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) × 100GDP DeflatorGDP deflator = (Nominal GDP ÷ Real GDP) × 100Inflation RateInflation rate = [(CPI₂ − CPI₁) ÷ CPI₁] × 100Unemployment RateUnemployment rate = (Unemployed ÷ Labor force) × 100 | Labor force = Employed + UnemployedPrice 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 ÷ MPSConsumer 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) × 100Real Interest RateReal interest rate ≈ Nominal interest rate − Inflation rateMPCMPC = ΔC ÷ ΔY | MPS = 1 − MPC | spending multiplier = 1 ÷ MPS | tax multiplier = −MPC ÷ MPSMoney MultiplierMoney multiplier = 1 ÷ required reserve ratio | Δmoney supply = money multiplier × excess reservesComparative AdvantageOpportunity cost of 1 unit of Good A = (units of Good B given up) ÷ (units of Good A gained). Lower ratio = comparative advantage.Total Revenue TestTR = P × Q. P↑ & TR↓ (or P↓ & TR↑) → elastic. P↑ & TR↑ (or P↓ & TR↓) → inelastic. TR unchanged → unit elastic.Price Elasticity of SupplyPES = %ΔQs ÷ %ΔP, with %Δ = (new − old) ÷ ((new + old) ÷ 2) on AP exams. PES > 1 elastic, < 1 inelastic, = 1 unit elastic.Cross-Price ElasticityXED = %ΔQd of good A ÷ %ΔP of good B. XED > 0 → substitutes; XED < 0 → complements; XED ≈ 0 → unrelated goods.Income ElasticityYED = %ΔQd ÷ %Δincome. YED > 0 → normal good (0–1 necessity, > 1 luxury); YED < 0 → inferior good.Tax MultiplierTax multiplier = −MPC ÷ (1 − MPC) = −MPC ÷ MPS | ΔGDP = tax multiplier × ΔtaxesMPC & MPSMPC = ΔC ÷ ΔY | MPS = ΔS ÷ ΔY | MPC + MPS = 1Marginal CostMC = ΔTC ÷ ΔQ = ΔVC ÷ ΔQ (fixed costs don't change, so only variable costs matter)Average Total CostATC = TC ÷ Q = AFC + AVC | AFC = FC ÷ Q | AVC = VC ÷ QMarginal RevenueMR = ΔTR ÷ ΔQ, where TR = P × Q. Perfect competition: MR = P. Monopoly/imperfect competition: MR < P.Economic ProfitEconomic profit = TR − explicit costs − implicit costs = accounting profit − implicit costs | Per-unit form: (P − ATC) × QMarginal Revenue ProductMRP = MP × P (competitive output market) = ΔTR ÷ Δlabor. Hire until MRP = wage (MRC).Labor Force ParticipationLFPR = (Labor force ÷ working-age population) × 100 | Labor force = employed + unemployedVelocity of MoneyM × V = P × Q (quantity theory of money), so V = (P × Q) ÷ M = nominal GDP ÷ money supplyProducer SurplusProducer surplus = ½ × base × height = ½ × quantity × (price − supply curve's price intercept)Opportunity CostPer-unit opportunity cost of good A = units of good B given up ÷ units of good A gainedGDP per CapitaGDP per capita = Real GDP ÷ PopulationEconomic Growth RateGrowth rate (%) = ((Real GDP in year 2 − Real GDP in year 1) ÷ Real GDP in year 1) × 100Gini CoefficientGini = Area A ÷ (Area A + Area B) = Area A ÷ 0.5 = 2 × Area A (where A = area between the line of equality and the Lorenz curve, B = area under the Lorenz curve, and A + B = 0.5 on a unit square)Tax IncidenceConsumer burden per unit = P(paid, after tax) − P(before tax)
Producer burden per unit = P(before tax) − P(received, after tax)
Consumer burden + Producer burden = tax per unit
Burden rule: Consumer burden ÷ Producer burden = Es ÷ Ed (the more inelastic side pays the larger share)Percentage ChangePercentage change = ((New value − Old value) ÷ Old value) × 100Balanced Budget MultiplierBalanced budget multiplier = spending multiplier + tax multiplier = 1 ÷ (1 − MPC) + (−MPC ÷ (1 − MPC)) = (1 − MPC) ÷ (1 − MPC) = 1 | ΔGDP = 1 × Δspending (when Δspending = Δtaxes)Present ValuePV = FV ÷ (1 + r)ⁿ where r = interest (discount) rate as a decimal, n = number of yearsHerfindahl-Hirschman Index (HHI)HHI = (s₁)² + (s₂)² + ... + (sₙ)² = Σ (share%)² where each share is a whole-number percent (0 to 100)Marginal UtilityMU = ΔTU ÷ ΔQ = (TU₂ − TU₁) ÷ (Q₂ − Q₁)MU per DollarMU per dollar = MU ÷ P | compare MUx ÷ Px against MUy ÷ Py to decide what to buy nextUtility-Maximizing RuleMUx ÷ Px = MUy ÷ Py and PxQx + PyQy = Income (both conditions must hold)Total UtilityTU = MU₁ + MU₂ + ... + MUn | TU at Q = TU at (Q − 1) + MU of unit QBudget ConstraintPxQx + PyQy = Income | slope = −Px ÷ Py | intercepts = Income ÷ Px and Income ÷ PyMRSMRS = MUx ÷ MUy = absolute slope of the indifference curve | at the optimum, MRS = Px ÷ PyConsumer EquilibriumMUx ÷ Px = MUy ÷ Py and PxQx + PyQy = Income | equivalently MUx ÷ MUy = Px ÷ PyAverage Variable CostAVC = VC ÷ Q = ATC − AFC | VC = TC − FCAverage Fixed CostAFC = FC ÷ Q = ATC − AVCTotal CostTC = FC + VC = ATC × Q | FC = AFC × Q, VC = AVC × QTotal Variable CostVC = TC − FC = AVC × Q = the sum of the marginal costs from the first unit up to QMarginal ProductMP = ΔTP ÷ ΔL (change in total product ÷ change in units of the input, usually labor)Average ProductAP = TP ÷ L (total product ÷ quantity of the variable input)Break-Even PointBreak-even quantity: Q = FC ÷ (P − AVC) | Break-even price: P = minimum ATC, where TR = TC and economic profit = 0Marginal Factor CostMFC = ΔTotal factor cost ÷ ΔQuantity of the input hired | Perfectly competitive labor market: MFC = wage | Monopsony: MFC > wage, and the MFC curve lies above the labor supply curveLabor's Marginal ProductMPL = ΔTotal output ÷ ΔQuantity of labor = ΔQ ÷ ΔL | With one-worker steps, MPL is simply the extra output that worker addsOptimal HiringHire where MRP = MFC | Competitive labor market: MRP = W (the wage) | Monopsony: hire where MRP = MFC, then read the wage off the labor supply curve at that quantity | MRP = MP × PLeast-Cost RuleMPL ÷ PL = MPK ÷ PK (marginal product per dollar equal across every input) | Profit-maximizing version: MRPL ÷ PL = MRPK ÷ PK = 1Marginal Social CostMSC = MPC + Marginal external cost | No externality: MSC = MPC, the supply curve | Negative externality: MSC lies above MPC by the external cost per unitMarginal Social BenefitMSB = MPB + Marginal external benefit | No externality: MSB = MPB, the demand curve | Positive externality: MSB lies above MPB by