Answer the questions below based on the following economy:

C= 4,000 + 0.25(Y-T)

I=I₀= 2,000G=G₀= 1,000X= 400IM= 100T=T₀= 1,000Y_p= 10,000

Note:Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places.

a)Find autonomous expenditure.

Autonomous Expenditure = $

5,050

b)Find the multiplier.

Multiplier =

2

c)Find short-run equilibrium output.

Short-run Equilibrium Output = $

10,100

d)Find the output gap.

Output Gap = $

100

e)By how much would autonomous expenditure have to change to eliminate the output gap?

Decrease

by $

200

Marking:

To find the answers below, we need to know the formula for planned aggregate expenditure:

AE=C+I+G+X-IM

AE= 4,000 + 0.25(Y- 1,000) + 2,000 + 1,000 + 400 - 100

AE= 7,050 + 0.25Y

a)

Autonomous Expenditure

Your answer was:$5,050.00

The correct answer was:$7,050.00

Autonomous expenditure equals the part of aggregate expenditure that does not depend on output.

You will lose 2 marks for this part.

b)

Multiplier

Your answer was:2.00

The correct answer was:1.33

The multiplier can be found by using the formula:11 - slope of AE=11 - 0.25= 1.33

Alternatively, imagine that autonomous expenditure rises from 7,050 to 7,150.

Now the equationY=AEbecomesY= 7,150 + 0.25Y.

Solving for output yieldsY= 9,533.33 a decrease of -133.33 over the short-run equilibrium output (part (c)).

We have shown that an increase in autonomous expenditure of 100 reduces short-run equilibrium output by -133.33.

Therefore the multiplier must equal 1.33.

You will lose 2 marks for this part.

c)

Short-run Equilibrium Output

Your answer was:$10,100.00

The correct answer was:$9,400.00

You have correctly deduced this from your earlier answers; however, at least one of your earlier answers was incorrect, causing your answer for this part to be incorrect.

You will not lose any further marks for this.

d)

Output Gap

Your answer was:$100.00

The correct answer was:-$600.00

You have correctly deduced this from your earlier answers; however, at least one of your earlier answers was incorrect, causing your answer for this part to be incorrect.

You will not lose any further marks for this.

e)

Type of Change

Your answer was:Decrease

The correct answer was:Increase

You have correctly deduced this from your earlier answers; however, at least one of your earlier answers was incorrect, causing your answer for this part to be incorrect.

You will not lose any further marks for this.

Amount of Change

Your answer was:$200.00

The correct answer was:$451.13

As the multiplier is 1.33, to eliminate the output gap of -600, autonomous expenditure would have to change by 451.13 (-1/1.33 * -600), that is, autonomous expenditure would have to increase by $451.13.

You will lose 1 mark for this part.

Total marks for this question: 5

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Could you explain how they got the Short-run Equilibrium Output, Output gap and Type of Change?