Question

Consider an open economy where aggregate expenditure is AE = C + I + G + NX. Investment (I), government purchases (G), and net export (NX) are constants, which do not vary with output level (Y). Only consumption (C) is an increasing function of Y; in particular, C is a linear function of Y: C = a + b(Y –T +TR), where T is tax and TR is transfer payment. 1. Recall that the equilibrium condition is Y = AE. Solve for the equilibrium Y of the open economy. 2. Solve for the equilibrium disposable income (YD) 3. Solve for the equilibrium consumption (substitute the equilibrium Y into the consumption function). 4. Solve for the equilibrium private saving (the saving of households) and total saving (private saving + government saving). 5. the private saving and total saving depend on autonomous consumption(a)or marginal propensity to consume(b)?

Answer 1

(1)

In equilibrium, Y = AE

Y = C + I + G + NX

Y = a + b(Y - T + TR) + I + G + NX

Y = a + bY - bT + bTR + I + G + NX

(1 - b)Y = a - bT + bTR + I + G + NX

Y = [a - bT + bTR + I + G + NX] / (1 - b)

(2)

YD = Y - T + TR

YD = {[a - bT + bTR + I + G + NX] / (1 - b)} - T + TR

YD = [a - bT + bTR + I + G + NX - T + bT + TR - bTR] / (1 - b)

YD = [a - T + TR + I + G + NX] / (1 - b)

(3)

C = a + bYD

C = a + b x {[a - T + TR + I + G + NX] / (1 - b)}

C = [(a - ab + ab - bT + bTR + bI + bG + bNX) / (1 - b)]

C = (a - bT + bTR + bI + bG + bNX) / (1 - b)

(4)

Private saving (Sp) = Y - C

Sp = {[a - bT + bTR + I + G + NX] / (1 - b)} - {(a - bT + bTR + bI + bG + bNX) / (1 - b)}

Sp = (a - bT + bTR + I + G + NX - a + bT - bTR - bI - bG - bNX) / (1 - b)

Sp = (I + G + NX - bI - bG - bNX) / (1 - b)

Sp = [(I + G + NX) (1 - b)] / (1 - b)

Sp = I + G + NX

Total saving (S) = Sp + T - G - TR

S = I + G + NX + T - G - TR

S = I + NX + T - TR

NOTE: As per Answering Policy, 1st 4 parts are answered.