The following equations describe an economy. IS Function C = 600 + (.7)(1-t) Y t

Question

The following equations describe an economy.

IS Function C = 600 + (.7)(1-t) Y t = .15 I = 1500 – 75 (i) I = 6 (6%) G = 1000

LM Function L = .3 Y – 65 (i) M/P = 900

a. What is the equilibrium income level and rate of interest?

b. Suppose, as is being debated today, there is an decrease in the tax rate, t, from .15 to .10. What will be the change in the equilibrium level of income and interest rate?

c. Suppose there is new federal government infrastructure spending increasing government expenditures (G) from 1000 to 1500, given the parameters in part “a” what will be the new equilibrium income level and interest rate?

d. Suppose there is an increase in the money supply from 900 to 1200 given the parameters given in part “a” what will be the new equilibrium level of income and interest rate?

Explanation / Answer

C = 600 + 0.7 x (1- t) x Y

I = 1,500 - 75i

G = 1,000

L = 0.3Y - 65i

M/P = 900

(a)

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

Y = 600 + 0.7 x (1 - 0.15) x Y + 1,500 - 75i + 1,000

Y = 3,100 + 0.7 x 0.85Y - 75i

Y = 3,100 + 0.595Y - 75i

(1 - 0.595)Y = 3,100 - 75i

0.405Y = 3,100 - 75i

Y = 7,654 - 185i.........(1) [Equation of IS]

In money market equilibrium (M/P) = L

900 = 0.3Y - 65i

0.3Y = 900 + 65i

Y = 3,000 + 217i..........(2) [Equation of LM]

In general equilibrium, IS = LM

7,654 - 185i = 3,000 + 217i

402i = 4,654

i = 11.58%

Y = 3,000 + (217 x 11.58) = 3,000 + 2,512.86 = 5,512.86

(b) When t = 0.1, new IS equation is

Y = 600 + 0.7 x (1 - 0.1) x Y + 1,500 - 75i + 1,000

Y = 3,100 + 0.7 x 0.9Y - 75i

Y = 3,100 + 0.63Y - 75i

0.37Y = 3,100 - 75i

Y = 8,378 - 203i

Equating with LM equation,

8,378 - 203i = 3,000 + 217i

420i = 5,378

i = 12.8%

Y = 3,000 + (217 x 12.8) = 3,000 + 2,777.6 = 5,777.6

(c) When G increases by 500 (= 1,500 - 1,000), for IS equation,

(1 - 0.595)Y = 3,100 + 500 - 75i

0.405Y = 3,600 - 75i

Y = 8,889 - 185i

Equating with LM equation,

8,889 - 185i = 3,000 + 217i

402i = 5,889

i = 14.65%

Y = 3,000 + (217 x 14.65) = 3,000 + 3,179 = 6,179

(d) (M/P) = 1,200. From LM equation,

1,200 = 0.3Y - 65i

0.3Y = 1,200 + 65i

Y = 4,000 + 217i [Equation of new LM]

Equating with IS equation,

7,654 - 185i = 4,000 + 217i

402i = 3,654

i = 9.09%

Y = 4,000 + (217 x 9.09) = 4,000 + 1,972.53 = 5,972.53

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