Question

An economy is described by the following equations:

C	= 100 + 0.8 (Y – T)
I p	= 80
G	= 140
NX	= 20
T	= 170
Y*	= 980

The multiplier in this economy is 5.

a. Find a numerical equation relating planned aggregate expenditure to output.

Instruction: Enter your response for mpc rounded to one decimal place.

PAE = + Y.

b. Construct a table to find the value of short-run equilibrium output.

Instruction: If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.

Output Y	Planned aggregate expenditure (PAE)	Y – PAE
820
920
1,020
1,120
1,220

Short-run equilibrium output is .

c. By how much would government purchases have to change in order to eliminate any output gap? By how much would taxes have to change?

Instruction: Enter your responses rounded to one decimal place.

In order to eliminate any output gap, government purchases would have to be (Click to select)reducedincreased by .

In order to eliminate any output gap, taxes would have to be (Click to select)reducedincreased by .

d. If Y* = 1,100, then by how much would government purchases have to change in order to eliminate any output gap? By how much would taxes have to change?

Instruction: Enter your responses as integer values.

In order to eliminate any output gap, government purchases would have to be (Click to select)reducedincreased by .

In order to eliminate any output gap, taxes would have to be (Click to select)increasedreduced by .

Answer 1

a. Find a numerical equation relating planned aggregate expenditure to output.

At equilibrium, PAE = Y

C + I + G + NX = PAE

100+0.8*(Y-170)+80+140+20 = PAE

204 + 0.8Y = PAE

b. Construct a table to find the value of short-run equilibrium output.

Output Y	Planned aggregate expenditure (PAE)	Y – PAE
820	860	-40
920	940	-20
1,020	1020	0
1,120	1100	20
1,220	1180	40

Short-run equilibrium output is 1020

c. By how much would government purchases have to change in order to eliminate any output gap? By how much would taxes have to change?

At the current level, equilibrium output is Y = 1020 and full employment equilibrium is 980. Hence output gap is +40. Tax multiplier is 0.8/1-0.8 = 4 and spending multiplier is 1/1-mpc = 1/1-0.8 = 5.

In order to eliminate any output gap of 40, government purchases would have to be reduced by 40/5 = $8.

In order to eliminate any output gap, taxes would have to be increased by 40/4 = $10.

d. If Y* = 1,100, then output gap is 1020 - 1100 = -$80.

In order to eliminate any output gap, government purchases would have to be increased by 80/5 = $16

In order to eliminate any output gap, taxes would have to be reduced by 80/4 = $20