Question

An economy is initially described by the following equations:

C=500+0.75(Y−T) I=1,000−50r M/P=Y−200r G=1,000

T=1,000 M=6,000

P=2
Y,C,I,G& T are all in billions of dollars.

1. Derive and graph the IS curve and the LM curve. Calculate the equilibrium interest rate and income. Label that point A on your graph.

2. To mitigate the economic impact of COVID_19 on the economy, suppose the government cuts taxes by 20 percent. Assuming that the money supply is held constant, what are the new equilibrium interest rate and income? What is the tax multiplier?

3. Now assume that the Fed adjusts the money supply to hold the interest rate constant. What is the new equilibrium income? What must the new money supply be? What is the tax multiplier?

4. Now assume that the Fed adjusts the money supply to hold income constant. What is the new equilibrium interest rate? What must the money supply be? What is the tax multiplier?

5. Show the equilibria you calculated in parts (b), (c), and (d) on the graph you drew in part (a). Label them points B, C, and D.

Answer 1

(1)

Goods market equilibrium condition: Y = C + I + G

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

Y = 2500 + 0.75Y - 750 - 50r

0.25Y = 1750 - 50r

Y = 7000 - 200r.............(IS curve)

Money market equilibrium condition: (M/P)d = (M/P)s

Y - 200r = 6000/2

Y - 200r = 3000

Y = 3000 + 200r..........(LM curve)

Equating IS = LM,

7000 - 200r = 3000 + 200r

400r = 4000

r = 10

Y = 3000 + 200 x 10 = 3000 + 2000 = 5000

(b)

New T = 1000 x 80% = 800

Y = 500 + 0.75(Y - 800) + 1000 - 50r + 1000

Y = 2500 + 0.75Y - 600 - 50r

0.25Y = 1900 - 50r

Y = 7600 - 200r.............(New IS curve)

Equating New IS = LM,

7600 - 200r = 3000 + 200r

400r = 4600

r = 11.5

Y = 3000 + 200 x 11.5 = 3000 + 2300 = 5300

Tax multiplier = Change in Y / Change in T = (5300 - 4500) / (800 - 1000) = 800 / (- 200) = - 4

(c)

When r = 11.5,

Using new IS equation from (b),

Y = 7600 - 200 x 11.5 = 7600 - 2300 = 5300

Tax multiplier = (5300 - 5000) / (- 200) = 300 / (- 200) = - 1.5

In money market,

Y - 200r = M/2

5300 - (200 x 11.5) = M/2

5300 - 2300 = M/2

3000 = M/2

M = 6000

Increase in M = 6000 - 6000 = 0

(d)

When Y = 5000, From new IS equation as in (b),

5000 = 7600 - 200r

200r = 2600

r = 13

Tax multiplier = 0 (Because output is the same)

In money market,

5000 - 200r = M/2

5000 - (200 x 13) = M/2

5000 - 2600 = M/2

2400 = M/2

M = 4800

Decrease in M = 6000 - 4800 = 1200