Question

Consider the following IS-LM model:

(1 - b)Y + i1r - a - G = i0 - bT (1)

c1Y = Ms + c2r (2)

where Y and r are the endogenous variables. Solve for Y and r using
matrix algebra.

How are these equilibrium values affected by increases in Ms?
Increases in T? (i.e.

nd the comparative statics)

Answer #1

Consider the following IS-LM model:
C=400+0.25YD
I=300+0.25Y-1500r
G=600
T=400
(M/P)D=2Y-1200r
(M/P)=3000
1-Derive the IS relation with Y on the left-hand side.
2-Derive the LM relation with r on the left-hand side.
3-Solve for equilibrium real output.
4-Solve for the equilibrium interest rate.
5-Solve for the equilibrium values of C, and I, and verify the
value you obtained for Y adding C, I and G.
6-Now suppose that the money supply increases to M/P=4320. Solve
for Y, r, C and I...

Solve the national income model in homework by matrix
inversionorby OR by Cramer’s Rule.
Y = C + I0+ G0+ (X-M)
C = a + b(Y-T+R), 0<b<1
T = tY, 0<t<1
where R is transfer payments, (X-M) is net exports, and the
other variables are as defined in class.

IS: Y = 7000 + 2.5*G – 1.5*T – 500*r
LM: r = [Y – 5*(MS/P)]/500
1. The AD curve of this economy, as a function of G, T, MS and P
is
[HINT: Note that you’ll get rid of the “500” in the denominator of
the LM curve since when you plug r from the LM curve into the IS
curve, you’ll have 500/500, which equals 1. Solve for Y]
(a) Y = 7500 + 2.5*G – 1.5*T +...

Assume the following IS-LM model: Y = C + I + G C = .8(1-t)Y t
=0.25 I = 900 - 50i G = 800 Md = 0.25Y -62.5i Ms =500.
(a)What will happen to the level of Y if G expands by 187.50?
(b) What will happen to the composition of GDP? Explain and derive
the numbers. (c). Was Investment crowded out? If so by how
much.

Problem 2. Consider the following example of
the IS-LM model:
C = 340 + 0.5(Y–T)
I = 400 – 1500(r + x) G = 150 T = 100 x=0.02
r = 0.04 ?e = 0.02
(1) Derive the IS equation.
(2) Find the equilibrium value of Y.
(3) Write down the zero lower bound constraint. Does the real
interest rate of r=0.04 satisfy the constraint?
(4) Suppose that the risk premium x has increased to x=0.09.
(a) Derive the new...

4.Consider the following IS-LM model:
C = 200+0.5 YD
I = 150+0.25Y-1000i
G=250
T=200
(M/P)d = 2Y-8000i
M/P=1600
a. Derive the IS relation
b. Derive the LM relation
c. Solve for the equilibrium real output.
d. Solve for the equilibrium interest rate.

Assume the following model of the economy, with the price level
fixed at 1.0:
C = 0.8(Y – T)
T = 1,000
I = 800 – 20r
G = 1,000
Y = C + I + G
Ms/P =
Md/P = 0.4Y –
40r
Ms = 1,200
A. Write a numerical formula for the IS curve, showing
Y as a function of r alone. (Hint:
Substitute out C, I, G, and
T.)
B. Write a numerical formula for the LM...

Consider the following Keynesian (short-run) model along with
the Classical (long-run) model of the economy.
Labor Supply: Le = 11
Capital Supply: K=11
Production Function:
Y-10K.3(Le).7
Depreciation Rate: &=.1
Consumption Function: C=12+.6Yd
Investment Function: I= 25-50r
Government Spending: G=20
Tax Collections: T=20
Money Demand Function: Ld=
2Y-200r
Money Supply: M=360
Price Level: P=2
Find an expression for the IS curve and plot it.
Find an expression for the LM curve and plot it.
Find the short run equilibrium level of...

Assume the following model of the economy, with the price level
fixed at 1.0:
C = 0.8(Y – T)
T = 1,000
I = 800 – 20r
G = 1,000
Y = C + I + G
Ms/P =
Md/P = 0.4Y –
40r
Ms = 1,200
a. Write a numerical formula for the IS curve, showing
Y as a function of r alone.
b. Write a numerical formula for the LM curve, showing
Y as a function of r...

Consider the following numerical example of the IS-LM model:
C = 100 + 0.3YD
I = 150 + 0.2Y - 1000i
T = 100
G = 200
i = 0.01
a) What is the equilibrium level out output (Y)?
b) suppose the government increase spending to G=300. What is
the new equilibrium level out output?
c) G = 200. What is the equilibrium supply of money id the
demand for money is given by (M/P)d = 2Y - 4000i?

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