the external benefit per unitSocially Optimal QuantitySocially optimal Q solves MSB = MSC, where MSB = MPB + marginal external benefit and MSC = MPC + marginal external cost | The market quantity instead solves MPB = MPCProfit Max QuantityProduce where MR = MC (MC rising). Profit = (P − ATC) × QShutdown PointShut down if P < minimum AVC. AVC = TVC ÷ Q, and minimum AVC occurs where MC = AVCAccounting ProfitAccounting profit = Total revenue − Explicit costsTotal RevenueTotal revenue = Price × Quantity (TR = P × Q)Markup Over MCDollar markup = P − MC. Percentage markup = [(P − MC) ÷ MC] × 100Lerner IndexLerner index = (P − MC) ÷ P (equals 1 ÷ |price elasticity of demand| at the profit-maximizing output)Concentration RatioCRn = share of firm 1 + share of firm 2 + ... + share of firm n, where each share = (firm sales ÷ total industry sales) × 100Recessionary GapRecessionary gap = Potential real GDP − Actual real GDP | As a percent of potential: [(Potential − Actual) ÷ Potential] × 100Inflationary GapInflationary gap = Actual real GDP − Potential real GDP | Required spending cut = Gap ÷ Spending multiplierOutput GapOutput gap = Actual real GDP − Potential real GDP | Output gap (%) = [(Actual − Potential) ÷ Potential] × 100Budget DeficitBudget deficit = Government outlays − Government revenue (one year) | Budget surplus = Revenue − Outlays | New debt = Old debt + this year's deficitDebt-to-GDP RatioDebt-to-GDP ratio = (Total government debt ÷ Nominal GDP) × 100Required Spending ChangeRequired Δspending = Gap ÷ Spending multiplier where Spending multiplier = 1 ÷ (1 − MPC) = 1 ÷ MPS | Rearranged from ΔGDP = Multiplier × ΔspendingRequired Tax ChangeRequired Δtaxes = Gap ÷ Tax multiplier where Tax multiplier = −MPC ÷ MPS | A negative Δtaxes is a tax cut | Required tax change = Required spending change ÷ MPCLabor ProductivityLabor productivity = Real output ÷ Labor hoursGains From TradeGains from trade = Consumption with trade − Production without trade (computed per good, per country)Terms of Trade RangeLower opportunity cost of 1 X < Terms of trade for 1 X < Higher opportunity cost of 1 X (both bounds measured in units of good Y)Compound GrowthEnd value = Start value × (1 + g)ⁿ where g = growth rate as a decimal, n = number of periods. Average growth rate = (End ÷ Start) raised to the power (1 ÷ n), minus 1Future ValueFV = PV × (1 + r)ⁿ where r = interest rate as a decimal, n = number of yearsExpected ValueExpected value = Σ (probability of an outcome × payoff of that outcome), where the probabilities must sum to 1Real WageReal wage = (Nominal wage ÷ Price index) × 100Rule of 70Years to double = 70 ÷ annual growth rate (in percent)Misery IndexMisery index = Inflation rate (%) + Unemployment rate (%)Natural RateNatural rate = Frictional rate + Structural rate | Natural rate = Actual unemployment rate − Cyclical rateCyclical UnemploymentCyclical unemployment rate = Actual unemployment rate − Natural rate of unemploymentEmployment-Population RatioEmployment-population ratio = (Employed ÷ Civilian noninstitutional population age 16+) × 100Cost-of-Living AdjustmentCOLA = Benefit × Inflation rate | New benefit = Benefit + COLA = Benefit × (1 + Inflation rate)Currency ConversionAmount in target currency = amount in starting currency × (target currency per 1 unit of starting currency)
Reverse rate = 1 ÷ original rate
Dividing by a rate is the same as multiplying by its reciprocalCurrency AppreciationAppreciation % = [(new rate − old rate) ÷ old rate] × 100
The rate must be quoted as foreign currency per 1 unit of the currency you are tracking
A positive result is appreciation, a negative result is depreciationCurrency DepreciationDepreciation % = [(new rate − old rate) ÷ old rate] × 100
Rate = foreign currency per 1 unit of the currency you are tracking
A negative result is depreciation, and its absolute size is the percentage fallPurchasing Power ParityPPP exchange rate = price of the basket in currency A ÷ price of the same basket in currency B
The result is units of currency A per 1 unit of currency B
Overvaluation or undervaluation % = (market rate − PPP rate) ÷ PPP rate × 100Real Exchange RateReal exchange rate = nominal exchange rate × (domestic price level ÷ foreign price level)
Convention used here: the nominal rate is quoted as foreign currency per 1 unit of domestic currency
A rise means domestic goods have become relatively more expensiveCurrent AccountCurrent account = balance on goods and services + net primary income + net secondary income
Balance on goods and services = exports − imports
Net primary income = investment income and worker pay received − paid out
Net secondary income = transfers received − transfers sentTerms of TradeTerms of trade = (index of export prices ÷ index of import prices) × 100
Above 100 means export prices have risen faster than import prices since the base year
Percent change = (new index − old index) ÷ old index × 100Nominal GDPNominal GDP = sum of (current-year price × current-year quantity) | Nominal GDP = C + I + G + (X − M) at current pricesNet ExportsNet exports (Xn) = exports (X) − imports (M) | GDP = C + I + G + XnDisposable IncomeDisposable income (DI) = personal income − personal taxes | DI = consumption (C) + saving (S)National IncomeNational income (NI) = compensation of employees + rental income + net interest + proprietors' income + corporate profitsNet Domestic ProductNDP = GDP − depreciation (consumption of fixed capital) | Net investment = gross investment − depreciationValue AddedValue added = value of a firm's sales − cost of intermediate goods purchased | GDP = sum of value added at every stageGDP Income ApproachGDP = wages + rent + interest + profit + depreciation + taxes on production and imports (plus a statistical discrepancy)Pigouvian TaxPigouvian tax per unit = MSC − MPC measured at Q(optimal)
