AP Economics Formulas — Complete Cheat Sheet

Every key AP Microeconomics and Macroeconomics formula in one place. Each links to its full definition or a step-by-step worked example. Bookmark this for exam review.

Step-by-step calculations

GDPGDP = C + I + G + (X − M) where Xn = X − M (net exports)Real GDPReal GDP = (Nominal GDP ÷ GDP deflator) × 100 GDP DeflatorGDP deflator = (Nominal GDP ÷ Real GDP) × 100 Inflation RateInflation rate = [(CPI₂ − CPI₁) ÷ CPI₁] × 100 Unemployment RateUnemployment rate = (Unemployed ÷ Labor force) × 100 | Labor force = Employed + Unemployed Price Elasticity of DemandPED = %ΔQ ÷ %ΔP, where %Δ = (new − old) ÷ ((new + old) ÷ 2). |PED| > 1 elastic, < 1 inelastic, = 1 unit elastic.Spending MultiplierSpending multiplier = 1 ÷ (1 − MPC) = 1 ÷ MPS | ΔGDP = multiplier × Δspending | Tax multiplier = −MPC ÷ MPS Consumer SurplusConsumer surplus = ½ × base × height = ½ × quantity × (maximum willingness to pay − price)Deadweight LossDWL = ½ × base × height = ½ × |Q_efficient − Q_actual| × (price wedge)CPICPI = (cost of basket in current year ÷ cost of basket in base year) × 100 Real Interest RateReal interest rate ≈ Nominal interest rate − Inflation rate Money MultiplierMoney multiplier = 1 ÷ required reserve ratio | Δmoney supply = money multiplier × excess reserves Comparative AdvantageOpportunity cost of 1 unit of Good A = (units of Good B given up) ÷ (units of Good A gained). Lower ratio = comparative advantage.

Core Economic Concepts

Allocative EfficiencyPrice = Marginal Cost Comparative AdvantageOpportunity cost of 1 unit of A = (units of B given up) ÷ (units of A gained). The producer with the lower ratio has the comparative advantage in A.Marginal AnalysisMB = MC Opportunity CostOpportunity cost = value of the next-best alternative forgone. Example: studying for an hour instead of working a $15/hr job has a $15 opportunity cost.Terms of TradeTerms of Trade = (Index of Export Prices) / (Index of Import Prices)

Supply & Demand

Deadweight LossDWL = ½ × base × height = ½ × |Q_efficient − Q_actual| × (price wedge between supply and demand).Binding vs. Non-Binding Price ControlBinding ceiling: P_ceiling < P_equilibrium ⇒ shortage. Binding floor: P_floor > P_equilibrium ⇒ surplus.

Elasticity

Cross-Price Elasticity of DemandCross-Price Elasticity of Demand = (% Change in Quantity Demanded of Good A) / (% Change in Price of Good B)Elastic DemandPrice Elasticity of Demand > 1 Income Elasticity of DemandIncome Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)Inelastic DemandPrice Elasticity of Demand < 1 Midpoint MethodElasticity = [(Q₂−Q₁)/((Q₁+Q₂)/2)] ÷ [(P₂−P₁)/((P₁+P₂)/2)].Perfectly ElasticPrice Elasticity of Demand = ∞Perfectly InelasticPrice Elasticity of Demand = 0 Price Elasticity of DemandPED = %Δ quantity demanded ÷ %Δ price. Midpoint method: %Δ = (Q₂ − Q₁) ÷ ((Q₁ + Q₂)/2). |PED| > 1 elastic, < 1 inelastic, = 1 unit elastic.Price Elasticity of SupplyPrice Elasticity of Supply = (% Change in Quantity Supplied) / (% Change in Price)Total Revenue TestTotal revenue = Price × Quantity. Elastic: price and TR move oppositely; inelastic: same direction.Unit ElasticPrice Elasticity of Demand = 1 Marginal Revenue and ElasticityMR = P(1 − 1/|E_d|); MR > 0 if elastic, MR = 0 at unit elastic, MR < 0 if inelastic.Total Revenue and the Linear Demand CurveTR maximized at the midpoint of linear demand, where |E_d| = 1 and MR = 0.Arc vs. Point ElasticityArc: %ΔQ ÷ %ΔP using midpoints. Point: E = (dQ/dP) × (P/Q) at one point.

