Question

C = 100 + 0.75YD

I = 225 + 0.15Y - 600i

G = 450

T = 100

a. Derive the IS relation.

b. The central bank sets an interest rate of 75% (i = 0.75). How is
that decision represented in the equations?

c. What is the level of real money supply when the interest rate is
75%? Use the expression:

?? = 3 ? − 9 9 0 0 ?

d. Solve for the equilibrium values of C and I, and verify the value you obtained for Y by adding C, I, and G.

e. Now suppose that the central bank cuts the interest rate to 5% (i=0.05). How does this change the LM curve? Solve for Y, I, and C, and describe in words the effects of an expansionary monetary policy. What is the new equilibrium value of M/P supply?

f. Return to the initial situation in which the interest rate set by the central bank is 75%. Now suppose that government spending increases to G = 600. Summarize the effects of an expansionary fiscal policy on Y, I, and C. What is the effect of the expansionary fiscal policy on the real money supply?

Answer #1

(a)

YD = Y - T = Y - 100

In goods market equilibrium, Y = C + I + G

Y = 100 + 0.75(Y - 100) + 225 + 0.15Y - 600i + 450

Y = 775 + 0.75Y - 75 + 0.15Y - 600i

(1 - 0.75 - 0.15)Y = 700 - 600i

0.1Y = 700 - 600i

Y = 7000 - 6000i..........(1) (Equation of IS curve)

(b)

When i = 0.75,

I = 225 + 0.15Y - (600 x 0.75) = 225 + 0.15Y - 450 = 0.15Y - 225

Y = 7000 - (6000 x 0.75) = 7000 - 4500 = 2500

(c)

When i = 0.75, Y = 2500. So

MP = 3Y - 9900i = (3 x 2500) - (9900 x 0.75) = 7500 - 7425 = 75

(d)

When i = 0.75, Y = 2500. So

C = 100 + 0.75 x (2500 - 100) = 100 + 0.75 x 2400 = 100 + 1800 = 1900

I = 225 + (0.15 x 2500) - (600 x 0.75) = 225 + 375 - 450 = 150

Therefore, Y = 1900 + 150 + 450 = 2500 (Value of Y derived in part b)

NOTE: As per Answering Policy, 1st 4 parts are answered.

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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...

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C = 500 + 0.75(Y - T); I = 1000 - 50r; M/P = Y - 200r;
G = 1000; T = 1000; M = 6000; P = 2;
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government spending, T is taxes, r is the
real interest rate, M is the money supply, and P is the price
level.
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MS/P = 3,000
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G = 3,000
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I= 200-2500r, G=400, T=120+0.2Y
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LM: Y= (1/50) /( 50000+800000r)
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T = 100
G = 200
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Consider an economy characterized by the following equations for
consumption (C), investment (I), government spending (G), taxes
(T), aggregate demand (Z), output (Y), and the interest rate
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I = 16 + 0.1*Y – 300*i
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consumption (C), investment (I), government spending (G), taxes
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(i):
C = 54 + 0.3*(Y – T)
I = 16 + 0.1*Y – 300*i
G = 35
T = 30
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Suppose the central bank has set the interest rate equal to 2%
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a)...

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I = 150+0.25Y-1000i
G=250
T=200
(M/P)d = 2Y-8000i
M/P=1600
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b. Derive the LM relation
c. Solve for the equilibrium real output.
d. Solve for the equilibrium interest rate.

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