Q(optimal) is where MSB = MSCPer-Unit SubsidyPer-unit subsidy = MSB − MPB measured at Q(optimal)
Total cost to government = per-unit subsidy × quantity traded after the subsidyExcise Tax RevenueExcise tax revenue = per-unit tax × Q(after tax)
Revenue from consumers = consumer burden per unit × Q(after tax)
Revenue from producers = producer burden per unit × Q(after tax)Externality DWLDWL = ½ × base × height
base = |Q(market) − Q(optimal)|
height = vertical gap between MSC and MSB at Q(market), which equals the external cost or benefit per unit when that spillover is constantTariff RevenueTariff revenue = tariff per unit × imports after the tariff
Imports after the tariff = Qd − Qs, both read at the price (world price + tariff)Effective Tax RateEffective (average) tax rate = (total tax paid ÷ total income) × 100Marginal Tax RateMarginal tax rate = [(tax₂ − tax₁) ÷ (income₂ − income₁)] × 100Market EquilibriumSet Qd = Qs, solve for P*, then Q* = Qd at P* = Qs at P*ShortageShortage = Qd − Qs at the given price (positive only when that price is below equilibrium)Market SurplusSurplus = Qs − Qd at the given price (positive only when that price is above equilibrium)Price CeilingShortage = Qd − Qs at the ceiling; quantity traded = Qs; DWL = ½ × (Q equilibrium − Q traded) × (demand price − supply price at Q traded)Price FloorSurplus = Qs − Qd at the floor; quantity traded = Qd; DWL = ½ × (Q equilibrium − Q traded) × (floor price − supply price at Q traded)Total SurplusTotal surplus = consumer surplus + producer surplus = ½ × Q × (demand's price intercept − supply's price intercept)Midpoint Method%Δ = (new − old) ÷ ((new + old) ÷ 2), then elasticity = %ΔQ ÷ %ΔPRequired ReservesRequired reserves = required reserve ratio × checkable depositsExcess ReservesExcess reserves = total reserves − required reserves | required reserves = required reserve ratio × checkable depositsDeposit ExpansionMaximum deposit expansion = excess reserves × (1 ÷ required reserve ratio)Nominal Interest RateNominal interest rate ≈ real interest rate + expected inflation rateFisher EquationNominal ≈ real + expected inflation | real ≈ nominal − expected inflation | expected inflation ≈ nominal − realEquation of ExchangeM × V = P × Q (P × Q = nominal GDP) | growth form: %ΔM + %ΔV ≈ %ΔP + %ΔQM1 and M2M1 = currency in circulation + checkable deposits + traveler's checks | M2 = M1 + savings deposits + small time deposits + retail money market fundsProduction FunctionQ = f(L, K) | Cobb-Douglas form: Q = A × L^α × K^β | APL = Q ÷ L | MPL = α × Q ÷ L | MPK = β × Q ÷ K | Returns to scale: read the sum α + βExcess CapacityExcess capacity = Q at minimum ATC − Q actual | Capacity utilization = (Q actual ÷ Q at minimum ATC) × 100 | The firm carries excess capacity whenever Q actual < Q at minimum ATCNational DebtNational debt = Starting debt + Sum of past deficits − Sum of past surpluses | Yearly interest cost = Debt × Interest ratePrivate SavingPrivate saving = Disposable income − Consumption = Y − T − C | Public saving = T − G | National saving = Private saving + Public saving = Y − C − GGNPGNP = GDP + net foreign factor income | Net foreign factor income = income residents earn abroad − income foreigners earn domesticallyMarket CapitalizationMarket cap = share price × shares outstanding | Percent change in market cap = percent change in share price, when the share count is unchangedCapital GainCapital gain = selling price − purchase price (cost basis) | Percent return = (gain ÷ purchase price) × 100 | After-tax gain = gain × (1 − tax rate)P/E RatioP/E ratio = share price ÷ earnings per share (EPS) | EPS = net income ÷ shares outstanding | Earnings yield = (EPS ÷ share price) × 100Marginal-Average RuleNew ATC = (TC + MC of the next unit) ÷ (Q + 1) | MC < ATC ⇒ ATC falls | MC > ATC ⇒ ATC rises | MC = ATC at minimum ATCTwo-Part TariffTotal charge = access fee (A) + (per-unit price × quantity) | Identical buyers: per-unit price = MC, and A = consumer surplus = ½ × (choke price − MC) × quantity boughtMonopoly InefficiencyMonopoly output: MR = MC, where MR = choke price − (2 × slope × Q) | Efficient output: P = MC | Deadweight loss = ½ × (efficient Q − monopoly Q) × (monopoly price − MC)Growth Accounting%ΔY = %ΔA + α(%ΔK) + (1 − α)(%ΔL)
α = capital's share of income, so labor's share is 1 − α
Solow residual: %ΔA = %ΔY − α(%ΔK) − (1 − α)(%ΔL)Marshall-Lerner ConditionMarshall-Lerner condition: |εx| + |εm| > 1
Change in export value = |εx| × depreciation
Change in import value = (1 − |εm|) × depreciation
Change in the trade balance ≈ trade value × depreciation × (|εx| + |εm| − 1)Twin Deficits(S − I) + (T − G) = NX
S = private saving, I = domestic investment, T = net tax revenue, G = government spending, NX = net exports
National saving = S + (T − G), so NX = national saving − IMonetary BaseMonetary base (MB) = currency in circulation + bank reserves | maximum checkable deposits = bank reserves ÷ required reserve ratio | maximum money supply (M1) = currency in circulation + maximum checkable deposits | deposit multiplier = 1 ÷ required reserve ratioReal Money BalancesReal money balances = M ÷ P | with a price index based at 100: real balances = (M ÷ price index) × 100Taylor Rulei = r* + π + 0.5(π − π*) + 0.5(output gap) | r* is the neutral real rate, π* is the inflation targetYield to MaturityApproximate YTM = [C + (F − P) ÷ n] ÷ [(F + P) ÷ 2] | exact YTM = the discount rate that makes the present value of every coupon plus the face value equal the priceTerm Structure(1 + long rate)ⁿ = (1 + r₁) × (1 + r₂) × ... × (1 + rₙ) | n-year yield = [(1 + r₁)(1 + r₂)...