Question

An economy is initially described by the following equations:
C = 500 + 0.75(Y - T); I = 1000 - 50r; M/P = Y - 200r;
G = 1000; T = 1000; M = 6000; P = 2;
where Y is income, C is consumption, I is investment, G is government spending, T is taxes, r is the
real interest rate, M is the money supply, and P is the price level.
a. Derive the IS equation and the LM equation. Calculate the equilibrium interest rate and level of
income.
b. Derive the AD (aggregate demand) equation.

c. Suppose that a newly elected president cuts taxes by 20 percent. Assuming the money supply is held constant, what are the new equilibrium interest rate and level of income?
d. Now assume that the central bank adjusts the money supply to hold the interest rate constant. What is the new level of income? What must the new money supply be?
e. Now assume that the central bank adjusts the money supply to hold the level of income constant. What is the new equilibrium interest rate? What must the money supply be?

Answer 1

A) IS Equation;Y= C+ I+G

Y=500 + 0.75(Y -1000 )+1000 - 50r+ 1000=1750+0.75y-50r

Y=7000-200r{ IS Equation}

LM Equation;real money demand= real Money supply

Y-200r=6000/2

Y-200r=3000

Y=3000+200r { LM Equation}

Putting IS Equation into LM,

7000-200r=3000+200r

4000=400r

r=4000/400=10

Y=7000-200*10=5000

B)Y-200r=6000/P{ LM Equation}

r=0.005Y-30/P { inverse LM Equation}

Putting inverse LM into IS,

Y=7000-200(0.005Y-30/p)

Y=7000-Y+6000/p

Y=3500+3000/p{ AD equation}

C)New T=1000-0.2*1000=800

New IS Equation: Y=500 + 0.75(Y -800 )+1000 - 50r+ 1000=1900+0.75y-50r

Y=7600-200r { New IS Equation}

Putting same LM into new IS Equation:,

3000+200r=7600-200r

10,600=400r

r=4600/400=11.5

Y=7600-200*11.5=5300

D) Setting interest equal to initial level ,r=10, into new IS Equation.

Y=7600-200*10=5600

Y-200r= Ms/p

5600-200*10=Ms/2

3600=Ms/2

Ms=7200( new Money supply}