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.

1. 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:

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

1. 2. Taxes must be cut in order to restore the initial equilibrium level of income, given no change in government spending or the interest rate.
2. 3. 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.

Answer 1

Consumption function: C = Ca + c x (Y - Ta) = 1,500 - 10r + 0.6 x (Y - 1,800) = 1,500 - 10r + 0.6Y - 1,080 = 420 + 0.6Y - 10r

(a)

Ep = C + Ip + G + NX

Ep = 420 + 0.6Y - 10r + 2,400 - 50r + 2,000 - 200

Ep = 4,620 + 0.6Y - 60r

Ap = 4,620 - 60r, which includes autonomous consumption (ca), Investment, government spending and net exports.

(b)

In equilibrium, Y = Ep

Y = 4,620 + 0.6Y - 60r

0.4Y = 4,620 - 60r

Y = 11,550 - 150r

Multiplier = 1 / (1 - c) = 1 / (1 - 0.6) = 1 / 0.4 = 2.5

(c)

MPS = 1 - MPC = 1 - 0.6 = 0.4

(d)

When r = 5,

Ap = 4,620 - 60 x 5 = 4,620 - 300 = 4,320

(e)

When r = 5,

Y = 11,550 - 150 x 5 = 11,550 - 750 = 10,800

NOTE: As HOMEWORKLIB Answering Policy, 1st 5 parts have been answered.