How to Calculate Key AP Economics Formulas

Opportunity cost of 1 unit of Good A = (units of Good B given up) ÷ (units of Good A gained). Lower ratio = comparative advantage.

Per-unit opportunity cost of good A = units of good B given up ÷ units of good A gained

Scarcity 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 years

Consumer surplus = ½ × base × height = ½ × quantity × (maximum willingness to pay − price)

DWL = ½ × base × height = ½ × |Q_efficient − Q_actual| × (price wedge)

Producer surplus = ½ × base × height = ½ × quantity × (price − supply curve's price intercept)

Set Qd = Qs, solve for P*, then Q* = Qd at P* = Qs at P*

Shortage = Qd − Qs at the given price (positive only when that price is below equilibrium)

Surplus = Qs − Qd at the given price (positive only when that price is above equilibrium)

Shortage = Qd − Qs at the ceiling; quantity traded = Qs; DWL = ½ × (Q equilibrium − Q traded) × (demand price − supply price at Q traded)

Surplus = Qs − Qd at the floor; quantity traded = Qd; DWL = ½ × (Q equilibrium − Q traded) × (floor price − supply price at Q traded)

Total surplus = consumer surplus + producer surplus = ½ × Q × (demand's price intercept − supply's price intercept)

%Δ = (new − old) ÷ ((new + old) ÷ 2), then elasticity = %ΔQ ÷ %ΔP

PED = %ΔQ ÷ %ΔP, where %Δ = (new − old) ÷ ((new + old) ÷ 2). |PED| > 1 elastic, < 1 inelastic, = 1 unit elastic.

TR = P × Q. P↑ & TR↓ (or P↓ & TR↑) → elastic. P↑ & TR↑ (or P↓ & TR↓) → inelastic. TR unchanged → unit elastic.

PES = %ΔQs ÷ %ΔP, with %Δ = (new − old) ÷ ((new + old) ÷ 2) on AP exams. PES > 1 elastic, < 1 inelastic, = 1 unit elastic.

XED = %ΔQd of good A ÷ %ΔP of good B. XED > 0 → substitutes; XED < 0 → complements; XED ≈ 0 → unrelated goods.

YED = %ΔQd ÷ %Δincome. YED > 0 → normal good (0–1 necessity, > 1 luxury); YED < 0 → inferior good.

Total 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 period

MU = ΔTU ÷ ΔQ = (TU₂ − TU₁) ÷ (Q₂ − Q₁)

MU per dollar = MU ÷ P | compare MUx ÷ Px against MUy ÷ Py to decide what to buy next

MUx ÷ Px = MUy ÷ Py and PxQx + PyQy = Income (both conditions must hold)

TU = MU₁ + MU₂ + ... + MUn | TU at Q = TU at (Q − 1) + MU of unit Q

PxQx + PyQy = Income | slope = −Px ÷ Py | intercepts = Income ÷ Px and Income ÷ Py

MRS = MUx ÷ MUy = absolute slope of the indifference curve | at the optimum, MRS = Px ÷ Py

MUx ÷ Px = MUy ÷ Py and PxQx + PyQy = Income | equivalently MUx ÷ MUy = Px ÷ Py

PV = V ÷ (1 + k × t) | exponential form for comparison: PV = V ÷ (1 + r)^t

Weight on a payoff today = 1 | Weight on a payoff t periods away = beta × delta^t, with 0 < beta < 1

EU = p₁ × U(x₁) + p₂ × U(x₂) + ... + pₙ × U(xₙ), where the probabilities sum to 1

U(CE) = expected utility of the gamble | with utility = wealth^r, CE = EU^(1 ÷ r) | risk premium = expected value − CE

CV = (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 good

MC = ΔTC ÷ ΔQ = ΔVC ÷ ΔQ (fixed costs don't change, so only variable costs matter)

ATC = TC ÷ Q = AFC + AVC | AFC = FC ÷ Q | AVC = VC ÷ Q

Economic profit = TR − explicit costs − implicit costs = accounting profit − implicit costs | Per-unit form: (P − ATC) × Q

AVC = VC ÷ Q = ATC − AFC | VC = TC − FC

AFC = FC ÷ Q = ATC − AVC

TC = FC + VC = ATC × Q | FC = AFC × Q, VC = AVC × Q

VC = TC − FC = AVC × Q = the sum of the marginal costs from the first unit up to Q

MP = ΔTP ÷ ΔL (change in total product ÷ change in units of the input, usually labor)

AP = TP ÷ L (total product ÷ quantity of the variable input)

