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)

1. Identify what you’re converting:
   • Nominal = current-year prices
   • Real = base-year prices (inflation removed)
2. If you have a price index (CPI or GDP deflator):
   • $\text{Real} = \frac{\text{Nominal}}{\text{Price Index}/100}$
   • $\text{Nominal} = \text{Real} \cdot \frac{\text{Price Index}}{100}$
3. Sanity check: if the index is above 100, prices are higher than base year, so Real < Nominal.

2) Compute Inflation from an Index

1. Use the percent change formula:
   • $\text{Inflation rate} = \frac{\text{Index}_t - \text{Index}_{t-1}}{\text{Index}_{t-1}} \times 100$
2. Watch your units: the result is a percent, not “index points.”

3) Fiscal Policy Multiplier Questions

1. Identify the policy type:
   • Government spending $\Delta G$
   • Taxes $\Delta T$
2. If given MPC, compute multipliers:
   • Spending multiplier $= \frac{1}{1-\text{MPC}}$
   • Tax multiplier $= -\frac{\text{MPC}}{1-\text{MPC}}$
3. Apply:
   • $\Delta Y = (\text{spending multiplier})\cdot \Delta G$
   • $\Delta Y = (\text{tax multiplier})\cdot \Delta T$
4. Sign check:
   • $\Delta G > 0$ raises $Y$.
   • $\Delta T > 0$ lowers $Y$ (negative multiplier).

4) Money Creation (Banking) Problems

1. Convert reserve requirement percent to a decimal: e.g. $10\% = 0.10$.
2. Money multiplier:
   • $\text{Money multiplier} = \frac{1}{\text{rr}}$
3. If Fed increases reserves by $\Delta R$ (often via open-market purchase):
   • $\Delta D_{\max} = \frac{1}{\text{rr}}\cdot \Delta R$
4. 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

1. Use the identity:
   • $MV = PY$
2. Growth-rate form (high yield):
   • $g_M + g_V \approx \pi + g_Y$
3. Common AP assumption: velocity stable $g_V \approx 0$, so:
   • $\pi \approx g_M - g_Y$

6) Real vs Nominal Interest (Fisher Equation)

1. Exact relationship is more complex, but AP uses the approximation:
   • $i \approx r + \pi^e$
2. Solve for what you need:
   • $r \approx i - \pi^e$

Key Formulas, Rules & Facts

National Income & Price Level

Unemployment & Labor Metrics

MPC/MPS & Multipliers

Money, Banking, and the Fed

Quantity Theory & Interest Rates

Economic Growth Quick Math

Foreign Exchange & Balance of Payments (AP-level)

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

1. 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.

2. 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 $\text{Index}/100$.

3. 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: $\frac{\Delta}{\text{old}}\times 100$.

4. 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.

5. 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**: $-\frac{\text{MPC}}{1-\text{MPC}}$.

6. 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.

7. 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?”

8. 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

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.