Question

Principles of Macroeconomics

Assignment (2)

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Given the following equations (all numbers are in million $)

C = 100 + 0.60Y_d

I_P = 80

G = 70

T = 30 + 0.10Y

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1. Find the equilibrium output (Income)?
2. Find the consumption and saving at equilibrium?
3. Show that leakages (S+T) = Injections (I+G)
4. What is the government’s budget deficit (or surplus)?
5. What happens to equilibrium output if:

1. I_P decreases to 50
2. G increases by 30
3. T₀ increases by 10

Answer 1

A) C = 100 + 0.60Yd

C = 100 + 0.60(Y-T)

C = 100 + 0.60(Y-(30+ 0.1Y)

C = 100 + 0.60(Y- 30 - 0.1Y)

C = 100 + 0.60Y- 18 - 0.06Y

C = 82 + 0.54Y

So,

Y = C + IP + G

Y = 82 + 0.54Y+ 80 + 70

Y = 232 + 0.54Y

Y - 0.54Y = 232

0.46Y = 232

Y = 232 / 0.46 = $504.35 million

Thus, the equilibrium output is $504.35 million.

B) C = 82 + 0.54Y = 82 + 0.54(504.35) = $354.35 million

Yd = Y - T = Y - 30 - 0.10Y = 504.35 - 30 - 0.10(504.35) = $423.92

Savings (S) = Yd - C = $423.92 - $354.35 = $69.57

Thus, the consumption is $354.35 million and saving $69.57.

C) T = 30 + 0.10Y = 30 + 0.10(504.35) = $80.43

S + T = I + G

69.57 + 80.43 = 80 + 70

150 = 150          [proved]

D) The government’s budget surplus = 80.43 - 70 = $10.43 million.

E) If, IP decreases to 50

G increases by 30

T increases by 10

T = 30 + 0.1Y + 10 = 40 + 0.1Y

C = 100 + 0.60Yd

C = 100 + 0.60(Y-T)

C = 100 + 0.60(Y-(40+ 0.1Y)

C = 100 + 0.60(Y- 40 - 0.1Y)

C = 100 + 0.60Y- 24 - 0.06Y

C = 76 + 0.54Y

G = 70 + 30 = 100

So,

Y = C + IP + G

Y = 76 + 0.54Y+ 50 + 100

Y = 226 + 0.54Y

Y - 0.54Y = 226

0.46Y = 226

Y = 226 / 0.46 = $491.30 million

Thus, the equilibrium output is $491.30 million.