An economy's current equilibrium national income is \1,200\text{ billion}, while its full-… — JAMB UTME

An economy's current equilibrium national income is $\$1,200\text{ billion}$ , while its full-employment potential national income is $\$1,500\text{ billion}$ . The consumption function is $C = 150 + 0.75Y_d$ , where $Y_d$ is disposable income ( $Y_d = Y - T$ ), and the tax function is $T = 40 + 0.20Y$ , where $Y$ is national income. To achieve economic stabilization at full employment using fiscal policy, by how much (in billions of dollars) must the government increase its expenditure ( $G$ )?

Answer: 120 billion dollars

Answer

The government must increase its expenditure by 120 billion dollars.

To close the

\$300\text{ billion}

recessionary gap, the government spending multiplier must incorporate the proportional tax rate (

t = 0.20

). The effective MPC out of national income is

0.75 \times (1 - 0.20) = 0.60

, yielding a government spending multiplier of

K_g = \frac{1}{1 - 0.60} = 2.5

. Dividing the gap of

\$300\text{ billion}

2.5

gives the required spending increase of 120 billion dollars.

Step-by-Step Solution

Determine the output gap

Output gap

\Delta Y = \$1,500\text{ billion} - \$1,200\text{ billion} = \$300\text{ billion}

Economic stabilization requires increasing national income by the difference between potential output and current equilibrium output.

Calculate the effective marginal propensity to consume out of total national income (

MPC_Y

)

MPC_Y = 0.75 \times (1 - 0.20) = 0.60

The proportional income tax reduces disposable income to

(1 - t)Y

, altering the overall spending response to changes in total output.

Calculate the government spending multiplier (

K_g

)

K_g = \frac{1}{1 - 0.60} = 2.5

The spending multiplier accounts for income tax leakages in the circular flow.

Calculate the required increase in government spending (

\Delta G

)

\Delta G = \frac{\$300\text{ billion}}{2.5} = 120\text{ billion}

Dividing the output gap by the fiscal multiplier yields the exact injection of expenditure needed to achieve full employment.

Key Concept

Fiscal policy tools, government expenditure multiplier with proportional taxation, and economic stabilization of output gaps.

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