📖 财政政策工具与乘数效应

Economics

I. Lesson Focus

This lesson examines the main tools of fiscal policy—government spending, taxes, and transfer payments—and explains how they affect aggregate demand. It derives the spending multiplier, tax multiplier, and balanced-budget multiplier from the marginal propensity to consume (MPC), demonstrates their application in closing recessionary and inflationary gaps, and discusses automatic stabilizers, crowding-out effects, and the differences between closed and open economies. Candidates must be able to calculate exact policy changes required to achieve a target GDP change and evaluate the limitations of fiscal policy under different economic conditions.

II. The Problem

Suppose an economy is in recession with a GDP gap of –800 billion and an MPC of 0.75. Policymakers must decide whether to increase government purchases or cut taxes, and by exactly how much, to close the gap. At the same time, if the economy is already near full employment, the same policy will create inflationary pressure. This lesson solves these practical and exam-style questions by teaching the precise transmission mechanisms, multiplier formulas, quantitative impact calculations, and common conceptual traps.

III. Definition and Objectives of Fiscal Policy

Fiscal policy refers to the government’s use of taxation and spending to influence aggregate demand (AD), aggregate supply (AS), output, employment, and the price level.
Primary objectives include:
- Stabilizing the business cycle (reducing recessions and overheating)
- Achieving full employment
- Controlling inflation
- Promoting long-term economic growth

Fiscal policy is classified as expansionary (increasing government spending or cutting taxes to fight recession and unemployment) or contractionary (reducing spending or raising taxes to combat inflation and overheating).

IV. Main Tools of Fiscal Policy

1. Government Purchases (G)
   Directly enter GDP (Y = C + I + G + NX) and therefore have the most immediate and powerful impact on aggregate demand.
2. Transfer Payments
   Such as unemployment benefits and pensions; they do not directly count in GDP but raise disposable income and thereby stimulate consumption indirectly.
3. Taxes (T)
   Include direct taxes (income tax) and indirect taxes (VAT). Tax cuts increase disposable income, boosting consumption and investment.

Tool Selection Logic:
- To quickly boost aggregate demand, prioritize an increase in government purchases (larger multiplier).
- To stimulate private-sector investment and consumption over the longer term, prioritize tax cuts.

V. The Multiplier Effect – Mechanism and Formulas

The multiplier effect is the phenomenon whereby an initial change in spending leads to a much larger ultimate change in total output and income. It rests on the marginal propensity to consume (MPC):
$$ \text{MPC} = \frac{\Delta C}{\Delta \text{Disposable Income}} \quad (0 < \text{MPC} < 1) $$
Marginal propensity to save (MPS) = 1 – MPC.

Simple (Spending) Multiplier:
$$ \text{Multiplier} = \frac{1}{1 - \text{MPC}} = \frac{1}{\text{MPS}} $$

Government Spending Multiplier:
$$ \text{G Spending Multiplier} = \frac{1}{1 - \text{MPC}} $$

Tax Multiplier:
Because a tax change first affects disposable income and only then consumption, the multiplier is smaller in absolute value and negative:
$$ \text{Tax Multiplier} = -\frac{\text{MPC}}{1 - \text{MPC}} $$

Balanced-Budget Multiplier:
When government simultaneously increases spending and taxes by the same amount, the net multiplier equals 1. The spending multiplier exceeds the absolute value of the tax multiplier; the two effects cancel to leave a net multiplier of exactly 1.

Open-Economy Multiplier (with taxes and imports):
$$ \text{Open-Economy Multiplier} = \frac{1}{1 - \text{MPC}(1-t) + \text{MPM}} $$
where t is the marginal tax rate and MPM is the marginal propensity to import. The denominator is larger, so the multiplier is smaller than in a closed economy.

VI. Fiscal Policy in the AD-AS Framework

• Expansionary fiscal policy shifts AD to the right: output rises and the price level rises (extent depends on AS slope).
• In the Keynesian range (horizontal AS), the policy mainly increases real output with little price pressure.
• In the classical range (vertical AS), the policy mainly causes inflation with almost no increase in output (complete crowding-out).

Crowding-Out Effect:
Higher government borrowing raises interest rates, reducing private investment and net exports and thereby partially offsetting the fiscal stimulus. The stronger the crowding-out, the smaller the effective multiplier.

