An economy is characterized by the following behavioral equations: C = 100 + .5

Question

An economy is characterized by the following behavioral equations:

C = 100 + .5 Y D

I = 50 + .1 Y

G = 100

T = .2 Y

Solve for each of the following at equilibrium. Show your calculations.

a) Equilibrium GDP ( Y ), 10 pts.

Be sure to calculate the correct value of Y at equilibrium, Y = 500.

b) Disposable income ( Y D ), 5 pts.

c) Consumption spending ( C ), 5 poionts

Question I, continued

To repeat, the economy of this question is characterized by the following behavioral equations:

C = 100 + .5 Y D

I = 50 + .1 Y

G = 100

T = .2 Y

Solve for each of the following at equilibrium. Show your calculations.

d) Private saving ( S ), 5 pts.

e) Public saving ( T – G ), 5 pts.

f) Suppose government spending increases by 10 (G=10).

a. By how much will private saving change? (S=?), 5 pts.

b. Why does private saving change when the government spends more in this

economy (i.e., in the economy of this question)? 5 pts.

Explanation / Answer

a) Y = C + I + G

       = 100 + .5 Y + 50 + .1 Y + 100

Y = 250 + 0.6Y

=> Y - 0.6Y = 250

=> 0.4Y = 250

=> Y = 250 / 0.4 = $625

b) T = .2 Y = 0.2 (625) = $125

Thus, Disposable Income(YD) = Y - T = 625 - 125 = $500

c) C = 100 + .5 YD = 100 + .5 (500) = $350

d) Private savings = Y - T - C = 625 - 125 - 350 = $150

e) Public Savings = T - G = 125 - 100 = $25

f) If government spending increases by 10 (G=10),

    a) Y = C + I + G

       = 100 + .5 Y + 50 + .1 Y + 110

Y = 260 + 0.6Y

=> Y - 0.6Y = 260

=> 0.4Y = 260

=> Y = 260 / 0.4 = $650

T = .2 Y = 0.2 (650) = $130

Disposable Income(YD) = Y - T = 650 - 130 = $520

C = 100 + .5 YD = 100 + .5 (520) = $360

Private savings = Y - T - C = 650 - 130 - 360 = $160

Thus, S= $160 - $150 = $10

b) In a closed economy;

G – T = S – I

G – T is referred to as the budget deficit or government balance. And, S – I is referred to as net private saving or the private sector balance.

S = Y – T – C

S – I = (Y – T) – (C + I)

When the private sector spends less than its disposable income, it is said to be in surplus. When it spends more than its income, it is in deficit.

It can be written as:

Budget Deficit = Net Private Saving

or

Government Deficit = Private Sector Surplus

Therefore, when government spends, it means there is budget deficit and it increase private saving(S).

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