Consider the following dynamic IS-LM model. C(t) = 20+ 0.8% a(t-1) Ya(t) = Y(t) - Tx(t) Tx(t) 5 +0.25Y(t) (iv) = I(t) = 20 – 2r(t) G = 50 (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? E (t) = C(t) + 1(t) + G AY(t + 1) = 0.05 [E(t) - Y(t)] Ma(t) = 10+ 0.25Y(t) 0.5r(t) M,(t) = 55 Ar(t+1)=0.8 [Ma(t)- M, (t)] Y(t + 1) = 86a +(1- a)Y(t) + 0.6aY(t-1)-2ar(t) r(t + 1) = -45ß +0.25BY(t) + (1 - 0.5ß) 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

Answered: Consider the following dynamic IS-LM model. C(t) = 20+ 0.8% a(t-1) Ya(t) = Y(t) - Tx(t) Tx(t) 5 +0.25Y(t) (iv) = I(t) = 20 – 2r(t) G = 50 (i) What is the…

ENGR.ECONOMIC ANALYSIS

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Question

just need graph for (iv) please

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)
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0.8
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Consider the following dynamic IS-LM model.
C(t) = 20 +0.8Y(t-1)
(i) What is the equilibrium level of Y and r?
(ii) Show that dynamic IS and LM equations are the recursive equations for Y(t+1) and
r(t+1). That is,
(iv)
Ya(t) = Y(t) - Tx(t)
Tx(t) = 5 +0.25Y(t)
I(t) = 20 2r(t)
G = 50
E (t) = C(t) + 1(t) + G
AY(t+1) = 0.05 [E(t) - Y(t)]
Ma(t) = 10+ 0.25Y(t)
0.5r(t)
M,(t) = 55
Ar(t+1)= 0.8[Ma(t) - Ms(t)]
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]
this policy change?
plot the trajectory of the economy resulting from

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.

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