Question

Consider an economy in which taxes, planned investment,
government spending on goods and services, and net exports are
autonomous, but consumption and planned investment change as the
interest rate changes. You are given the following information
concerning autonomous consumption, the marginal propensity to
consume, planned investment, government purchases of goods and
services, and net exports:

Ca = 1,500 – 10r; c = 0.6; Ta = 1,800; Ip = 2,400 – 50r; G =
2,000; NX = -200

(a)Derive Ep and determine its autonomous (Ap) and induced
components.

(b)Derive equilibrium Y and determine multiplier.

(c)Compute the value of marginal propensity to save.

(d)Compute the amount of autonomous planned spending, Ap,
given that the interest rate equals 5.

(e)Compute the equilibrium level of income, given that the
interest rate equals 5.

(f)Suppose that autonomous consumption changes by 4 percent of
any change in household wealth and that the decline in the housing
market in 2006-07 and drop in the stock market in the summer of
2007 reduces household wealth by $750 billion. Compute the decrease
in autonomous consumption that results from the decline in
household wealth.

(g)Calculate the new amount of autonomous planned spending,
Ap, and the new equilibrium level of income, given that the
interest rate equals 5.

(h)Using your answers to parts d-g, compute the value of
multiplier

(i) Fiscal and monetary policymakers can respond to the
decline in household wealth by taking actions that restore income
to its initial equilibrium level. Fiscal policy makers can increase
government spending or cut taxes or do both. Monetary policymakers
can reduce interest rates. Given the values of the multiplier, the
tax multiplier, and the balanced budget multiplier, compute by how
much:

i. Government spending must be increased in order to restore
the initial equilibrium level of income, given no change in taxes
or the interest rate.

ii. Taxes must be cut in order to restore the initial
equilibrium level of income, given no change in government spending
or the interest rate.

iii. Government spending and taxes must be increased in order
to restore the initial equilibrium level of income, given no change
in the government budget balance or the interest rate.

iv. The interest rate must be reduced in order to restore the
initial equilibrium level of income, given no change in government
spending or taxes.

Answer #1

a) Planned expenditure (Ep)=C+Ip+G+Nx=1500-10r+0.6(y-1800)+2400-50r+2000+(-200)

Ep=4620+0.6Y- 60r

Autonomous components(Ap)=Ca+Ia+G+Nx=1500-10r+2400-50r+2000-200=5700-60r

Induced components=0.6(Y-Ta)=0.6y-0.6*1800=0.6Y-1080

B)The equilibrium where ,

Y=Ep

Y=4620+0.6Y-60r

0.4Y=4620-60r

Y=11,550-150r

Multiplier=1/(1-mpc)=1/(1-0.6)=1/0.4=10/4=2.5

C) marginal propensity to save=1- MPC ( marginal propensity to consume)=1-0.6=0.4

D)Ap=5700-60r

r=5

Ap=5700-60*5=5700-300=5400

E)Y=11,550 -150r=11,550-150*5=11,550-750=10,800

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Aggregate Output/Income
Net Taxes
Planned Investment
Aggregate Consumption
Government Spending
1,000
200
200
680
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200
760
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200
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1,600
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