Problem 4 Suppose an imaginary economy is represented by the following equations

Question

Problem 4 Suppose an imaginary economy is represented by the following equations: GDP = C+I C I $100 + 0.8YD I Planned + |Unplanned = = IPlanned$200 AEPlannedCIPlanned Make sure you show your work in your answers. (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 of $200, suppose that autonomous consumption spending decreases from $100 to 860. What will the new equilibrium GDP be? Show your work. (A) Calculate the value of the multiplier.

Explanation / Answer

Since tax=0

YD=Y

C=100+0.8Y

1) At equilibrium

GDP = AEd

C+I= C+Iplanned

I= Iplanned = $ 200

GDP=Y=C+I=100+0.8Y+200

0.2 Y= 300

Y=1500

GDP =$ 1500

2) Whn Iplanned decreases by $ 50, Iplanned= 200-50 =150

I=I planned= $ 150

Y=100+0.8Y+150

Y=1250

GDP=Y=$ 1250

3) new C= 60+0.8Y

Y=60+0.8 Y+200

Y=260*10/2 = $ 1300

GDP = $ 1300

4) multiplier = 1/(1-c)

c=0.8

multiplier = 1/(1-0.8) = 5

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