economy resulting from tY(t + 1) = 86a + (1 − a)Y(t) + 0.6aY(t− 1) −2ar(t)r(t + 1) = -xx.xß +0.25Y(t) + (1 - 0.5p)r(t)01234567891012345678 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4142434456F48 491147Y(t)190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190190r(t)555555555555555555555555555555555555555555555555556r3102040Monetary contraction6080alpha=beta =100Y1201401600.050.8180200

Answered: Consider the following dynamic IS-LM…

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

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Question

iii. just need the answer

Consider the following dynamic IS-LM model.
C(t) = 20+ 0.8Y(t-1)
(iv)
Ya(t) = Y(t) - Tx(t)
Tx(t) = 5 +0.25Y(t)
I(t) = 20 2r(t)
G = 50
E (t) = C(t) + I (t) + G
AY(t+1)= 0.05 [E(t) - Y(t)]
0.5r(t)
Ma(t) 10+ 0.25Y(t)
M,(t) = 55
Ar(t+1)=0.8 [Ma(t) – M,(t)]
(i) What is the equilibrium level of Y and r?
(ii) Show that dynamic IS and LM equations are the recursive equations for Y(+1) and
r(t+1). That is,
=
this policy change?
Y(t+1) = 86a + (1 − a)Y(t) + 0.6aY(t - 1) - 2ar(t)
r(t + 1) = -45ß +0.25ßY(t) + (1 - 0.5B)r(t)
where a = 0.05 is the speed of good market adjustment and ß = 0.8 is the speed of
money market adjustment. [Hint: Substitute all the relationships in each of the
adjustment equations in turn. The algebra can be somewhat tedious but not
intellectually difficult.]
Suppose the Reserve Bank reduces the money supply (Ms) to 53.6 in period 2, given Y and r
are at their equilibrium values in periods 0 and 1.
(iii)
calculate the new equilibrium
output and interest rate. [Hint: The LM curve shifts left so you need to re-calculate the
dynamic LM curve]
plot the trajectory of the economy resulting from

t
Y(t + 1) = 86a + (1 − a)Y(t) + 0.6aY(t− 1) −2ar(t)
r(t + 1) = -xx.xß +0.25Y(t) + (1 - 0.5p)r(t)
0
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Y(t)
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r(t)
5
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r3
1
0
20
40
Monetary contraction
60
80
alpha=
beta =
100
Y
120
140
160
0.05
0.8
180
200

Expert Solution

Step 1: Define IS LM model

The IS-LM model is a macroeconomic model that shows the relationship between interest rates and output in the economy. The model is divided into two parts: the IS curve and the LM curve.

The IS curve shows the combinations of interest rates and output that result in equilibrium in the goods and services market. The IS curve is downward-sloping because lower interest rates lead to higher investment and higher output.

The LM curve shows the combinations of interest rates and output that result in equilibrium in the money market. The LM curve is upward-sloping because higher interest rates lead to higher demand for money and lower output.

Step 2: Calculate the income and interest rate

To find the equilibrium level of output (Y) and the interest rate (r) in this dynamic IS-LM model, we need to set the aggregate output and money market equal to each other.

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