Ultimate AP Macroeconomics Formula Sheet
What You Need to Know
This is the high-yield equation toolkit for AP Macroeconomics: the formulas that show up constantly in MCQs/FRQs for measuring the economy, fiscal/monetary policy, money creation, and international trade/finance. If you can (1) pick the right formula, (2) plug in correctly, and (3) interpret the sign/direction, you’ll scoop up a lot of points fast.
Critical reminder: If a question gives you indexes (CPI, deflator), you’re usually doing percent change. If it gives you levels (GDP, price, quantity), you’re often doing real vs nominal or multipliers.
Core idea: most “math” in AP Macro boils down to:
- Index math (inflation, real vs nominal)
- Rates (unemployment, reserve ratio, interest)
- Simple multipliers (spending/tax)
- Money identity MV = PY
Step-by-Step Breakdown
1) Convert Nominal ↔ Real (GDP or any value)
- Identify what you’re converting:
- Nominal = current-year prices
- Real = base-year prices (inflation removed)
- If you have a price index (CPI or GDP deflator):
- \text{Real} = \frac{\text{Nominal}}{\text{Price Index}/100}
- \text{Nominal} = \text{Real} \cdot \frac{\text{Price Index}}{100}
- Sanity check: if the index is above 100, prices are higher than base year, so Real < Nominal.
2) Compute Inflation from an Index
- Use the percent change formula:
- \text{Inflation rate} = \frac{\text{Index}_t - \text{Index}_{t-1}}{\text{Index}_{t-1}} \times 100
- Watch your units: the result is a percent, not “index points.”
3) Fiscal Policy Multiplier Questions
- Identify the policy type:
- Government spending \Delta G
- Taxes \Delta T
- If given MPC, compute multipliers:
- Spending multiplier = \frac{1}{1-\text{MPC}}
- Tax multiplier = -\frac{\text{MPC}}{1-\text{MPC}}
- Apply:
- \Delta Y = (\text{spending multiplier})\cdot \Delta G
- \Delta Y = (\text{tax multiplier})\cdot \Delta T
- Sign check:
- \Delta G > 0 raises Y.
- \Delta T > 0 lowers Y (negative multiplier).
4) Money Creation (Banking) Problems
- Convert reserve requirement percent to a decimal: e.g. 10\% = 0.10.
- Money multiplier:
- \text{Money multiplier} = \frac{1}{\text{rr}}
- If Fed increases reserves by \Delta R (often via open-market purchase):
- \Delta D_{\max} = \frac{1}{\text{rr}}\cdot \Delta R
- Know the key assumption: this “max” requires banks loan out all excess reserves and the public redeposits funds.
5) Quantity Theory / Inflation from Money Growth
- Use the identity:
- MV = PY
- Growth-rate form (high yield):
- g_M + g_V \approx \pi + g_Y
- Common AP assumption: velocity stable g_V \approx 0, so:
- \pi \approx g_M - g_Y
6) Real vs Nominal Interest (Fisher Equation)
- Exact relationship is more complex, but AP uses the approximation:
- i \approx r + \pi^e
- Solve for what you need:
- r \approx i - \pi^e
Key Formulas, Rules & Facts
National Income & Price Level
| Formula / Rule | When you use it | Notes / Traps |
|---|---|---|
| GDP = C + I + G + (X - M) | Expenditure approach | X-M = NX. Transfers (SS, welfare) are not directly in GDP. |
| GNP = GDP + \text{net factor income from abroad} | Income earned by nationals | AP occasionally tests conceptually. |
| NDP = GDP - \text{depreciation} | Adjust for capital wear | Less common, but shows up. |
| \text{GDP Deflator} = \frac{\text{Nominal GDP}}{\text{Real GDP}}\times 100 | Price level for domestically produced final goods | Uses current basket (unlike CPI). |
| \text{Real} = \frac{\text{Nominal}}{\text{Index}/100} | Convert nominal to real | Works for CPI/deflator. |
| \%\Delta = \frac{\text{new} - \text{old}}{\text{old}}\times 100 | Any percent change | Your bread-and-butter. |
| \text{Inflation} = \frac{\text{CPI}_t - \text{CPI}_{t-1}}{\text{CPI}_{t-1}}\times 100 | CPI inflation | Same structure for deflator inflation. |
Unemployment & Labor Metrics
| Formula / Rule | When you use it | Notes / Traps |
|---|---|---|
