Macro
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AP Macroeconomics — Cheatsheet

Formulas, exam-day tips, and key terms on one page.

Formulas & relationships

The rational decision rule
Do one more unit while MB ≥ MC; stop where MB = MC
Marginal benefit is the extra benefit from one more unit; marginal cost is the opportunity cost of that unit. Net benefit is maximized where the two are equal.
Opportunity cost along a straight-line PPC
Opportunity cost of 1 unit of X = (units of Y given up) / (units of X gained)
Read the trade-off directly off the axes. On a bowed PPC this ratio grows as you specialize; on a straight-line PPC it stays constant.
Opportunity cost from an output table
OC of 1 unit of Good A = (units of Good B produced) / (units of Good A produced)
Compute this ratio for each producer. Lower opportunity cost = comparative advantage. Remember "Other Over Own" when using output data.
GDP — expenditure approach
GDP = C + I + G + Xn (where Xn = exports − imports)
The four spending categories. Transfer payments and purely financial transactions are excluded because no new good or service is produced.
Real vs. nominal GDP
Real GDP = (Nominal GDP / GDP deflator) × 100
Nominal GDP uses current-year prices; real GDP holds prices constant at a base year to strip out inflation. Only real GDP reflects a true change in output.
Unemployment rate & natural rate
Unemployment rate = (Unemployed / Labor force) × 100 · Natural rate = frictional % + structural %
Labor force = employed + unemployed. The natural rate excludes cyclical unemployment, which is zero at full employment.
Inflation rate from the CPI
Inflation rate = [(CPI_new − CPI_old) / CPI_old] × 100
A simple percentage change in the index. The same formula finds the rate between any two years once you know the CPI for each.
The components of aggregate demand
AD ≡ C + I + G + Xn
A rise in any component shifts AD right; a fall shifts AD left. This mirrors the GDP expenditure identity, now viewed as a demand relationship at each price level.
The multipliers
Spending multiplier = 1 / (1 − MPC) = 1 / MPS · Tax multiplier = −MPC / (1 − MPC)
MPC + MPS = 1. Total ΔGDP = (multiplier) × (initial change). The tax multiplier is always smaller in absolute value than the spending multiplier.
Spending needed to close a gap
Required ΔG = Output gap / Spending multiplier
Using taxes instead: Required ΔT = − Output gap / Tax multiplier. Because the tax multiplier is smaller, the required tax change is larger than the required spending change.
Real vs. nominal interest rate (Fisher)
Real interest rate ≈ Nominal interest rate − Expected inflation rate
The money market sets the nominal rate; borrowers and lenders care about the real rate. Rearranged: nominal rate = real rate + expected inflation.
Money multiplier & maximum money creation
Money multiplier = 1 / RR · Max Δ money supply = Excess reserves × (1 / RR)
RR is the required reserve ratio as a decimal. From a new deposit, excess reserves = deposit × (1 − RR); the required portion is deposit × RR.
The monetary transmission chain (expansionary)
Buy bonds → MS ↑ → interest rate ↓ → investment ↑ → AD ↑ → real GDP ↑, unemployment ↓
Reverse every arrow for contractionary policy (sell bonds → MS ↓ → interest rate ↑ → investment ↓ → AD ↓).
Phillips curve ↔ AD–AS correspondence
AD ↑ ⇒ move up-left along SRPC (inflation ↑, unemployment ↓) · negative supply shock ⇒ SRPC shifts right
Demand changes are movements along the SRPC; supply shocks shift it. The LRPC sits vertically at the natural rate of unemployment.
Deficit, debt, and crowding out
Debt(this year) = Debt(last year) + Deficit(this year) · Gov’t borrowing ↑ ⇒ real interest rate ↑ ⇒ private investment ↓
The deficit is a yearly flow that adds to the debt stock. In loanable funds, government borrowing raises demand for funds, lifting the real rate and crowding out investment.
Growth in real GDP
Growth rate of real GDP = [(Real GDP_new − Real GDP_old) / Real GDP_old] × 100
Sustained positive growth in *real* GDP (and in real GDP per capita, which divides by population) reflects a rising standard of living.
Balance of payments identity
Current account + Financial (capital) account ≈ 0
A current account deficit is matched by a financial account surplus (net capital inflow), and vice versa. The two accounts offset.
