An economy is described by the following equations: = 80 + 0.75 ( Y – T ) = 100

Question

An economy is described by the following equations:

= 80 + 0.75 (Y – T)

= 100

= 150

= 30

= 180

= 840

The multiplier in this economy is 4.

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

700

800

900

1,000

1,100

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)increasedreduced by .

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

d. If Y* = 948, 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)reducedincreased by .

C

= 80 + 0.75 (Y – T)

I p

= 100

G

= 150

NX

= 30

T

= 180

Y*

= 840

Explanation / Answer

(a) PAE = C + I + G + NX

            = 80 + 0.75 (Y – T) + 100 + 150 + 30

             = 80 + 0.75 (Y – 180) + 100 + 150 + 30

            = 80 + 0.75Y – 135 + 100 + 150 + 30

        PAE    = 225 + 0.75Y

(b)

Short-run equilibrium output is = 900

(c) Output gap = Y* - Y = 840 - 900 = - 60 (inflationary gap)

As the multiplier is 4, this gap can be eliminated by reducing government purchases by 15 (i.e. 60/4=15). Alternatively, increase taxes by 15/0.75 = 20. Because the MPC is 0.75, an increase in taxes of 20 will also reduce autonomous expenditure by 15 and output by 15*4 = 60.

(d) If Y* = 948, Output gap = Y* - Y = 948 - 900 = 48 (recessionary gap)

As the multiplier is 4, this gap can be eliminated by raising government purchases by 12 (i.e. 48/4 = 12). Alternatively, cut taxes by 12/0.75 = 16. Because the MPC is 0.75, a cut in taxes of 16 will also stimulate autonomous expenditure by 12 and output by 12 * 4 = 48.

Y PAE= 225 + 0.75Y Y - PAE 700 750 -50 800 825 -25 900 900 0 1000 750 250 1100 1050 50

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