(1 + rₙ)]^(1 ÷ n) − 1Default Risk PremiumDefault risk premium = Risky bond yield − Risk-free yield (same maturity) | Break-even default rate = Premium ÷ (1 − Recovery rate)Hotelling's RuleNet price = P − MC | Net price after t years = (P₀ − MC) × (1 + r)ᵗ | Price after t years = MC + (P₀ − MC) × (1 + r)ᵗStackelberg Modelq_leader = (a − c) ÷ (2b) | q_follower = (a − c) ÷ (4b) | P = a − b × (q_leader + q_follower) | Profit = (P − c) × qCournot Competitionq per firm = (a − c) ÷ [(n + 1) × b] | Q = n × q | P = a − bQ = (a + n × c) ÷ (n + 1) | Profit per firm = (P − c) × qHyperbolic DiscountingPV = V ÷ (1 + k × t) | exponential form for comparison: PV = V ÷ (1 + r)^tPresent BiasWeight on a payoff today = 1 | Weight on a payoff t periods away = beta × delta^t, with 0 < beta < 1Leverage RatioLeverage ratio = Assets ÷ Equity | Wipeout threshold = Equity ÷ Assets = 1 ÷ leverage ratioPMIPMI = (% reporting better) + (0.5 × % reporting no change) | equivalently PMI = 50 + 0.5 × (% better − % worse)Core InflationCore inflation rate = ((core index now − core index a year earlier) ÷ core index a year earlier) × 100Capacity UtilizationCapacity utilization rate = (actual output ÷ sustainable maximum output) × 100 | Idle capacity = sustainable maximum output − actual outputInventory-to-SalesInventory-to-sales ratio = inventories ÷ monthly sales | Days of sales covered = ratio × 30Sacrifice RatioSacrifice ratio = cumulative percent of one year's output lost ÷ percentage-point fall in inflationIndex NumberIndex number = (Value in the period ÷ Value in the base period) × 100Nominal ValueNominal value = Real value × (Price index ÷ 100) | Real value = Nominal value ÷ (Price index ÷ 100)Adaptive ExpectationsExpected inflation next period = Expected inflation now + a × (Actual inflation now − Expected inflation now), with a between 0 and 1Scarcity RentScarcity rent = price − marginal extraction cost
Scarcity rent after t years = scarcity rent today × (1 + r)^t
Price after t years = marginal extraction cost + scarcity rent after t yearsContingent ValuationAggregate benefit = mean willingness to pay per household × number of affected households
Net benefit = aggregate benefit − cost
Break-even mean willingness to pay = cost ÷ number of affected householdsPermit PriceRequired abatement = baseline emissions − cap
Trading sets MAC(firm A) = MAC(firm B) = permit price
Permit price = the common marginal abatement cost once the required cuts are splitArbitrage ProfitArbitrage profit = (selling price − buying price) × quantity − transaction costs
Break-even quantity = transaction costs ÷ (selling price − buying price)Total Economic ValueTotal economic value = use value + option value + non-use value
Non-use value = existence value + bequest value
Net gain from preserving = total economic value − net benefit of the alternative useHedge Fund FeesManagement fee = management fee rate × assets | Performance fee = performance fee rate × gross gain | Investor's net gain = gross gain − management fee − performance feeMixed Strategy EquilibriumLet q = the chance the column player picks Left. Set EV(Up) = EV(Down) and solve for q | Let p = the chance the row player picks Up. Set EV(Left) = EV(Right) and solve for p | q = (Down-Right payoff − Up-Right payoff) ÷ (Up-Left − Up-Right − Down-Left + Down-Right), all read off the row player's payoffsRepeated Game PayoffsCooperating = cooperate payoff × rounds still to come | Cheating = cheat payoff + punishment payoff × (rounds still to come − 1) | Break-even rounds = (cheat payoff − punishment payoff) ÷ (cooperate payoff − punishment payoff) | Open-ended version: cooperation holds when the discount factor is at least gain from cheating ÷ (gain from cheating + per-round loss)Market for LemonsBuyer's maximum offer = (share good × value if good) + (share lemon × value if lemon) | Good units trade only when that offer is at least what a good unit's owner will acceptExport SubsidyDomestic price with the subsidy = world price + subsidy per unit | Exports = domestic quantity supplied − domestic quantity demanded, both read at that price | Government cost = subsidy per unit × exports after the subsidy | Net welfare loss = ½ × subsidy × rise in domestic output + ½ × subsidy × fall in domestic consumptionCustoms Union WelfareNet welfare = trade creation gain − trade diversion loss
Trade creation gain = ½ × price fall × rise in imports
Trade diversion loss = old import volume × (partner price − world price)
Price fall = (world price + tariff) − partner pricePoverty LinePoverty line per person = annual food budget + non-food allowance
Annual food budget = daily cost of the calorie-minimum basket × days covered
Non-food allowance = food budget × the non-food share
Household line = line per person × household sizePoverty Headcount RatioHeadcount ratio (P0) = people below the line ÷ total population × 100
Poverty gap index (P1) = headcount ratio × (average shortfall ÷ poverty line)
Total shortfall = people below the line × average shortfallRelative Poverty ThresholdRelative poverty threshold = threshold percentage × median equivalized household income
A household is in relative poverty when its equivalized income falls below that threshold
Relative poverty rate = households below the threshold ÷ all households × 100Flat-Rate Loan InterestTotal interest = amount borrowed × flat rate × years
Average balance owed = amount borrowed × (n + 1) ÷ (2n) where n = number of equal installments
Effective rate = total interest ÷ (average balance × years) × 100Skilled Emigration RateSkilled emigration rate = skilled emigrants ÷ (skilled emigrants + skilled workers at home) × 100
Skilled stock trained at home = skilled emigrants + skilled workers at home