Exchange rate movements
Increase in demand for a currency ⇒ appreciation · Increase in supply of a currency ⇒ depreciation
One currency’s appreciation is the other’s depreciation. Appreciation raises export prices and lowers import prices; depreciation does the reverse.
The interest rate → exchange rate → net exports chain
Domestic real interest rate ↑ → capital inflow → currency appreciates → net exports ↓ → AD ↓
Reverse every arrow when the domestic interest rate falls: capital outflow, depreciation, higher net exports, AD up.
Why GDP can be measured two ways
total expenditure ≡ total output ≡ total income
Not an approximation — an accounting identity forced by the circular flow. It is why the expenditure and income approaches to GDP must agree.
Opportunity cost, by problem type
OUTPUT table: cost of 1 unit = other good / own good · INPUT table: cost of 1 unit = own good / other good
Check yourself: in an output table, a country good at making a good has a LOW opportunity cost for it. If your answer says otherwise, you inverted.
The optimum
continue while MB > MC · stop where MB = MC · you have gone too far when MB < MC
The optimum is where the *marginal* quantities are equal, never where total benefit is largest or average cost is lowest.
The utility-maximizing rule
MU_x / P_x = MU_y / P_y (subject to spending the whole budget)
Equalize the satisfaction bought per dollar. Not MU_x = MU_y — a good that costs three times as much must deliver three times the utility to be worth the same.
Per capita, and why it matters
GDP per capita = GDP / population
A country can grow GDP while GDP per capita falls, if population grows faster. Per capita is the better proxy for living standards, though it still says nothing about distribution.
The two rates
unemployment rate = unemployed / labor force × 100 · LFPR = labor force / adult population × 100
Different denominators. The unemployment rate divides by the labor force; participation divides by the whole adult population.
Index and inflation rate
CPI = (cost of basket now / cost in base year) × 100 · inflation = (CPI_new − CPI_old) / CPI_old × 100
The inflation rate divides by the OLD index, not the new one and not 100. Dividing by 100 is the most common error here.
Deflating
real GDP = nominal GDP / price index × 100 · deflator = nominal / real × 100
The same equation rearranged. Given any two of nominal, real and the deflator, you can find the third.
The Fisher equation
real rate ≈ nominal rate − inflation rate · nominal ≈ real + expected inflation
Read the second form as how lenders set rates: they add expected inflation to the real return they require.
The output gap
output gap = (actual real GDP − potential real GDP) / potential real GDP × 100
Negative is a recessionary gap, positive an inflationary gap. Zero is full employment — with unemployment at the natural rate, not at zero.
Slope versus shift
PRICE LEVEL changes → movement ALONG AD · C, I, G or Xn changes for any other reason → SHIFT of AD
The single most useful discriminator in the unit. If the cause is the price level, you move along; if it is anything else, you shift.
What shifts what
SRAS shifts: input prices, nominal wages, supply shocks, productivity, inflation expectations · LRAS shifts: labor force, capital stock, technology, institutions
Anything that changes real productive capacity shifts BOTH. Anything that only changes costs shifts SRAS alone.
Self-correction outcomes
recessionary gap → wages fall → SRAS right → output ↑ to potential, price level ↓ · inflationary gap → wages rise → SRAS left → output ↓ to potential, price level ↑
Output always ends at potential. What differs between the two cases is the direction the price level moves.
Reading the direction of a shock
AD shift → output and price level move the SAME way · SRAS shift → output and price level move OPPOSITE ways
Given what happened to output and prices, this identifies which curve moved. The single most useful diagnostic in Unit 3.
The cyclical budget
recession → tax revenue ↓ and transfers ↑ → deficit widens automatically
A deficit that grows in a recession may reflect no policy change at all. This is why the *structural* balance — what the budget would be at potential output — is the meaningful measure of fiscal stance.
The chain most questions follow
