In an open four-sector economy, the circular flow of income is in equilibrium when total l… — JAMB UTME

In an open four-sector economy, the circular flow of income is in equilibrium when total leakages (withdrawals) equal total injections. If planned savings ( $S$ ) is $\$80\text{ million}$ , imports ( $M$ ) are $\$45\text{ million}$ , planned investment ( $I$ ) is $\$95\text{ million}$ , government expenditure ( $G$ ) is $\$60\text{ million}$ , and exports ( $X$ ) are $\$40\text{ million}$ , what is the required value of government tax revenue ( $T$ ) in millions of dollars?

Answer: 70 million dollars

Answer

The required government tax revenue to achieve circular flow equilibrium is 70 million dollars.

Circular flow equilibrium in a four-sector economy occurs when total leakages (withdrawals) equal total injections:

S + T + M = I + G + X

. Summing total injections gives

\$95 + \$60 + \$40 = \$195\text{ million}

. Substituting known leakages gives

\$80 + T + \$45 = \$125 + T

. Equating total leakages to total injections yields

\$125 + T = \$195

, which solves to

T = 70\text{ million dollars}

Step-by-Step Solution

Identify the equilibrium condition for a four-sector circular flow model

S + T + M = I + G + X

Macroeconomic equilibrium in a four-sector economy requires total withdrawals (savings, taxation, imports) to equal total injections (investment, government spending, exports).

Compute total injections into the income stream

I + G + X = 95 + 60 + 40 = 195\text{ million dollars}

Summing investment spending, government purchases, and export earnings provides the total injection.

Substitute known values into the leakages-injections identity

80 + T + 45 = 195 \implies 125 + T = 195

Combining known leakages (savings and imports) with the unknown tax revenue variable.

Solve for tax revenue (

T

)

T = 195 - 125 = 70\text{ million dollars}

Subtracting non-tax withdrawals from total injections yields the required tax value.

Key Concept

Four-Sector Circular Flow Equilibrium (Total Leakages = Total Injections)

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