Crowding-In Effect:
In deep recession, government spending may improve business confidence and actually stimulate private investment.

VII. Automatic Stabilizers

These are fiscal mechanisms that operate without new legislation, such as:
- Progressive income tax systems (tax revenue automatically rises in booms and falls in recessions).
- Unemployment benefits (transfer payments automatically increase when unemployment rises).

Automatic stabilizers dampen the amplitude of economic fluctuations but cannot eliminate the cycle entirely.

Worked Cases

Case 1: Government-Spending Multiplier

An economy has MPC = 0.8 and a recessionary gap of 600 billion.
Question: How much must government purchases rise to close the gap?

Solution:
Spending multiplier = 1 / (1 – 0.8) = 5
Required ΔG = 600 / 5 = 120 billion.
An increase of 120 billion in G raises GDP by 600 billion.

Case 2: Tax Multiplier and Policy Choice

MPC = 0.75, recessionary gap = 400 billion.
Question: How large a tax cut is needed if only tax policy is used?

Solution:
Tax multiplier = –0.75 / (1 – 0.75) = –3
ΔT = 400 / (–3) ≈ –133.33 billion.
A tax cut of 133.33 billion closes the gap.
Comparing with Case 1 shows that, for any given MPC, a change in government spending is more powerful (multiplier of 5 > absolute tax multiplier of 3).

Case 3: Balanced-Budget Multiplier and Crowding-Out

Government simultaneously raises spending and taxes by 200 billion each; MPC = 0.8.
Question: What is the final change in GDP? If higher interest rates reduce private investment by 80 billion, what is the final GDP change?

Solution:
Balanced-budget multiplier = 1
ΔY = 1 × 200 = +200 billion.
After crowding-out, net injection = 200 – 80 = 120 billion.
Final ΔY = 120 × 5 = +600 billion.
(The multiplier now applies to the net injection after crowding-out.)

Traps

Key Formulas

• Government spending multiplier = $1 / (1 - MPC)$
• Tax multiplier = $-MPC / (1 - MPC)$
• Balanced-budget multiplier = 1
• MPS = $1 - MPC$
• Open-economy multiplier = $1 / [1 - MPC(1-t) + MPM]$
• Change in GDP = Initial policy change × Relevant multiplier
• Effective multiplier is reduced by crowding-out and by openness of the economy

Practice Questions

Q1. If MPC = 0.6, the government-spending multiplier is:
A. 1.67
B. 2.5
C. 4.0
D. 0.4

Q2. The absolute value of the tax multiplier compared with the spending multiplier is:
A. Larger
B. Smaller
C. Equal
D. Depends on MPS

Q3. In a closed economy the balanced-budget multiplier equals:
A. 0
B. 1
C. MPC
D. 1/(1–MPC)

Q4. An economy has MPC = 0.8 and a 300 billion recessionary gap. The tax cut required to close the gap using only tax policy is closest to:
A. 60 billion
B. 75 billion
C. 240 billion
D. 375 billion

Q5. In the classical range (vertical AS), the main effect of expansionary fiscal policy is:
A. Large increase in output, little change in prices
B. Large increase in prices, almost no change in output
C. Proportional rise in both output and prices
D. No significant change in either

Q6. Which of the following is an automatic stabilizer?
A. A temporary tax-cut bill passed by Congress
B. A progressive income-tax system
C. Central-bank interest-rate cuts
D. Government-initiated infrastructure spending

Q7. Given MPC = 0.75, marginal tax rate t = 0.2, and MPM = 0.1, the open-economy multiplier is closest to:
A. 2.0
B. 2.5
C. 3.33
D. 4.0

Q8. When crowding-out is severe, the effective fiscal-policy multiplier will:
A. Increase
B. Decrease
C. Remain unchanged
D. Become negative

Answers

Takeaways

• The government-spending multiplier is always larger than the absolute value of the tax multiplier; this is the key reason spending changes are more powerful for short-term demand management.
• The balanced-budget multiplier is exactly 1 regardless of the value of MPC.
• Crowding-out is strongest near full employment and significantly reduces the real impact of fiscal policy.
• Automatic stabilizers dampen cycles but cannot replace discretionary policy.
• In open economies with taxes, the actual multiplier is substantially smaller than the simple closed-economy multiplier.
• The size of any multiplier is directly proportional to MPC: higher MPC produces stronger policy effects.