Question

Consider a closed economy where aggregate expenditure is AE = C + I + G. Government purchases (G) is a constant, which do not vary with output level (Y). Consumption (C) is an increasing function of disposable income YD: C = a + bYD. In this economy, we have lump sum tax only; YD = Y –T. Investment is an increasing function of Y: I = k + iY.

1. The equilibrium condition is Y = AE. Solve for the equilibrium Y of the economy.

2. What are the multipliers with respect to the autonomous expenditures (a, k, G) and tax (T)?

3. Solve for the equilibrium disposable income.

4. Solve for the equilibrium consumption.

5. Solve for the equilibrium investment.

6. Solve for the equilibrium private saving (the saving of households) and total saving (private saving + government saving). Is the total saving equal to investment?

7. Do the private saving and total saving vary with autonomous consumption(a) or marginal propensity to consume(b)? If it is the case, how do the private saving and total saving vary with a?

Answer 1

(1)

In equilibrium, Y = AE

Y = C + I + G

Y = a + bYD + I + G

Y = a + b(Y - T) + k + iY + G

Y = a + bY - bT + k + iY + G

(1 - b - i)Y = a - bT + k + G

Y = (a - bT + k + G) / (1 - b - i)

(2)

Y = (A - bT) / (1 - b - i), where A = Autonomous expenditure = a + k + G

Multiplier with respect to autonomous expenditures = Y/A = 1 / (1 - b - i)

Multiplier with respect to tax = Y/T = -b / (1 - b - i)

(3)

YD = Y - T

YD = [(a - bT + k + G) / (1 - b - i)] - T

YD = (a - bT + k + G - T + bT + iT) / (1 - b - i)

YD = (a + k + G - T + iT) / (1 - b - i)

(4)

C = a + bYD

C = a + [b x {(a + k + G - T + iT) / (1 - b - i)}]

C = (a - ab - ai + ab + bk + bG - bT + biT) / (1 - b - i)

C = (a - ai + bk + bG - bT + biT) / (1 - b - i)

(5)

I = k + iY

I = k + [i x {(a + k + G - T + iT) / (1 - b - i)}]

I = (k - bk - ki + ai + ki + iG - iT + i²T) / (1 - b - i)

I = (k - bk + ai + iG - iT + i²T) / (1 - b - i)

NOTE: As per Answering Policy, 1st 5 parts are answered.