Overview
Concise notes on GDP multipliers and marginal propensities, including definitions, formulas, examples, and applications to spending, taxes, and budget scenarios.
Disposable Income and Uses
- Disposable income: money available to spend on goods/services after taxes.
- Formula: Disposable Income = Personal Income − Taxes.
- Two uses only: consumption (spending) or saving.
- Identity: Consumption + Saving = Disposable Income.
- Example: Income $100,000; Taxes $20,000; Disposable $80,000; Save $8,000; Spend $72,000.
Average Propensities (APC and APS)
- Average Propensity to Save (APS): fraction of disposable income saved.
- APS formula: Savings ÷ Disposable Income (decimal).
- Average Propensity to Consume (APC): fraction of disposable income spent.
- APC formula: Consumption ÷ Disposable Income (decimal).
- Identity: APC + APS = 1.
- Example: Save $8,000; Spend $72,000; Income $80,000 → APS = 0.1; APC = 0.9.
Marginal Propensities (MPC and MPS)
- Marginal Propensity to Consume (MPC): share of new income spent.
- MPC formula: Change in Consumption ÷ Change in Income.
- Marginal Propensity to Save (MPS): share of new income saved.
- MPS formula: Change in Saving ÷ Change in Income.
- Identity: MPC + MPS = 1.
- Example 1: ΔIncome $20,000; ΔConsumption $15,000 → MPC = 0.75. ΔSaving $5,000 → MPS = 0.25.
- Example 2: ΔIncome $1,000; ΔConsumption $800; ΔSaving $200 → MPC = 0.8; MPS = 0.2.
Spending Multiplier and Chain Effect
- New spending circulates; each round, spend MPC, save MPS.
- Spending multiplier (k): measures total GDP change from initial spending change.
- Formulas: k = 1 ÷ MPS = 1 ÷ (1 − MPC).
- Larger MPC → larger multiplier; larger MPS → smaller multiplier.
- Maximum change equals initial change times multiplier (leakages can reduce in reality).
Islandia Illustration
- MPC = 0.8; MPS = 0.2; k = 1/0.2 = 5.
- Initial consumption increase $800 → Max GDP increase $4,000.
Applications to GDP Components
- Applies to: Consumption (C), Investment (I), Government Purchases (G), Net Exports (NX).
Structured Examples
| Scenario | Given | Multiplier | Computation | Max GDP Change |
|---|
| Consumption increase | MPC = 0.8; Initial C = $800 | k = 1/0.2 = 5 | $800 × 5 | +$4,000 |
| Investment increase | MPC = 0.75; ΔI = $10,000 | k = 1/(1−0.75) = 4 | $10,000 × 4 | +$40,000 |
| Government decrease | MPS = 0.1; ΔG = −$5,000,000 | k = 1/0.1 = 10 | −$5,000,000 × 10 | −$50,000,000 |
| Net exports decrease | MPC = 0.95; ΔNX = −$1,000,000 | k = 1/(1−0.95) = 20 | −$1,000,000 × 20 | −$20,000,000 |
Tax Multiplier
- Taxes affect disposable income; part of tax change is saved.
- Tax multiplier (t): t = −MPC ÷ MPS = −MPC ÷ (1 − MPC).
- Absolute value of t is one less than spending multiplier.
- Example: MPC = 0.8; MPS = 0.2 → t = −0.8/0.2 = −4.
- If ΔTaxes = −$10,000,000 → Max ΔGDP = (−$10,000,000) × (−4) = +$40,000,000.
- Transfer payments increases act like tax reductions.
Balanced Budget Multiplier
- Equal changes in G and Taxes; keeps budget balance unchanged.
- Balanced budget multiplier = 1.
- If G and Taxes both rise by X → Max ΔGDP = +X.
- Example 1: MPC = 0.9; MPS = 0.1; ΔG = +$10M; ΔT = +$10M → k = 10; t = −9 → Net = +$10M.
- Example 2: MPC = 0.8; MPS = 0.2; ΔG = −$20M; ΔT = −$20M → k = 5; t = −4 → Net = −$20M.
Advanced Applications
- Closing an output gap by targeted policy using multipliers.
- Work backward: Required policy change = Gap ÷ Multiplier.
Structured Advanced Examples
| Problem | Given | Multiplier(s) | Computation | Result |
|---|
| Close recessionary gap | MPC = 0.9; MPS = 0.1; Actual GDP = $150M; Potential = $200M | k = 10 | Gap $50M ÷ 10 | ΔG = +$5M needed |
| Combined shocks | MPC = 0.9; MPS = 0.1; ΔNX = −$4B; ΔT = −$5B | k = 10; t = −9 | NX: −$4B×10=−$40B; Taxes: −$5B×(−9)=+$45B | Net +$5B |
Key Terms & Definitions
- Disposable Income: Income after taxes; available to spend or save.
- Consumption (C): Household spending on goods and services.
- Saving (S): Portion of disposable income not spent.
- APC: Consumption ÷ Disposable Income; fraction spent.
- APS: Saving ÷ Disposable Income; fraction saved.
- MPC: ΔConsumption ÷ ΔIncome; fraction of new income spent.
- MPS: ΔSaving ÷ ΔIncome; fraction of new income saved.
- Spending Multiplier (k): 1 ÷ MPS = 1 ÷ (1 − MPC); scales initial spending change.
- Tax Multiplier (t): −MPC ÷ MPS = −MPC ÷ (1 − MPC); effect of tax changes.
- Balanced Budget Multiplier: Equals 1; equal ΔG and ΔT change GDP by same amount.
- Net Exports (NX): Exports − Imports; component of GDP.
- Output Gap: Difference between potential and actual GDP; negative implies recession.
Action Items / Next Steps
- Practice computing MPC, MPS, APC, APS, and multipliers with varied scenarios.
- Apply spending and tax multipliers to C, I, G, and NX changes.
- Use backward calculation to size policies to close output gaps.