In an economy, the consumption function is given as C = ₦50\text{ billion} + 0.8 Y_d, wher… — JAMB UTME

In an economy, the consumption function is given as $C = ₦50\text{ billion} + 0.8 Y_d$ , where $Y_d$ represents disposable income. The government levies a flat proportional income tax rate of $25\%$ ( $t = 0.25$ ) on total national income ( $Y$ ). If the economy is currently experiencing a recessionary output gap of $₦200\text{ billion}$ , calculate the required increase in government expenditure ( $\Delta G$ ), in billions of Naira, to achieve full-employment equilibrium.

Answer: 80 billion Naira

Answer

The required increase in government expenditure is 80 billion Naira.

With a marginal propensity to consume of

0.8

and a proportional tax rate of

0.25

, the effective consumption propensity relative to total income is

0.8 \times (1 - 0.25) = 0.6

. The spending multiplier is

K_g = \frac{1}{1 - 0.6} = 2.5

. Closing a

₦200\text{ billion}

recessionary gap requires an initial government spending increase of

\frac{₦200\text{ billion}}{2.5} = ₦80\text{ billion}

Step-by-Step Solution

Determine the effective marginal propensity to consume out of total income (

MPC_Y

)

MPC_Y = 0.8 \times (1 - 0.25) = 0.6

Taxation reduces disposable income, so out of every additional unit of national income, only

(1 - t)

remains available for consumption.

Calculate the fiscal spending multiplier (

K_g

)

K_g = \frac{1}{1 - 0.6} = 2.5

The expenditure multiplier accounts for the automatic leakage caused by proportional income taxes.

Calculate the necessary government spending injection (

\Delta G

)

\Delta G = \frac{200}{2.5} = 80\text{ billion Naira}

Dividing the target increase in national output by the multiplier yields the required initial discretionary fiscal boost.

Key Concept

Fiscal policy expenditure multiplier with proportional taxation

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