Consumer Choice

Budget ConstraintIncome = (Pₓ × Qₓ) + (Pᵧ × Qᵧ).Marginal UtilityMU = ΔTotal Utility ÷ ΔQuantity consumed.Total UtilityTotal Utility = Σ (marginal utility of each unit consumed).Utility Maximization RuleMUₓ ÷ Pₓ = MUᵧ ÷ Pᵧ, subject to the budget constraint.

Production & Costs

Average Fixed CostAFC = FC / Q Average ProductAP = TP / L Average Total CostATC = TC / Q Average Variable CostAVC = VC / Q Law of Diminishing Marginal ReturnsSets in when ΔTotal Product ÷ Δvariable input begins to fall.Marginal CostMC = ΔTC / ΔQ Marginal ProductMP = ΔTP / ΔL Production FunctionQ = f(L, K), where L is labor and K is capital.Total CostTC = FC + VC Least-Cost RuleMP_L / P_L = MP_K / P_K (output per dollar equal across inputs)Marginal-Average RuleIf MC < ATC, ATC falls; if MC > ATC, ATC rises; MC = ATC at min ATC (same for AVC).

Market Structures

Break-Even PointTR = TC or P = ATC Excess CapacityQ < Q_min ATC Long-Run EquilibriumP = MC = min ATC Marginal RevenueMR = ΔTotal Revenue ÷ ΔQuantity. Perfect competition: MR = P. Monopoly: MR < P. Profit max: MR = MC.Profit Maximization Rule (MR = MC)MR = MC Shutdown PointP = min AVC Marginal Revenue Curve Twice as SteepIf P = a − bQ, then TR = aQ − bQ², MR = a − 2bQ (twice the slope; x-intercept at half of demand's).Allocative Inefficiency of MonopolyMonopoly: P > MC at MR = MC output ⇒ underproduction and deadweight loss.Stackelberg ModelLeader maximizes profit anticipating follower's reaction function q_f = R(q_L); solve by backward induction Cournot CompetitionEach firm sets MR = MC given rivals' output; equilibrium where reaction functions intersect Bertrand CompetitionWith homogeneous goods and equal MC, equilibrium price P = MC (Bertrand paradox)

Factor Markets

Marginal Resource CostMRC = ΔTC / ΔQ of factor Marginal Revenue ProductMRP = MP × MR Marginal Productivity Theory of DistributionHire factor until MRP = MRC; in competition each factor earns its marginal revenue product.

Market Failure & Government

Gini CoefficientGini Coefficient = Area between Lorenz curve and line of equality / Total area under line of equality Marginal Social BenefitMSB = Marginal Private Benefit + Marginal External Benefit.Marginal Social CostMSC = Marginal Private Cost + Marginal External Cost.Negative ExternalityOverproduction occurs because MSC > MSB at the market quantity.Pigouvian TaxOptimal tax = marginal external cost at the efficient quantity.Positive ExternalityUnderproduction: marginal social benefit > marginal private benefit, so Q_market < Q_social.Marginal-Cost Pricing (Socially Optimal Price)Set P = MC; for a natural monopoly this gives P < ATC ⇒ economic loss (subsidy needed).Fair-Return Price (Average-Cost Pricing)Set P = ATC ⇒ zero economic profit; still P > MC, so some deadweight loss remains.

