Questions: Demand Shocks and the Multiplier Mechanism

Question 1

An economy has MPC = 0.8, a proportional income tax rate of 25%, and a marginal propensity to import of 0.15. A student using the simple formula 1/(1 − MPC) estimates the government spending multiplier at 5. The actual multiplier is best described as:

• A. Equal to 5, because the formula accounts for all relevant economic forces
• B. Less than 5, because taxes and imports are leakages that reduce the multiplier
• C. Greater than 5, because tax revenue is recirculated through government spending
• D. Less than 5 in the short run but converging to 5 over many spending rounds

Answer: (B)

The simple formula 1/(1−MPC) = 5 assumes a closed economy with no taxes. In reality, taxes reduce the disposable income available for spending (effective MPC = 0.8 × 0.75 = 0.6), and imports divert spending abroad rather than back into the domestic economy. The corrected formula 1/(1 − MPC(1−t) + m) = 1/(1 − 0.6 + 0.15) ≈ 1.8 is far below 5. Leakages are the key reason real-world multipliers fall well short of the simple Keynesian formula.

Question 2

Government spends $200 billion on infrastructure during a deep recession with high unemployment. The central bank holds interest rates constant. Compared to an identical spending package implemented when the economy is at full employment, the real output multiplier during the recession is likely:

• A. Smaller, because firms are pessimistic and reduce investment regardless
• B. The same, because the multiplier depends only on MPC
• C. Larger, because idle capacity allows output to expand without hitting supply constraints
• D. Larger at full employment, because higher productive capacity amplifies spending

Answer: (C)

At full employment, a demand injection runs into supply constraints — firms and workers are already fully utilized — so the shock mainly raises prices rather than real output, shrinking the real multiplier. During a recession with slack capacity (idle factories, unemployed workers), additional demand can be met by expanding real output without inflationary bottlenecks. The multiplier is not a fixed constant; it depends on how much spare capacity exists to absorb the demand without price increases.

Question 3

A government that cuts spending during a recession amplifies the downturn through the multiplier mechanism.

• T. True
• F. False

Answer: True

The multiplier works symmetrically in both directions. Each dollar cut in government spending reduces someone's income, which reduces their consumption in the next round, which reduces income further, and so on. A spending cut during a recession propagates as a negative geometric series, amplifying the initial contractionary shock. This is the macroeconomic case for countercyclical fiscal policy: cutting spending during a downturn deepens it, while expanding spending can offset private-sector contraction through the same propagation mechanism in reverse.

Question 4

The multiplier effect guarantees that a $100 increase in government spending will generally increase total output by more than $100.

• T. True
• F. False

Answer: False

The multiplier can fall below 1 under certain conditions. If the economy is at full employment and the central bank raises interest rates in response to inflationary pressure, crowding out of private investment can partially or fully offset the demand stimulus. In a very open economy with high imports (m close to 1), spending leaks abroad rapidly and the domestic multiplier is small. Empirical multipliers range from below 1 in booms with active monetary policy to above 2 at the zero lower bound during deep recessions. The simple formula overstates real-world effects.

Question 5

Why does a demand shock produce a total output increase larger than the initial injection, and what prevents real-world multipliers from reaching the 1/(1 − MPC) prediction?

Model answer: Each dollar of new spending becomes income for someone else, who spends a fraction MPC of it, generating more income, which generates more spending — a geometric series summing to 1/(1−MPC) times the original injection. Real-world multipliers fall short because of leakages: taxes reduce disposable income available for spending, imports divert spending to foreign workers, and crowding out (higher interest rates from government borrowing) reduces private investment, partially offsetting the stimulus.

The core mechanism is an income-consumption feedback loop. The formula 1/(1−MPC) captures the closed-economy, no-tax, no-crowding-out ideal. Each leakage — taxes, imports, interest-rate effects — reduces the effective MPC in each spending round, shrinking the geometric series and thus the total multiplier. Understanding that the multiplier is a propagation process (not a magic amplifier) makes it clear why real-world estimates cluster around 1.5–2 rather than 5.