Question

Difficulty: HardCircular Flow of Income

In a four-sector open economy, circular flow equilibrium requires that total leakages (S+T+MS + T + M) equal total injections (I+G+XI + G + X). If domestic investment (II) increases by $40 billion\$40\text{ billion}, government spending (GG) decreases by $15 billion\$15\text{ billion}, exports (XX) rise by $25 billion\$25\text{ billion}, tax revenues (TT) increase by $20 billion\$20\text{ billion}, and imports (MM) remain constant, what change in household savings (SS) is required to maintain equilibrium?

  1. An increase of $30 billion\$30\text{ billion}Answer
  2. B
    A decrease of $30 billion\$30\text{ billion}
  3. C
    An increase of $50 billion\$50\text{ billion}
  4. D
    An increase of $70 billion\$70\text{ billion}

Answer

An increase of $30 billion\$30\text{ billion} in household savings is required.
Circular flow equilibrium holds when total leakages (S+T+MS + T + M) equal total injections (I+G+XI + G + X). The net change in total injections is ΔI+ΔG+ΔX=4015+25=+$50 billion\Delta I + \Delta G + \Delta X = 40 - 15 + 25 = +\$50\text{ billion}. For equilibrium to be restored without changing output, total leakages must also increase by $50 billion\$50\text{ billion}. Since tax leakages increased by $20 billion\$20\text{ billion} and imports are unchanged, savings must increase by $30 billion\$30\text{ billion} (5020=3050 - 20 = 30).

Step-by-Step Solution

1
Calculate the total change in injections
ΔInjections=ΔI+ΔG+ΔX=40+(15)+25=+$50 billion\Delta \text{Injections} = \Delta I + \Delta G + \Delta X = 40 + (-15) + 25 = +\$50\text{ billion}
Investment, government spending, and exports are injections into the circular flow.
2
Set total change in injections equal to total change in leakages
ΔLeakages=ΔS+ΔT+ΔM=+$50 billion\Delta \text{Leakages} = \Delta S + \Delta T + \Delta M = +\$50\text{ billion}
Circular flow equilibrium requires total injections to equal total leakages.
3
Solve for the missing change in savings (ΔS\Delta S)
ΔS+20+0=50    ΔS=5020=+$30 billion\Delta S + 20 + 0 = 50 \implies \Delta S = 50 - 20 = +\$30\text{ billion}
Isolating ΔS\Delta S gives the required increase in private savings.

Key Concept

Four-Sector Circular Flow Equilibrium
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