Measuring the Economy

Expenditure ApproachGDP = C + I + G + (X - M)GDP DeflatorGDP Deflator = (Nominal GDP / Real GDP) × 100 Per Capita GDPPer Capita GDP = GDP / Population Real GDPReal GDP = (Nominal GDP / GDP Deflator) × 100

Unemployment & Inflation

Inflation Rate(CPI2 - CPI1) / CPI1 * 100 Labor Force Participation RateLabor Force Participation Rate = (Labor Force ÷ Civilian Non-Institutional Population) × 100 Real vs. Nominal WageReal Wage = (Nominal Wage ÷ CPI) × 100. Example: a $50 nominal wage with CPI = 130 gives a real wage of (50 ÷ 130) × 100 = $38.46 in base-year dollars.Unemployment Rate(Number of unemployed workers / Labor force) * 100

Aggregate Demand & Supply

AD-AS ModelShort-run equilibrium: AD = SRAS. Long-run equilibrium: AD = SRAS = LRAS at potential output (Yf).Marginal Propensity to Consume (MPC)MPC = ΔConsumption ÷ ΔDisposable income. Spending multiplier = 1 ÷ (1 − MPC) = 1 ÷ MPS.Marginal Propensity to Save (MPS)MPS = ΔSaving ÷ ΔDisposable income; MPS = 1 − MPC.Multiplier EffectMultiplier = 1 ÷ (1 − MPC) = 1 ÷ MPS.Spending MultiplierSpending multiplier = 1 ÷ (1 − MPC) = 1 ÷ MPS; ΔGDP = multiplier × Δspending.Tax MultiplierTax multiplier = −MPC ÷ (1 − MPC) = −MPC ÷ MPS.Determinants of Aggregate DemandAD = C + I + G + Xn

Fiscal Policy

Budget DeficitBudget deficit = Government spending − Tax revenue (when positive).Budget SurplusBudget surplus = Tax revenue − Government spending (when positive).Crowding OutHigher deficit → ↑ demand for loanable funds → ↑ real interest rate → ↓ private investment.Expansionary Fiscal PolicyΔAD = Δgovernment spending × [1 ÷ (1 − MPC)].Fiscal PolicyΔAD ≈ ΔG × [1 ÷ (1 − MPC)] for a change in government spending.Fiscal Policy vs. Monetary PolicyFiscal: change G or T → shift AD. Monetary: change money supply → change interest rate → shift AD.National DebtNational debt = sum of past deficits − past surpluses.Balanced Budget MultiplierSpending multiplier + Tax multiplier = 1/(1-MPC) + (-MPC/(1-MPC)) = 1

Money & Monetary Policy

Contractionary Monetary PolicySell bonds → ↓ money supply → ↑ interest rate → ↓ investment → ↓ AD.Excess ReservesExcess reserves = Total reserves − Required reserves.Expansionary Monetary PolicyBuy bonds → ↑ money supply → ↓ interest rate → ↑ investment → ↑ AD.M1 and M2M2 = M1 + savings deposits + small time deposits + retail money market funds.Monetary PolicyBuy bonds → ↑ money supply → ↓ nominal interest rate → ↑ investment and AD.Money MarketEquilibrium: Money supply = Money demand → nominal interest rate.Money MultiplierMoney multiplier = 1 ÷ required reserve ratio; Δmoney = multiplier × Δexcess reserves.Quantity Theory of MoneyMV = PQ Required Reserve RatioMoney multiplier = 1 ÷ required reserve ratio.Velocity of MoneyV = PQ / M Money NeutralityMV = PQ (with V, Q fixed long run, ΔM ⇒ proportional ΔP)Vault CashTotal reserves = Vault cash + Deposits at the Fed Monetary Base (High-Powered Money)Monetary base (MB) = Currency in circulation + Bank reserves; Money supply ≈ m × MB Real Money BalancesReal money balances = M / P Taylor Rulei = r* + π + 0.5(π − π*) + 0.5(output gap), where r* is the neutral real rate and π* the inflation target Currency in CirculationMonetary base = Currency in circulation + Bank reserves