shock → which curve, which direction → real GDP and price level → unemployment (opposite to GDP) → interest rate (same direction as GDP, via money demand)
Unemployment moves opposite to real GDP. The nominal interest rate moves with real GDP, because higher income raises money demand.
Bond yield
yield ≈ annual payment / price → price and yield move in OPPOSITE directions
The payment is fixed by contract. The only way the yield can change is for the price to move, which is the whole mechanism.
Reserve arithmetic
required reserves = reserve ratio × demand deposits · excess reserves = total reserves − required reserves · max new loans = excess reserves
A bank can lend out its excess reserves only. Required reserves must stay put.
Axes and shifters
vertical: REAL interest rate · horizontal: quantity of loanable funds · supply shifts: private saving, government surplus, foreign capital inflows · demand shifts: investment demand, government borrowing
The real rate, not the nominal rate. This is the first thing that distinguishes this graph from the money market.
The discriminator
Fed action, money supply, nominal rate → MONEY MARKET · deficit, saving, investment, growth, real rate → LOANABLE FUNDS
Read the question for the actor. The central bank lives in one graph, the government budget in the other.
Direction of each tool
EXPANSIONARY: buy bonds · lower discount rate · lower interest on reserves · lower reserve requirement · CONTRACTIONARY: the reverse of each
All four work on the same variable — the quantity of reserves banks want to lend — and therefore on the policy rate.
The transmission chain
buy bonds → MS ↑ → nominal rate ↓ → I and C ↑ (and currency depreciates → Xn ↑) → AD right → real GDP ↑, price level ↑, unemployment ↓
Write the arrows. Free-response rubrics award individual links, so a partial chain still earns partial credit.
The two curves, mapped to AD–AS
SRPC ↔ SRAS (both rest on sticky wages) · LRPC ↔ LRAS (both vertical, both at the natural level)
They are the same model in different coordinates. A rightward AD shift is a movement up-left along the SRPC.
The quantity theory, in growth rates
MV = PY → %ΔM + %ΔV ≈ %ΔP + %ΔY → with V stable: inflation ≈ money growth − real growth
The growth-rate form is what the exam uses. Money growing 8% with real output growing 3% implies roughly 5% inflation.
The chain
deficit ↑ → demand for loanable funds right → real interest rate ↑ → private investment ↓ → capital stock grows more slowly → LRAS shifts right more slowly
The last two links are what make crowding out a long-run problem rather than merely an offsetting short-run effect.
The relationship, and the ratio
debt_this year = debt_last year + deficit_this year · debt-to-GDP = debt / nominal GDP
The ratio falls whenever nominal GDP grows faster than the debt — which can happen while deficits continue.
What shifts LRAS right
more labor · more physical capital · more human capital · better technology · stronger institutions and property rights · more efficient resource allocation
Every genuine growth policy operates through one of these. If a proposal does not, it is a demand policy.
The balance of payments identity
current account + financial account ≈ 0 → CA deficit ⇔ FA surplus
Approximately, because of statistical discrepancies. Conceptually exact: a country that imports more than it exports must sell assets or borrow to cover the gap.
The mirror rule
dollar appreciates ⇔ euro depreciates · demand for dollars ↑ ⇔ supply of euros ↑
Buying dollars with euros is simultaneously demanding dollars and supplying euros — one transaction, two graphs.
The monetary chain, extended
MS ↑ → nominal rate ↓ → (a) investment ↑ and (b) capital outflow → currency depreciates → Xn ↑ → both raise AD
Two channels, same direction. This is why monetary policy is often described as more powerful in an open economy.
The capital flow rule
capital flows toward the higher expected REAL return → inflow shifts loanable funds SUPPLY right → domestic real rate falls
This is the link between Unit 6 and the Unit 4 loanable funds graph.
The consistency checks
real GDP ↑ ⇒ unemployment ↓, money demand ↑, nominal rate ↑ · real rate ↑ ⇒ investment ↓, capital inflow, currency appreciates, Xn ↓
If any two of your answers violate these, one of them is wrong. Use it as a self-check before moving on.