| \text{Unemployment rate} = \frac{\text{unemployed}}{\text{labor force}}\times 100 | Standard unemployment | Labor force = employed + unemployed (actively searching). |
| \text{LFPR} = \frac{\text{labor force}}{\text{adult population}}\times 100 | Participation changes | Discouraged workers are not in labor force. |
MPC/MPS & Multipliers
| Formula / Rule | When you use it | Notes / Traps |
|---|---|---|
| \text{MPC} = \frac{\Delta C}{\Delta Y_d} | Consumption response | Y_d is disposable income. |
| \text{MPS} = \frac{\Delta S}{\Delta Y_d} | Savings response | |
| \text{MPC} + \text{MPS} = 1 | Quick fill-in | If you have one, you have the other. |
| k_G = \frac{1}{1-\text{MPC}} | Spending multiplier | Sometimes written \frac{1}{\text{MPS}}. |
| k_T = -\frac{\text{MPC}}{1-\text{MPC}} | Tax multiplier | Negative sign is essential. |
| k_{BB} = 1 | Balanced budget multiplier | If \Delta G = \Delta T (same direction, same amount). |
Money, Banking, and the Fed
| Formula / Rule | When you use it | Notes / Traps |
|---|---|---|
| M1 = \text{currency} + \text{checkable deposits} | Money definition | Savings accounts are not in M1. |
| \text{rr} = \frac{\text{required reserves}}{\text{deposits}} | Reserve requirement definition | Use decimal form. |
| \text{Required reserves} = \text{rr}\cdot \text{deposits} | Bank balance sheet | Excess reserves = actual − required. |
| \text{Money multiplier} = \frac{1}{\text{rr}} | Simple deposit creation | Assumes no currency drain + full lending. |
| \Delta D_{\max} = \frac{1}{\text{rr}}\cdot \Delta R | Max change in deposits | \Delta R usually from OMO. |
| Expansionary MP lowers i, raises AD | Direction questions | Via OMO buy / discount rate ↓ / rr ↓. |
| Contractionary MP raises i, lowers AD | Direction questions | Via OMO sell / discount rate ↑ / rr ↑. |
Quantity Theory & Interest Rates
| Formula / Rule | When you use it | Notes / Traps |
|---|---|---|
| MV = PY | Link money to nominal GDP | PY is nominal GDP. |
| g_M + g_V \approx \pi + g_Y | Growth rates | Often assume g_V \approx 0. |
| i \approx r + \pi^e | Fisher equation | If inflation expectations rise, nominal rates tend to rise. |
| r \approx i - \pi^e | Real interest | Don’t subtract actual inflation unless told expectations = actual. |
Economic Growth Quick Math
| Formula / Rule | When you use it | Notes / Traps |
|---|---|---|
| \text{Rule of 70: } \text{Doubling time} \approx \frac{70}{\text{growth rate (\%)}} | Growth comparison | Growth rate must be in percent form (e.g. 3 not 0.03). |
Foreign Exchange & Balance of Payments (AP-level)
| Formula / Rule | When you use it | Notes / Traps |
|---|---|---|
| \%\Delta e = \frac{e_{new}-e_{old}}{e_{old}}\times 100 | Exchange rate percent change | Define e carefully based on quote. |
| Appreciation: currency value ↑ | Forex shifts | Typically makes exports pricier, imports cheaper (NX ↓). |
| Depreciation: currency value ↓ | Forex shifts | Typically makes exports cheaper, imports pricier (NX ↑). |
| \text{Current Account} + \text{Financial Account} \approx 0 | Directional BOP logic | AP often uses “net exports” vs “net capital outflow” intuition. |
Forex quote trap: If the exchange rate is stated as “\text{USD per 1 EUR},” then an increase means EUR appreciates and USD depreciates.
Examples & Applications
Example 1: Real GDP from Nominal GDP and Deflator
Nominal GDP = \$22{,}000, GDP deflator = 110.
- \text{Real GDP} = \frac{22{,}000}{110/100} = \frac{22{,}000}{1.10} = 20{,}000
Insight: deflator above 100 means inflation since base year, so real must be smaller.
Example 2: Inflation rate using CPI
CPI last year = 200, CPI this year = 210.
- \pi = \frac{210-200}{200}\times 100 = 5\%
Exam variation: They may ask for “percent change in price level” (same computation).
Example 3: Fiscal multiplier with MPC
MPC = 0.8, government spending increases by \$50.