Financial Sector & Loanable Funds

Fisher EquationNominal Interest Rate = Real Interest Rate + Expected Inflation Long-Run Phillips CurveVertical at the natural rate of unemployment (NRU).Phillips CurveShort-run: inflation ↑ ⇒ unemployment ↓. Long-run Phillips curve is vertical at the natural rate of unemployment (NRU).Private SavingPrivate Saving = Disposable Income - Consumption Real Interest RateReal Interest Rate = Nominal Interest Rate - Inflation Rate

Economic Growth

Economic GrowthGrowth rate = (Real GDP₂ − Real GDP₁) ÷ Real GDP₁ × 100.ProductivityLabor productivity = Total output ÷ Total labor hours.Aggregate Production FunctionY = A · F(K, L, H)Growth Accounting%ΔY = %ΔA + α(%ΔK) + (1−α)(%ΔL)

International Trade & Finance

Balance of PaymentsCurrent account + Capital and financial account ≈ 0.Capital and Financial AccountRoughly offsets the current account balance.Current AccountCurrent account = Net exports + Net income + Net transfers.Exchange RateExample: $1.10 per €1 means one euro costs $1.10.Net ExportsNet exports = Exports − Imports.TariffDomestic price with tariff = world price + tariff per unit.Trade DeficitTrade deficit = Imports − Exports (when positive).Trade SurplusTrade surplus = Exports − Imports (when positive).Marshall-Lerner Condition|εx| + |εm| > 1 Twin Deficits Hypothesis(S − I) + (T − G) = NX Effective Rate of ProtectionERP = (V' - V) / V, where V = free-trade value added and V' = value added with tariffs

Money, Banking & Finance

Compound InterestFuture value = Principal × (1 + r)ⁿ, where r is the rate per period and n is the number of periods.Present ValuePresent value = Future value ÷ (1 + r)ⁿ.Prime RatePrime rate ≈ Federal funds rate + 3% (typical, not fixed)Credit RiskRisky bond rate = Risk-free rate + Default risk premium (compensation for credit risk)Interest Rate RiskBond price ↓ when market interest rates ↑ (inverse relationship); larger effect for longer maturities Term Structure of Interest RatesExpectations theory: (1 + long rate)^n ≈ product of (1 + expected short rates) over n periods Default Risk PremiumDefault risk premium = Risky bond yield − Risk-free yield (same maturity)

Microeconomic Theory

Two-Part TariffTotal charge = Fixed fee (A) + (per-unit price × quantity); optimal with identical buyers: per-unit price = MC, A = consumer surplus.

Economic Indicators & Data

Misery IndexMisery index = unemployment rate + inflation rate.

International & Development Economics

Gross National Product (GNP)GNP = GDP + net income earned abroad by residents.

Financial Markets & Investing

Market CapitalizationMarket cap = share price × shares outstanding.Capital GainCapital gain = selling price − purchase price (cost basis).Price-to-Earnings (P/E) RatioP/E ratio = share price ÷ earnings per share (EPS).Yield to Maturity (YTM)If price < face value → YTM > coupon rate; if price > face value → YTM < coupon rate

Public Finance & Taxation

Marginal Tax RateMarginal tax rate = Δtax paid ÷ Δincome.Average Tax RateAverage tax rate = total tax ÷ total income.Tax WedgeTax wedge = P_buyers − P_sellers = tax per unit; Deadweight loss = ½ × (tax) × (ΔQ)Excess Burden of TaxationExcess burden ≈ ½ × t² × (elasticity-weighted base); area of the Harberger triangle = ½ × tax wedge × ΔQ

Environmental Economics

Marginal Abatement CostEfficient abatement: Marginal Abatement Cost = Marginal Benefit of abatement Hotelling's Rule(P_t - MC) grows at rate r: net priceₙ₊₁ = net priceₙ × (1 + r)

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