Consider the following dynamic IS-LM model. C(t) = 20+ 0.8Y(t-1) 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) M₂(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(t+1) and r(t+1). That is, 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.]
Consider the following dynamic IS-LM model. C(t) = 20+ 0.8Y(t-1) 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) M₂(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(t+1) and r(t+1). That is, 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.]
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
just ii please !!
Transcribed Image Text: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
1
2
3
4
5
6
7
8
9
10
12345678 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4142434456F48 49
11
47
Y(t)
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
190
r(t)
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
6
r3
1
0
20
40
Monetary contraction
60
80
alpha=
beta =
100
Y
120
140
160
0.05
0.8
180
200
![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) + 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)]
(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,
=
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)
this policy change?
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2e65f2-c472-45bf-885c-00dffce84016%2F0c623335-5e47-40fb-8a44-f27208759a78%2Frrdy5ik_processed.png&w=3840&q=75)
Transcribed Image Text: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) + 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)]
(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,
=
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)
this policy change?
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
Expert Solution
Step 1: Define IS LM model
The IS-LM model is a macroeconomic framework used to analyze the relationship between real output (Y) and interest rates (r) in an economy. It was developed by John Hicks and Alvin Hansen in the 1930s and is an important part of Keynesian economics. The model consists of two main components: the IS curve and the LM curve.
Step by step
Solved in 3 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education