- Spending multiplier: k_G = \frac{1}{1-0.8} = 5
- Output change: \Delta Y = 5\cdot 50 = \$250
Exam variation: If instead taxes rise by \$50: - Tax multiplier: k_T = -\frac{0.8}{1-0.8} = -4
- \Delta Y = -4\cdot 50 = -\$200
Example 4: Money creation from new reserves
Reserve requirement \text{rr} = 0.10, Fed buys bonds creating \Delta R = \$100 of new reserves.
- Multiplier: \frac{1}{0.10}=10
- Max deposits: \Delta D_{\max} = 10\cdot 100 = \$1{,}000
Key insight: This is the maximum under idealized assumptions.
Common Mistakes & Traps
Mixing up CPI vs GDP Deflator
- Wrong: treating them as identical baskets.
- Why wrong: CPI uses a fixed consumer basket (includes imports); deflator covers domestically produced final goods with a changing basket.
- Fix: if it says “typical household,” think CPI; if it says “all final goods produced domestically,” think deflator.
Forgetting to divide the index by 100
- Wrong: \text{Real} = \frac{\text{Nominal}}{\text{Index}}.
- Why wrong: indexes are scaled to 100.
- Fix: always use \text{Index}/100.
Confusing percent change with index-point change
- Wrong: saying inflation is 210-200=10\%.
- Why wrong: 10 is index points, not percent.
- Fix: always divide by the old index: \frac{\Delta}{\text{old}}\times 100.
Using percentage points vs percent incorrectly (especially interest rates)
- Wrong: “rate increased by 50%” when it went from 4% to 6%.
- Why wrong: that’s +2 percentage points, but +50% relative increase.
- Fix: if asked “by how many percentage points,” subtract; if asked “by what percent,” use percent change formula.
Dropping the negative sign on the tax multiplier
- Wrong: k_T = \frac{\text{MPC}}{1-\text{MPC}}.
- Why wrong: higher taxes reduce disposable income and consumption.
- Fix: lock in k_T as **negative**: -\frac{\text{MPC}}{1-\text{MPC}}.
Using rr as 10 instead of 0.10
- Wrong: \frac{1}{10} instead of \frac{1}{0.10}.
- Why wrong: rr must be a decimal.
- Fix: convert percent to decimal before doing anything.
Misreading exchange rate quotes (who appreciated?)
- Wrong: thinking “USD per EUR rises” means USD strengthens.
- Why wrong: if it takes more USD to buy 1 EUR, USD is weaker.
- Fix: write the quote explicitly and ask: “Which currency buys more of the other now?”
Using actual inflation in Fisher equation when the question says expected
- Wrong: r = i - \pi when inflation expectations are given.
- Why wrong: the AP relationship emphasizes \pi^e.
- Fix: use r \approx i - \pi^e unless told otherwise.
Memory Aids & Quick Tricks
| Trick / Mnemonic | What it helps you remember | When to use it |
|---|---|---|
| “Real is smaller when the index is bigger.” | If index > 100 then Real < Nominal | Real/nominal conversions |
| MPC + MPS = 1 | Quick back-solving | Multiplier setups |
| Spending multiplier is positive; tax multiplier is negative | Sign discipline | Fiscal policy FRQs |
| “Buy bonds → bank reserves ↑ → money supply ↑ → i ↓” | Full monetary transmission direction | Fed policy direction questions |
| “OMO is the go-to.” | Open market ops are primary tool | Most Fed questions |
| Rule of 70 | Doubling time fast math | Growth comparisons |
| Forex quote check: ‘USD per EUR’ | If the number rises, EUR appreciates | Exchange-rate appreciation/depreciation |
Quick Review Checklist
- You can compute \text{Real} = \frac{\text{Nominal}}{\text{Index}/100} and interpret it.
- You can compute inflation with \frac{\text{new}-\text{old}}{\text{old}}\times 100 (not index-point change).
- You know GDP = C + I + G + (X-M) and what’s excluded (transfers, used goods, intermediate goods).
- You can compute unemployment rate and labor force participation rate.
- You can use \text{MPC}+\text{MPS}=1 and calculate k_G and k_T correctly (including the negative sign).
- You can do money multiplier problems: \frac{1}{\text{rr}} and \Delta D_{\max} = \frac{1}{\text{rr}}\Delta R.
- You can use MV=PY and the growth-rate shortcut \pi \approx g_M - g_Y (if g_V \approx 0).
- You can apply i \approx r + \pi^e and solve for the missing variable.
- You can interpret exchange rate quotes without flipping appreciation/depreciation.
You’ve got this—now drill a few FRQ-style plug-and-chug setups and you’ll be exam-ready.