Break-even quantity: Q = FC ÷ (P − AVC) | Break-even price: P = minimum ATC, where TR = TC and economic profit = 0

Q = 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 + β

New ATC = (TC + MC of the next unit) ÷ (Q + 1) | MC < ATC ⇒ ATC falls | MC > ATC ⇒ ATC rises | MC = ATC at minimum ATC

MES = 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) × 100

MRTS = −(ΔK ÷ ΔL) = MPL ÷ MPK | output is held constant along one isoquant | least-cost input mix: MRTS = w ÷ r

wL + rK = C | slope = −w ÷ r | intercepts: C ÷ w units of labor and C ÷ r units of capital

Scale 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)

Produce where MR = MC (MC rising). Profit = (P − ATC) × Q

Shut down if P < minimum AVC. AVC = TVC ÷ Q, and minimum AVC occurs where MC = AVC

Accounting profit = Total revenue − Explicit costs

Total revenue = Price × Quantity (TR = P × Q)

Dollar markup = P − MC. Percentage markup = [(P − MC) ÷ MC] × 100

Lerner index = (P − MC) ÷ P (equals 1 ÷ |price elasticity of demand| at the profit-maximizing output)

CRn = share of firm 1 + share of firm 2 + ... + share of firm n, where each share = (firm sales ÷ total industry sales) × 100

MR = ΔTR ÷ ΔQ, where TR = P × Q. Perfect competition: MR = P. Monopoly/imperfect competition: MR < P.

Total charge = access fee (A) + (per-unit price × quantity) | Identical buyers: per-unit price = MC, and A = consumer surplus = ½ × (choke price − MC) × quantity bought

Monopoly output: MR = MC, where MR = choke price − (2 × slope × Q) | Efficient output: P = MC | Deadweight loss = ½ × (efficient Q − monopoly Q) × (monopoly price − MC)

Allowed revenue = operating costs + (allowed rate of return × rate base) | Regulated price = allowed revenue ÷ units sold

MRP = MP × P (competitive output market) = ΔTR ÷ Δlabor. Hire until MRP = wage (MRC).

MFC = 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 curve

MPL = ΔTotal output ÷ ΔQuantity of labor = ΔQ ÷ ΔL | With one-worker steps, MPL is simply the extra output that worker adds

Hire 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 × P

MPL ÷ PL = MPK ÷ PK (marginal product per dollar equal across every input) | Profit-maximizing version: MRPL ÷ PL = MRPK ÷ PK = 1

MSC = MPC + Marginal external cost | No externality: MSC = MPC, the supply curve | Negative externality: MSC lies above MPC by the external cost per unit

MSB = MPB + Marginal external benefit | No externality: MSB = MPB, the demand curve | Positive externality: MSB lies above MPB by the external benefit per unit

Socially optimal Q solves MSB = MSC, where MSB = MPB + marginal external benefit and MSC = MPC + marginal external cost | The market quantity instead solves MPB = MPC

Phase-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 zero

Net payment = Guaranteed minimum − (Clawback rate × Earned income) | Break-even income = Guaranteed minimum ÷ Clawback rate | Income after the payment = Earned income + Net payment

Pigouvian tax per unit = MSC − MPC measured at Q(optimal) Q(optimal) is where MSB = MSC

Per-unit subsidy = MSB − MPB measured at Q(optimal) Total cost to government = per-unit subsidy × quantity traded after the subsidy

Excise 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)

DWL = 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 constant

Tariff revenue = tariff per unit × imports after the tariff Imports after the tariff = Qd − Qs, both read at the price (world price + tariff)

Effective (average) tax rate = (total tax paid ÷ total income) × 100

Marginal tax rate = [(tax₂ − tax₁) ÷ (income₂ − income₁)] × 100

Buyer'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 accept

Utilitarian: W = U1 + U2 + ... + Un | Rawlsian (maximin): W = min(U1, U2, ..., Un) | rank allocations by W under the rule you chose

Net price = P − MC | Net price after t years = (P₀ − MC) × (1 + r)ᵗ | Price after t years = MC + (P₀ − MC) × (1 + r)ᵗ

Aggregate 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 households

Required 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 split

Total 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 use

GDP = C + I + G + (X − M) where Xn = X − M (net exports)

Real GDP = (Nominal GDP ÷ GDP deflator) × 100

GDP deflator = (Nominal GDP ÷ Real GDP) × 100

Nominal GDP = sum of (current-year price × current-year quantity) | Nominal GDP = C + I + G + (X − M) at current prices