Retention rate = 100 − skilled emigration rateCatch-Up TimeYears to catch up = ln(rich income ÷ poor income) ÷ ln[(1 + g poor) ÷ (1 + g rich)] where g is the annual growth rate of real GDP per person, written as a decimalUnit Labor CostUnit labor cost = Wage per hour ÷ Output per hour | Output per hour = Total output ÷ Total hours workedJob Finding RateJob finding rate = Hires ÷ Unemployed | Vacancy filling rate = Hires ÷ Vacancies | Market tightness = Vacancies ÷ Unemployed | Expected spell length = 1 ÷ job finding rateHorizontal MergerChange in HHI = 2 × share A × share B | Post-merger HHI = pre-merger HHI + change | Pre-merger HHI = sum of every firm's squared percent shareSwitching CostsTotal switching cost = fees + (hours spent × value of an hour) | Switch if saving per period × periods > total switching cost | Break-even periods = total switching cost ÷ saving per periodMinimum Efficient ScaleMES = smallest output where long-run ATC reaches its minimum | Firms the market supports ≈ market quantity ÷ MES | MES as a share of the market = (MES ÷ market quantity) × 100Rate-of-Return RegulationAllowed revenue = operating costs + (allowed rate of return × rate base) | Regulated price = allowed revenue ÷ units soldLimit PricingLimit price = entrant's minimum ATC − undercut margin, with ATC of the incumbent < limit price < ATC of the entrant | Profit given up = profit with no entry threat − profit at the limit priceIsoquant MRTSMRTS = −(ΔK ÷ ΔL) = MPL ÷ MPK | output is held constant along one isoquant | least-cost input mix: MRTS = w ÷ rIsocost LinewL + rK = C | slope = −w ÷ r | intercepts: C ÷ w units of labor and C ÷ r units of capitalReturns to ScaleScale every input by t | Q(tK, tL) > t × Q(K, L) is increasing returns, = t × Q(K, L) is constant, < t × Q(K, L) is decreasing | elasticity of scale = ln(output multiplier) ÷ ln(t)Social Welfare FunctionUtilitarian: W = U1 + U2 + ... + Un | Rawlsian (maximin): W = min(U1, U2, ..., Un) | rank allocations by W under the rule you choseExpected UtilityEU = p₁ × U(x₁) + p₂ × U(x₂) + ... + pₙ × U(xₙ), where the probabilities sum to 1Certainty EquivalentU(CE) = expected utility of the gamble | with utility = wealth^r, CE = EU^(1 ÷ r) | risk premium = expected value − CESeigniorageReal seigniorage = (change in the monetary base ÷ price index) × 100 | Inflation tax = inflation rate × real money balancesCompensating VariationCV = (income needed at the new prices to reach the old utility) − actual income | Cobb-Douglas shortcut: CV = income × [(new price ÷ old price)^α − 1], where α is the share of income spent on the goodEstate TaxTaxable estate = gross estate − exemption − deductions | Estate tax owed = tax rate × taxable estate | Effective rate = tax owed ÷ gross estateCorporate Income TaxTaxable profit = revenue − deductible costs (wages, materials, interest, depreciation) | Tax owed = statutory rate × taxable profit | After-tax profit = taxable profit − tax owedTax ExpenditureTax expenditure = revenue under a clean base − revenue actually collected | Per taxpayer: marginal rate × amount removed from the base | Program cost = per-taxpayer amount × number of claimantsMeans-Tested BenefitBenefit = maximum benefit − [phase-out rate × (income − threshold)], floored at zero | Break-even income = threshold + (maximum benefit ÷ phase-out rate) | Effective marginal tax rate = phase-out rate + other taxes on the next dollarEITCPhase-in (earnings up to the ceiling): credit = phase-in rate × earnings | Plateau: credit = maximum = phase-in rate × phase-in ceiling | Phase-out: credit = maximum − [phase-out rate × (earnings − plateau end)], floored at zeroNegative Income TaxNet payment = Guaranteed minimum − (Clawback rate × Earned income) | Break-even income = Guaranteed minimum ÷ Clawback rate | Income after the payment = Earned income + Net paymentUniversal Basic Income CostGross cost = Payment per person × Number of recipients | Funding tax rate = Gross cost ÷ Taxable income base | Break-even earnings = Payment ÷ Funding tax rate | Net position = Payment − (Funding tax rate × Earnings)
Core Economic Concepts
Allocative EfficiencyPrice = Marginal CostComparative 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 = MCOpportunity 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
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 > 1Income Elasticity of DemandIncome Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)Inelastic DemandPrice Elasticity of Demand < 1Midpoint MethodElasticity = [(Q₂−Q₁)/((Q₁+Q₂)/2)] ÷ [(P₂−P₁)/((P₁+P₂)/2)].Perfectly ElasticPrice Elasticity of Demand = ∞Perfectly InelasticPrice Elasticity of Demand = 0Price 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 = 1Marginal 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
Production & Costs
Average Fixed CostAFC = FC / QAverage ProductAP = TP / LAverage Total CostATC = TC / QAverage Variable CostAVC = VC / QLaw of Diminishing Marginal ReturnsSets in when ΔTotal Product ÷ Δvariable input begins to fall.Marginal CostMC = ΔTC / ΔQMarginal ProductMP = ΔTP / ΔLProduction FunctionQ = f(L, K), where L is labor and K is capital.Total CostTC = FC + VCLeast-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 = ATCExcess CapacityQ < Q_min ATCLong-Run EquilibriumP = MC = min ATCMarginal RevenueMR = ΔTotal Revenue ÷ ΔQuantity. Perfect competition: MR = P. Monopoly: MR < P. Profit max: MR = MC.Profit Maximization Rule (MR = MC)MR = MCShutdown PointP = min AVCMarginal 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 inductionCournot CompetitionEach firm sets MR = MC given rivals' output; equilibrium where reaction functions intersectBertrand CompetitionWith homogeneous goods and equal MC, equilibrium price P = MC (Bertrand paradox)
Factor Markets
Market Failure & Government
Gini CoefficientGini Coefficient = Area between Lorenz curve and line of equality / Total area under line of equalityMarginal 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
Unemployment & Inflation
Inflation Rate(CPI2 - CPI1) / CPI1 * 100Labor Force Participation RateLabor Force Participation Rate = (Labor Force ÷ Civilian Non-Institutional Population) × 100Real 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) * 100Long-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).