On the exam

How to get a 5

Key terms

Components of M1 — Currency in circulation, checkable/demand deposits, and traveler's checks (the most liquid money).
Money multiplier — 1 / required reserve ratio. Maximum change in the money supply = excess reserves × money multiplier.
What shifts AD? — Changes in C, I, G, or Xn (consumption, investment, government spending, net exports).
Crowding-out effect — Government borrowing raises the real interest rate, reducing private investment.
GDP expenditure formula — GDP = C + I + G + Xn (Xn = exports − imports).
Fisher equation — real ≈ nominal − inflation. Rearranged, lenders set nominal ≈ real required return + EXPECTED inflation.
Contractionary monetary tools — Sell bonds, raise the discount rate, raise reserve requirement → MS falls, rate rises.
Spending multiplier — 1 / MPS, equivalently 1 / (1 − MPC). Applies to any autonomous change in spending — C, I, G or Xn.
Tax multiplier — −MPC / MPS, equivalently −MPC × spending multiplier. Negative, and always one smaller in magnitude than the spending multiplier, because the first round of a tax cut is partly saved.
Long-run Phillips curve — Vertical at the natural rate of unemployment; no long-run inflation–unemployment tradeoff.
Why AD slopes downward — Three effects, none of them the microeconomic substitution effect: the wealth effect, the interest-rate effect, and the exchange-rate (net exports) effect.
Larger budget deficit in loanable funds — Increases demand for loanable funds → real interest rate rises.
Spending multiplier vs. tax multiplier — Spending multiplier = 1/(1 − MPC) = 1/MPS. Tax multiplier = −MPC/(1 − MPC) = −MPC/MPS, and is always smaller in absolute value because the first round of a tax change is partly saved. With MPC = 0.8: spending multiplier 5, tax multiplier −4.
Money multiplier and why the actual expansion is smaller — Money multiplier = 1/required reserve ratio. Leakages shrink the real-world effect: banks holding excess reserves, currency drain (borrowers keeping cash instead of redepositing), and weak loan demand. A 10 percent requirement gives a maximum multiplier of 10.
Real vs. nominal interest rate (Fisher equation) — Real ≈ nominal − expected inflation, so nominal ≈ real + expected inflation. Unexpected inflation lowers the realized real rate, transferring purchasing power from lenders to borrowers; unexpected disinflation does the reverse.
GDP deflator and CPI — GDP deflator = (nominal GDP / real GDP) × 100. CPI = (cost of basket in current year / cost in base year) × 100. Inflation between years = (new index − old index) / old index × 100. The deflator covers all domestic production; the CPI covers a fixed urban consumer basket and so suffers substitution bias.
Unemployment rate and labor force participation rate — Labor force = employed + unemployed (actively seeking). Unemployment rate = unemployed / labor force. LFPR = labor force / working-age population. Discouraged workers who stop searching leave the labor force, which lowers the measured unemployment rate without any new jobs.
Three types of unemployment — Frictional (temporary job search and matching) and structural (skills or location mismatch, including technological displacement) together make up the natural rate. Cyclical unemployment comes from a recessionary gap and is the only type absent at full employment.
What shifts AD (the four components) — C, I, G, and NX. Consumer confidence and wealth shift C; interest rates, business expectations, and business taxes shift I; fiscal policy shifts G; foreign income, relative price levels, and exchange rates shift NX. A price-level change moves along AD rather than shifting it.
What shifts SRAS vs. LRAS — SRAS shifts on input prices, nominal wages, productivity, supply shocks (oil), and business taxes and subsidies. LRAS shifts only on real productive capacity: quantity and quality of labor, physical and human capital, technology, and institutions. Money supply changes shift neither.
Stagflation — the diagnostic — Higher price level with lower real output simultaneously. Only a leftward SRAS shift produces this combination; a leftward AD shift lowers output and the price level together. Look at what happens to the price level to tell demand shocks from supply shocks.
Contractionary vs. expansionary monetary policy tools — Expansionary: buy bonds, cut the discount rate, lower the required reserve ratio — reserves rise, federal funds rate falls, investment and AD rise. Contractionary: sell bonds, raise the discount rate, raise the required reserve ratio. The federal funds rate is the interbank overnight rate the Fed targets.
Loanable funds market — axes and shifters — Real interest rate on the vertical axis, quantity of loanable funds on the horizontal. Demand shifts with business investment demand and government borrowing (deficits shift demand right, raising r). Supply shifts with private saving and foreign capital inflows. Expected inflation shifts both, raising the nominal but not the real rate.
Crowding out — Deficit-financed government spending raises loanable funds demand, pushing up the real interest rate and reducing private investment. It weakens the multiplier in the short run and slows capital accumulation and growth in the long run. Nominal money supply is unchanged — this is fiscal, not monetary, in origin.