Question

n a simple closed economy where there is no government and investment, the consumption function of...

n a simple closed economy where there is no government and investment, the consumption function of households is given by C(Y)=60+0.6Y. The potential output in this economy at 450.

a. What is the consumption expenditure when income is equal to zero?

b.  What is the break-even point Y?

c. By how much will equilibrium income change due to the addition of investment?

d. Suppose, now our simple closed economy added an intended investment I=100, the consumption function of households is still given by C(Y)=60+0.6Y. The potential output in this economy is still at 450. If the government is to pursue a balanced budget, and tax is in the form of a head tax (a.k.a., lump-sum tax) what should G=T be for the economy to achieve the potential output of 450?

Consumption function is C(Y)=60+0.6Y

We have,

C(Y)=60+0.6Y

When Income Y = 0,

Consumption Expenditure      = 60 + 0.6 x 0

= 60

At Break even point the income = consumption or savings = 0.

Therefore,

Y=C

Y= 60 + 0.6 Y

Y - 0.6Y = 60

0.4 Y = 60

Y = 60 / 0.4 = 150

Hence, the break-even level of income is 150.

At equilibrium,

Y= C+I

=> Y= 60 + 0.6 (Y) + I

=> Y(1-0.6) = 60 + I

=> Y = 2.5 I + 150

Consumption Function is C = 60+ 0.6 Y where Y in the income in the economy.

At equilibrium level of income,

Y= C+I – T + G

=> Y= 450 + 0.6 Y + 100 – T + G

=> Y - 0.6 Y = 550 –T+G

=> 0.4 Y = 550 – T + G

=> 0.4 x 450 = -T + G

=> G = T + 180

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