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)) = 1Ricardian EquivalenceΔPrivate saving = ΔDeficit, so ΔNational saving = 0 and ΔConsumption = 0. The household budget is untouched because T_now + T_next ÷ (1 + r) is unchanged.Fiscal MultiplierFiscal multiplier = change in real GDP / change in the fiscal variable. Closed economy ceiling with only saving leakage: 1 / (1 - MPC). With income taxes and imports: 1 / (1 - MPC x (1 - t) + m), where t is the marginal tax rate and m the marginal propensity to import.
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 = PQRequired Reserve RatioMoney multiplier = 1 ÷ required reserve ratio.Velocity of MoneyV = PQ / MMoney NeutralityMV = PQ (with V, Q fixed long run, ΔM ⇒ proportional ΔP)Vault CashTotal reserves = Vault cash + Deposits at the FedMonetary Base (High-Powered Money)Monetary base (MB) = Currency in circulation + Bank reserves; Money supply ≈ m × MBReal Money BalancesReal money balances = M / PTaylor Rulei = r* + π + 0.5(π − π*) + 0.5(output gap), where r* is the neutral real rate and π* the inflation targetCurrency in CirculationMonetary base = Currency in circulation + Bank reserves
Financial Sector & Loanable Funds
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)Malthusian TrapFixed land: Y = A × N^0.5, so income per head y = A / N^0.5. Population settles where y equals subsistence y_s, giving N* = (A / y_s)²Infrastructure InvestmentFor a long-lived asset: NPV = (annual net benefit / discount rate) - upfront cost; build only if NPV > 0Solow Growth ModelChange in capital per worker: dk = s x f(k) - (delta + n) x k. Steady state where dk = 0: s x f(k*) = (delta + n) x k*Endogenous Growth TheoryAK version: Y = A x K, and the growth rate g = (s x A) - d, where s is the saving rate, A is output per unit of capital and d is the depreciation rate. Growth depends permanently on s because capital's marginal product stays at A instead of falling.Capital DeepeningCapital per worker k = K / L; change in k = s x y - (d + n) x k, where s is the saving rate, y is output per worker, d is the depreciation rate and n is the growth rate of the labor force
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| > 1Twin Deficits Hypothesis(S − I) + (T − G) = NXEffective Rate of ProtectionERP = (V' - V) / V, where V = free-trade value added and V' = value added with tariffsDevaluationSize of devaluation = (new rate − old rate) / old rate × 100, with the rate quoted as foreign currency per unit of domestic currencyCapital FlightResidual measure: Capital flight = (rise in external debt + net FDI inflows) − (current account deficit + rise in official reserves)Hot MoneyReturn on a hot-money position ≈ (domestic interest rate − foreign interest rate) − expected depreciation of the domestic currencyCrawling PegCrawl that holds the real exchange rate constant: (1 + e) = (1 + domestic inflation) / (1 + foreign inflation), approximated as e = domestic inflation - foreign inflation.Carry TradeReturn on a carry trade = (interest rate on the target currency - interest rate on the funding currency) + percentage change in the target currency against the funding currency.Balance of TradeBalance of trade = value of exports - value of imports; as a share of output, (exports - imports) / GDP x 100Sterilized InterventionMonetary base = net foreign assets + net domestic assets. Sterilization sets the change in net domestic assets equal to minus the change in net foreign assets, so the change in the monetary base is zero.
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 maturitiesTerm Structure of Interest RatesExpectations theory: (1 + long rate)^n ≈ product of (1 + expected short rates) over n periodsDefault Risk PremiumDefault risk premium = Risky bond yield − Risk-free yield (same maturity)Zero Lower BoundReal rate = nominal rate − expected inflation. With the nominal rate stuck at 0, real rate = 0 − expected inflation.SeigniorageReal seigniorage = (change in the monetary base) ÷ price level. Inflation tax = inflation rate × real money balances held by the public.Capital AdequacyCapital adequacy ratio = (Tier 1 capital + Tier 2 capital) ÷ Risk-weighted assets, where Risk-weighted assets = the sum of each asset multiplied by its risk weight; Leverage ratio = Tier 1 capital ÷ total unweighted exposure.
