Q1. Suppose that a closed economy is characterized by the following behavioral e

ID: 1153847 • Letter: Q

Question

Q1. Suppose that a closed economy is characterized by the following behavioral equations: C = co + c1YD YD = Y-T T, G and I are all constant.

(1) Please solve for equilibrium output.

(2) What is the multiplier?

(3) What is the autonomous spending? Suppose T = to + t1Y, C = co + c1YD, YD = Y-T G and I are both constant. Assume that 0< t1 <1 and to >0

(4) Please solve for equilibrium output.

(5) What is the multiplier?

(6) Compare your answer in parts (2) and (5). Does this economy respond more to changes in autonomous spending when t1 > 0?

(7) Why is fiscal policy in this case called an automatic stabilizer? (https://www.investopedia.com/terms/a/automaticstabilizer.asp)

C=co+c1YD

YD=Y-T

T,G and I are all constant

(1.) We know that, equilibrium output,Y=C+I+G

Putting all the values we get

Y=(co+c1(Y-T))+G+I

Y=co+c1Y-c1T+G+I

Y-c1Y=co-c1T+G+I

(1-c1)Y=co-c1T+G+I

Y=(co+G+I-c1T)/(1-c1)

(2.) Multiplier = 1/(1-c1)

(3.) Autonomous spending refers to the spending which doesn't depend on equilibrium output and is constant.

Autonomous spending,A= co+G+I-c1T

Now, C=co+c1YD

YD=Y-T T=to+t1Y

G and I are constant. 0<t1<1 and to>0

(4.) Equilibrium output,Y= C+I+G

Y=co+c1(Y-T)+I+G

Y= co+c1(Y-(to+t1Y))+I+G

Y=co+c1(Y-to-t1Y)+I+G

Y=co+c1Y-c1to-c1t1Y+I+G

Y-c1Y+c1t1Y=co-c1to+I+G

Y(1-c1(1-t1))=co-c1to+I+G

Y'=(co-c1to+I+G)/(1-c1(1-t1))

(5.) Multiplier= 1/(1-c1(1-t1))

(6.) Since, 1/(1-c1)>1/(1-c1(1-t1))

Therefore, economy respond more to change in autonomous spending when t1=0.

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