Question

3. The components of planned aggregate spending in a certain economy are given by Consumption Function: C = 800 + 0.75(Y - T) – 2000r Planned Investment: I p = 400–3000r Government Revenue and Spending: T = 300 and G = 450 Net Export: NX = 75 where r is the real interest rate (For example, r = 0.01 means that the real interest rate is 1 percent). (1) Find the level of public saving. (2) Suppose that the real interest rate is 5%. Show the autonomous consumption level and the autonomous expenditure level. (3) How does a two percentage point decrease in the real interest rate affect the short-run equilibrium output? 7 (4) Suppose that the potential output of this economy equals 4800. Find the short-run equilibrium real interest rate that brings the economy to full employment. (5) Suppose Government Revenue T = tY (0< t <1); r stays at the initial level (5%), Please calculate the multiplier effect of the government spending increase on the output change (ΔY/ΔG).

Answer 1

3.

C = 800 + 0.75(Y - T) – 2000r

Planned Investment: I p = 400–3000r

where r is the real interest rate

Government Revenue and Spending: T = 300 and G = 450

Net Export: NX = 75

1)

Public saving refers to the amount saved by the government out of its revenue.

Revenue of government= Tax= 300

Government expenditure= G= 450

Public saving= T-G= 300-450= -150

2)

Autonomous consumption refers to the level of consumption at zero level of disposable income(Y-T=0).

C = 800 + 0.75(Y - T) – 2000r

Autonomous consumption= 800+0.75(0)-2000(0.05)= 800-100= 700

Automous expenditure= Autonomus consumption + Autonomous investment+ G+NX

Autonomous investment refers to the investment which does not vary with real interest rate or income.

I p = 400–3000r

Autonomous investment= 400-3000(0)= 400

Automous expenditure= 700 +400+ 450+75= 1625

3)

Two percentage point decrease in real interest rate.

New real interest rate = 3%

Initial equilibrium(When r=0.05):

Y= C+I+G+NX

Y= 800 + 0.75(Y - T) – 2000r+400–3000r+450+75

Y= 700+0.75(Y-300)+400-3000(0.05)+525

Y= 1250+0.75Y

0.25Y = 1250

Y= 5000 Initial Equilibrium output

After decrease in r by 2% points:

Y= C+I+G+NX

Y= 800 + 0.75(Y - T) – 2000r+400–3000r+450+75

Y= 800+0.75(Y-300)-2000(0.03)+400-3000(0.03)+525

Y= 1350+0.75Y

0.25Y = 1350

Y= 5400 New Equilibrium output

Equilibrium output increases at real interest rate decreases by 2% points.

4) Potential output=Y= 4800

Y= C+I+G+NX

4800= 800 + 0.75(Y - T) – 2000r+400–3000r+450+75

4800-800-0.75(4800-300)-400-525= -5000r

-300 = -5000r

r = -300/-5000= 0.06= 6%

The short-run equilibrium real interest rate that brings the economy to full employment is 6%.