Microeconomic Theory
Two-Part TariffTotal charge = Fixed fee (A) + (per-unit price × quantity); optimal with identical buyers: per-unit price = MC, A = consumer surplus.Budget LinePx × X + Py × Y = I; slope = −Px ÷ Py; X-intercept = I ÷ Px; Y-intercept = I ÷ PyIsoquantMRTS = −(ΔK ÷ ΔL) = MP_L ÷ MP_K, with output held constant along one isoquantIsocost Linew × L + r × K = C; slope = −w ÷ r; least-cost input mix: MRTS = w ÷ r, equivalently MP_L ÷ w = MP_K ÷ rReturns to ScaleScale every input by t > 1: increasing returns if Q(tK, tL) > t × Q(K, L); constant if Q(tK, tL) = t × Q(K, L); decreasing if Q(tK, tL) < t × Q(K, L)Cobb-Douglas Production FunctionQ = A × K^α × L^β; constant returns to scale when α + β = 1, increasing when α + β > 1, decreasing when α + β < 1Edgeworth BoxAlong the contract curve: MRS of person A = MRS of person B (the two indifference curves are tangent)Social Welfare FunctionUtilitarian: W = U1 + U2 + ... + Un; Rawlsian (maximin): W = min(U1, U2, ..., Un)Compensating VariationCV = (income needed at the NEW prices to reach the OLD utility level) − (actual income)Risk AversionRisk premium = expected value of the gamble − certainty equivalent; risk averse when U(expected value) > expected utility of the gambleExpected UtilityEU = p1 × U(x1) + p2 × U(x2) + ... + pn × U(xn), with p1 + p2 + ... + pn = 1Certainty EquivalentU(certainty equivalent) = expected utility of the gamble; risk premium = expected value − certainty equivalentComparative StaticsFor equilibrium defined by Qd(P, a) = Qs(P): dP*/da = (dQd/da) / (dQs/dP - dQd/dP). The denominator is positive under normal slopes, so dP*/da carries the sign of dQd/da.Hedonic PricingP = b0 + b1x1 + b2x2 + ... + bkxk + e, where the implicit price of attribute i is bi = dP/dxi. In log form, ln P = b0 + b1x1 + ..., bi reads as roughly the percentage change in price per unit of xi.
Behavioral Economics
Present BiasWeight on a payoff today = 1; weight on a payoff t periods away = beta × delta^t, with 0 < beta < 1 (beta is the present bias)Hyperbolic DiscountingPV = V ÷ (1 + k × t), where k sets impatience and t is the delay; compare exponential discounting, PV = V ÷ (1 + r)^tUltimatum GameProposer offers x out of a pot M. If accepted: proposer gets M − x, responder gets x. If rejected: both get 0.Bayesian UpdatingP(H|E) = P(E|H) x P(H) / P(E), where P(E) = P(E|H) x P(H) + P(E|not H) x P(not H)
Game Theory & Information
Mixed StrategyFind the rival's equilibrium mix by setting your own expected payoffs equal: EV(your move 1) = EV(your move 2), where EV = the sum of (probability of each rival move × your payoff).Repeated GameIgnoring discounting, cooperation survives when: one-time gain from cheating < per-period loss during punishment × number of rounds still to be played.Market for LemonsBuyer's maximum offer = (share good × value if good) + (share lemon × value if lemon)
Economic Systems & Schools of Thought
Marxian EconomicsCommodity value = c + v + s (constant capital + variable capital + surplus value); rate of surplus value = s ÷ v; rate of profit = s ÷ (c + v)Rational ExpectationsExpected inflation = actual inflation + forecast error, where the forecast error averages zero over time (forecasts are unbiased)Adaptive ExpectationsExpected inflation = last period's expected inflation + a × (last period's actual inflation − last period's expected inflation), where a is between 0 and 1
Economic Indicators & Data
Misery IndexMisery index = unemployment rate + inflation rate.Purchasing Managers' IndexDiffusion index = (% reporting better) + (0.5 × % reporting no change); above 50 = expansion, below 50 = contractionCore InflationCore inflation rate = ((core index now − core index a year earlier) ÷ core index a year earlier) × 100Capacity UtilizationCapacity utilization rate = (actual output ÷ sustainable maximum output) × 100Inventory-to-Sales RatioInventory-to-sales ratio = inventories ÷ monthly salesBase YearReal GDP = current-year quantities × base-year prices; index in the base period = 100Index NumberIndex number = (value in the period ÷ value in the base period) × 100Nominal ValueNominal value = real value × (price index ÷ 100)Real ValueReal value = nominal value ÷ (price index ÷ 100)
International & Development Economics
Gross National Product (GNP)GNP = GDP + net income earned abroad by residents.Export SubsidyDomestic price with subsidy = world price + subsidy per unit; government cost = subsidy per unit × quantity exportedCustoms UnionNet welfare effect = trade creation gain − trade diversion lossPoverty LinePoverty line = cost of a food basket meeting a minimum calorie level + allowance for essential non-food needsAbsolute PovertyHeadcount ratio = number of people below the fixed line ÷ total populationRelative PovertyRelative poverty line = 50% or 60% × median equivalized household income (the fraction chosen varies by country)MicrofinanceEffective rate on a flat-rate loan repaid in equal installments ≈ 2 × the quoted flat rate (the average balance outstanding is about half the principal)RemittancesCurrent account = trade balance + net primary income + net secondary income (personal remittances sit mainly in secondary income)Brain DrainSkilled emigration rate = skilled emigrants ÷ (skilled emigrants + skilled workers remaining at home)Dutch DiseaseReal exchange rate = nominal exchange rate × (domestic price level ÷ foreign price level); a rise makes home-produced tradables cost more abroadImport Substitution IndustrializationDomestic price behind a tariff = world price × (1 + tariff rate)Convergence HypothesisConditional convergence: growth per person ≈ β × (own steady-state income − current income), in logs, where a positive β means countries further below their steady state grow fasterMiddle-Income TrapUnit labor cost = wage per hour ÷ output per hour; competitiveness worsens when wages rise faster than productivityTrade BlocIntra-bloc trade share = (trade between members / total trade of members) × 100Informal EconomyInformal share of true output = informal output / (measured GDP + informal output)Demographic TransitionNatural increase (percent per year) = (births per thousand - deaths per thousand) / 10; doubling time = 70 / growth rateSubsistence AgricultureMarketed surplus = harvest - household consumption - seed and feed retained; marketed surplus ratio = marketed surplus / harvestForeign AidFinancing gap = investment needed - domestic saving; grant element = (face value - present value of repayments) / face valueConditional Cash TransferHousehold complies when transfer ≥ foregone earnings + direct cost of the required behavior. Net gain = transfer − (foregone earnings + direct cost).Poverty TrapA trap exists when s x f(k) < (delta + n) x k for every k below a threshold k_T and s x f(k) > (delta + n) x k above it, so k_T separates a low steady state from a high oneSovereign DefaultHaircut = 1 - (present value of the new claims ÷ present value of the old claims).
