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For the following economy, find autonomous expenditure, the multiplier, short-run equilibrium output, and the output gap. By how much would autonomous expenditure have to change to eliminate the output gap? C = 3,000 + 0.5 (Y – T ) I p = 1,500 G = 2,500 NX = 200 T = 2,000 Y* = 12,000 Instruction: Enter your responses as integer values. Autonomous expenditure: . Multiplier: . Short-run equilibrium output: . Output gap: . Autonomous expenditure would need to by to eliminate the output gap.

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Answer:

1. Autonomous expenditure = 6200

2. multiplier = 2

3. short run equilibrium = $12,400

4. Output gap = $400

Explanation:

Given Data:

C = 3,000 + 0.5 (Y – T )

I p = 1,500

G = 2,500

NX = 200

T = 2,000

Y = 12,000

Calculating the planned aggregate expenditure using the formula;

PAE = C + Ip + G + Nx

Substituting, we have;

PAE = 3,000 + 0.5 (Y – T) +  Ip + G + Nx

PAE = 3,000 + 0.5 (Y – 2,000) + 1,500 + 2,500 + 200

       = 3000 + 0.5Y - 1000 + 1500 +  2,500 + 200

      = 6200 + 0.5Y

1. Calculating the autonomous expenditure, taking Y =0, we have;

autonomous expenditure = 6200 + 0.5*0

                                           = 6200

2. Calculating the multiplier using the formula;

Multiplier = 1/(1-Mpc)

               = 1/(1-0.5)

               = 2

3. Calculating the short run equilibrium, using the formula;

PAE = Y

6200 + 0.5Y= Y

Y - 0.5Y = 6200

0.5Y = 6200

Y = 6200/0.5

Y  = 12,400

(4) Output gap:

Given output = $12000

Short run equilibrium = $12,400

Expansionary output gap = 12,400 - 12,000

                                           = $400

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