Consider the following IS-LM model: C = XXXXXXXXXX25YD I = XXXXXXXXXX25Y -1000i G = 250 T = 200...

Question

Consider the following IS-LM model: C = XXXXXXXXXX25YD I = XXXXXXXXXX25Y -1000i G = 250 T = 200 (M/P)d = 2Y -8,000i i = i0 = 0.05 a. Derive the IS relation. (Hint: You want an equation with Y on the left side, all else on the right.) b. Derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation with i on the left side, all else on the right.) c. Solve for equilibrium real output. (Hint: Substitute the value for the interest rate into the IS equation and solve for output.) d.
	
Document Preview: Semester 2, 2012 
ECON204 
Macroeconomic Analysis 
Tutorial 2, Week 4 Questions 
 
1. Consider the following IS-LM model: 
C = XXXXXXXXXX25YD 
I = XXXXXXXXXX25Y - 1000i 
G = 250 
T = 200 
(M/P)d = 2Y - 8,000i 
i = i0 = 0.05 
 
a. Derive the IS relation. (Hint: You want an equation with Y on the left side, all else 
on the right.) 
 
b. Derive the LM relation. (Hint: It will be convenient for later use to rewrite this 
equation with i on the left side, all else on the right.) 
 
c. Solve for equilibrium real output. (Hint: Substitute the value for the interest rate 
into the IS equation and solve for output.) 
 
d. Solve for the equilibrium real money supply. (Hint: Substitute the value you 
obtained for Y in [c] into the LM equation and solve for M/P.) 
 
e. Solve for the equilibrium values of C and I and verify the value you obtained for Y 
by adding up C, I, and G. 
 
f. Now suppose that the interest rate, i0 was cut to 3% (i.e XXXXXXXXXXSolve for Y, M/P, C, 
and I, and describe in words the effects of an expansionary monetary policy. 
 
g. Set the interest rate back to 5%. Now suppose that government spending increases 
to G =400. If the central bank keeps the interest rate unchanged, find the effects of 
this fiscal expansion on Y and C. If the central bank responds by raising the interest 
rate by enough so that M/P is the same value as you found in part (d), what would be 
the effect on Y, i, and C. Summarize the effects of an expansionary fiscal policy on Y, 
i, and C.

2. Assume that consumption is described by a linear function C = c0 +c1YD. 
Using IS-LM framework, analyze the effects of an increase in consumer confidence 
on the economy (that is equilibrium output, interest rate, money supply, consumption 
and investment) under the 2 scenarios: 
 
a) The central bank controls money supply (that is keeps money supply constant). 
 
b) The central bank controls the interest rate. 
 
If the central bank is concerned about the possible overheating of the economy...

David · Accepted Answer

1
1. Consider the following IS-LM model:
C = 200 + .25YD
I = 150 + .25Y - 1000i
G = 250
T = 200
(M/P)d = 2Y - 8,000i
i = i0 = 0.05
a. Derive the IS relation. (Hint: You want an equation with Y on the left side, all else
on the right.);
Equation of IS curve:
Y=C+I+G
C=C(Y-T)
So, we have, 
Y=200+(.25*(Y-200))+150+.25Y-1000i+250
Or, Y=600-50+(.25+.25)Y-1000i
Or, Y(1-.5)=550-1000i
Or, Y=(550-1000i)/.5
Or, Y=1100-2000i
b. Derive the LM relation. (Hint: It will be convenient for later use to rewrite this
equation with i on the left side, all else on the right.)
Equation of LM curve:
(M/P)=M/Pd
Or, M/P=2Y-8000i
Or, 8000i=2Y-M/P
This is the required LM curve where, M/P=real money balance. 
c. Solve for equilibrium real output. (Hint: Substitute the value for the interest rate
into the IS equation and solve for output.)
Equation of IS curve:
Y=1100-2000i
for i=.05, Y=(1100-(2000*.05))=1000
d. Solve for the equilibrium real money supply. (Hint: Substitute the value you
obtained for Y in [c] into the LM equation and solve for M/P.)
Equation of LM curve:
M/P=2Y-8000i
For Y=1000,i=.05
M/P=(2*1000)-(8000*.05)= 1600
e. Solve for the equilibrium values of C and I and verify the value you obtained for Y
by adding up C, I, and G.
C=200+(.25*(1000-200))=400
I=(150+(.25*1000)-(1000*.05))=350
G=250
So, C+I+G=(400+350+250)=1000
Thus, the equality between C+I+G and Y is verified. 
f. Now suppose that the interest rate, i0 was cut to 3% (i.e. 0.03). Solve for Y, M/P, C,
and I, and describe in words the effects of an expansionary monetary policy.
Equation of IS curve:
Y=1100-2000i
for i=.03, Y=(1100-(2000*.03))=1040
Equation of LM curve:
M/P=2Y-8000i
For Y=1040,i=.03
M/P=(2*1040)-(8000*.03)= 1840
C=200+(.25*(1040-200))   =410
I=(150+(.25*1040)-(1000*.03))   =380
As, following a decrease in rate of interest, C,Y and I has increased, we can conclude that expansionary monetary policy leads to increase in national income, consumption and saving of the economy.

Consider the following IS-LM model: C = XXXXXXXXXX25YD I = XXXXXXXXXX25Y -1000i G = 250 T = 200 (M/P)d = 2Y -8,000i i = i0 = 0.05 a. Derive the IS relation. (Hint: You want an equation with Y on the...

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