Suppose an imaginary economy is represented by the following equations: GDP= C +

Question

Suppose an imaginary economy is represented by the following equations:

GDP= C + I

C= $100 + 0.8 Y D

I = I Planned + I Unplanned

Iplanned = $200

AEplanned = C+IPlanned

(1) Calculate the income- expenditure equilibrium level GDP. Show your work.

(2) Suppose the level of planned investment spending (Iplanned) drops by $50 . What will the new equilibrium GDP be? Show your work

(3) With Iplanned back at the original level $200, suppose that autonomous consumption spending decreases from $100 to $60. What will the new equilibrium be? Show your work.

(4) Calculate the value of the multiplier.

Explanation / Answer

GDP = 100+0.8Y+I

Under equilibrium, unplanned investment is zero, so Ip+iup = 200

Y=C+I, where C=100+0.8Y

Y = 100+0.8Y+200

Y-0.8Y=100+200

0.2Y=300; Y=1500.

So C=100+0.8*1500=100=1200=1300.

So the income- expenditure equilibrium level GDP will be $1500.

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If Iplanned drops by $50, then Ip will be $150

Y = 100+0.8Y+150 = 250+0.8Y

Y-0.8Y = 250; 0.2Y = 250

Y= 250x5 = $1250.

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When consumption reduces to $60. Y=C+I, where C=60+0.8Y

Y = 60+0.8Y+200

Y-0.8Y=100+160

0.2Y = 260; Y= 260x5 = $1300.

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