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 rateSystematic RiskTotal risk = systematic (market) risk + unsystematic (firm-specific) riskArbitrageArbitrage profit = (selling price − buying price) × quantity − transaction costsCredit RatingBond yield = risk-free rate + default risk premium, where the premium widens as the rating fallsHedge FundInvestor's net gain = gross gain − (management fee × assets) − (performance fee × gains)Credit Default SwapAnnual premium = spread x notional. Under the standard credit triangle, spread = annual default probability x (1 - recovery rate), so implied default probability = spread / (1 - recovery rate).SecuritizationLoss borne by a tranche = min( max(Pool loss - Subordination beneath the tranche, 0), Tranche size ).Random WalkP(t) = P(t-1) + m + e(t), where m is the drift and e(t) is a shock with mean zero and no correlation with earlier shocks; volatility over T periods = one-period volatility x the square root of T
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 × ΔQPayroll TaxPayroll tax owed = tax rate × earnings, up to the annual earnings cap (no additional tax on earnings above the cap)Capital Gains TaxCapital gain = sale price − purchase price (basis); Tax owed = capital gains rate × realized gainEstate TaxEstate tax owed = tax rate × (gross estate − exemption − deductions)Corporate Income TaxTaxable profit = revenue − deductible costs (wages, materials, interest, depreciation); Tax owed = statutory rate × taxable profitTax BaseTax revenue = tax base × tax rateTax ExpenditureTax expenditure = tax revenue under a clean base − tax revenue actually collectedMeans-Tested ProgramBenefit = maximum benefit − (phase-out rate × income above the threshold)Earned Income Tax CreditPhase-in: credit = phase-in rate × earnings; Plateau: credit = maximum; Phase-out: credit = maximum − (phase-out rate × earnings above the phase-out threshold)Negative Income TaxNet payment = guaranteed minimum − (clawback rate × earned income); Break-even income = guaranteed minimum ÷ clawback rateUniversal Basic IncomeGross cost = payment per person × number of recipients; Net cost = gross cost − extra tax collected to fund itBalanced Budget AmendmentRequirement: government outlays = tax revenue each year, so deficit = outlays − revenue = 0Sovereign DebtDebt at end of year = debt at start of year + this year's deficit; Debt-to-GDP ratio = total debt ÷ nominal GDPDebt-to-GDP RatioDebt-to-GDP ratio = (government debt / nominal GDP) x 100. Change in the ratio is approximately (r - g) x current ratio - primary balance as a share of GDP, where r is the average interest rate on the debt and g is the nominal GDP growth rate.Primary BalancePrimary balance = Total revenue - (Total spending - Interest payments); Overall balance = Primary balance - Interest payments; Debt-stabilizing primary balance as a share of GDP = ((r - g) ÷ (1 + g)) × (Debt ÷ GDP), where r is the nominal interest rate on the debt and g is nominal GDP growth.
Labor Economics
Labor Demand CurveMRP of labor = marginal product of labor × marginal revenue (= price in a competitive product market); hire until MRP = wageSearch and MatchingHires per period = m(U, V), where U is unemployed searchers and V is vacancies; job finding rate = hires ÷ U; vacancy filling rate = hires ÷ VUnion Wage PremiumUnion wage premium = (W_union − W_nonunion) ÷ W_nonunion × 100Automation and LaborNet change in labor demand = (productivity effect + new tasks created) − displacement effect. A firm automates a task when the machine's cost per unit of output falls below the wage cost it replaces.
Environmental Economics
Marginal Abatement CostEfficient abatement: Marginal Abatement Cost = Marginal Benefit of abatementHotelling's Rule(P_t - MC) grows at rate r: net priceₙ₊₁ = net priceₙ × (1 + r)Emissions TradingCost-minimizing outcome: marginal abatement cost of firm 1 = marginal abatement cost of firm 2 = permit priceSocial Cost of CarbonSocial cost of carbon = sum over future years of (damage in year t) ÷ (1 + r)^tNonrenewable ResourcePrice = marginal extraction cost + scarcity rent; in competitive equilibrium, scarcity rent next year = scarcity rent this year × (1 + r)Green GDPGreen GDP = GDP − depreciation of natural capital − monetary value of environmental damageExistence ValueTotal economic value = use value + option value + non-use value (existence + bequest)Contingent ValuationAggregate benefit = mean willingness to pay per household × number of affected householdsMarketable PermitEquilibrium permit price = marginal abatement cost of the last unit of abatement the cap requires
Economic History & Events
Subprime Mortgage CrisisLeverage ratio = assets ÷ equity; equity is wiped out when asset values fall by equity ÷ assets.Weimar HyperinflationM × V = P × Y (money supply × velocity = price level × real output); with Y fixed, rapid growth in M and V both drive P up.Japan's Lost DecadeReal interest rate = nominal interest rate − inflation rate; a 0 percent nominal rate with 1 percent deflation still leaves a real rate of +1 percent.Volcker DisinflationSacrifice ratio = cumulative percent of one year's output lost ÷ percentage-point fall in inflation
Market Structures & Industrial Organization
Contestable MarketPerfectly contestable ⇒ price = minimum average total cost and economic profit = 0, whatever the number of firms.Market PowerLerner index = (P − MC) ÷ P; equals 0 under perfect competition and approaches 1 as market power rises.Limit PricingSet P_limit just below the entrant's minimum ATC, and above the incumbent's own ATC: ATC_incumbent < P_limit < ATC_entrant.Horizontal MergerHHI = sum of each firm's percent market share squared (0 to 10,000); a merger raises it by 2 × share A × share B.Switching CostsSwitch only if (price saving per period × number of periods you expect to stay) > switching cost.Minimum Efficient ScaleMES = smallest output where long-run ATC reaches its minimum; firms the market can support ≈ market quantity demanded ÷ MES.Rate-of-Return RegulationAllowed revenue = operating costs + (allowed rate of return × rate base); price = allowed revenue ÷ units sold.
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