Net exports (Xn) = exports (X) − imports (M) | GDP = C + I + G + Xn

Disposable income (DI) = personal income − personal taxes | DI = consumption (C) + saving (S)

National income (NI) = compensation of employees + rental income + net interest + proprietors' income + corporate profits

NDP = GDP − depreciation (consumption of fixed capital) | Net investment = gross investment − depreciation

Value added = value of a firm's sales − cost of intermediate goods purchased | GDP = sum of value added at every stage

GDP = wages + rent + interest + profit + depreciation + taxes on production and imports (plus a statistical discrepancy)

GNP = GDP + net foreign factor income | Net foreign factor income = income residents earn abroad − income foreigners earn domestically

Nominal value = Real value × (Price index ÷ 100) | Real value = Nominal value ÷ (Price index ÷ 100)

Inflation rate = [(CPI₂ − CPI₁) ÷ CPI₁] × 100

Unemployment rate = (Unemployed ÷ Labor force) × 100 | Labor force = Employed + Unemployed

CPI = (cost of basket in current year ÷ cost of basket in base year) × 100

LFPR = (Labor force ÷ working-age population) × 100 | Labor force = employed + unemployed

Real wage = (Nominal wage ÷ Price index) × 100

Years to double = 70 ÷ annual growth rate (in percent)

Misery index = Inflation rate (%) + Unemployment rate (%)

Natural rate = Frictional rate + Structural rate | Natural rate = Actual unemployment rate − Cyclical rate

Cyclical unemployment rate = Actual unemployment rate − Natural rate of unemployment

Employment-population ratio = (Employed ÷ Civilian noninstitutional population age 16+) × 100

COLA = Benefit × Inflation rate | New benefit = Benefit + COLA = Benefit × (1 + Inflation rate)

Core inflation rate = ((core index now − core index a year earlier) ÷ core index a year earlier) × 100

Sacrifice ratio = cumulative percent of one year's output lost ÷ percentage-point fall in inflation

Index number = (Value in the period ÷ Value in the base period) × 100

Expected inflation next period = Expected inflation now + a × (Actual inflation now − Expected inflation now), with a between 0 and 1

Job finding rate = Hires ÷ Unemployed | Vacancy filling rate = Hires ÷ Vacancies | Market tightness = Vacancies ÷ Unemployed | Expected spell length = 1 ÷ job finding rate

Leverage ratio = Assets ÷ Equity | Wipeout threshold = Equity ÷ Assets = 1 ÷ leverage ratio

PMI = (% reporting better) + (0.5 × % reporting no change) | equivalently PMI = 50 + 0.5 × (% better − % worse)

Capacity utilization rate = (actual output ÷ sustainable maximum output) × 100 | Idle capacity = sustainable maximum output − actual output

Inventory-to-sales ratio = inventories ÷ monthly sales | Days of sales covered = ratio × 30

Spending multiplier = 1 ÷ (1 − MPC) = 1 ÷ MPS | ΔGDP = multiplier × Δspending | Tax multiplier = −MPC ÷ MPS

MPC = ΔC ÷ ΔY | MPS = 1 − MPC | spending multiplier = 1 ÷ MPS | tax multiplier = −MPC ÷ MPS

Tax multiplier = −MPC ÷ (1 − MPC) = −MPC ÷ MPS | ΔGDP = tax multiplier × Δtaxes

MPC = ΔC ÷ ΔY | MPS = ΔS ÷ ΔY | MPC + MPS = 1

Recessionary gap = Potential real GDP − Actual real GDP | As a percent of potential: [(Potential − Actual) ÷ Potential] × 100

Inflationary gap = Actual real GDP − Potential real GDP | Required spending cut = Gap ÷ Spending multiplier

Output gap = Actual real GDP − Potential real GDP | Output gap (%) = [(Actual − Potential) ÷ Potential] × 100

Budget deficit = Government outlays − Government revenue (one year) | Budget surplus = Revenue − Outlays | New debt = Old debt + this year's deficit

Debt-to-GDP ratio = (Total government debt ÷ Nominal GDP) × 100

Required Δspending = Gap ÷ Spending multiplier where Spending multiplier = 1 ÷ (1 − MPC) = 1 ÷ MPS | Rearranged from ΔGDP = Multiplier × Δspending

Required Δtaxes = Gap ÷ Tax multiplier where Tax multiplier = −MPC ÷ MPS | A negative Δtaxes is a tax cut | Required tax change = Required spending change ÷ MPC

National debt = Starting debt + Sum of past deficits − Sum of past surpluses | Yearly interest cost = Debt × Interest rate

Tax 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 claimants

Benefit = 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 dollar

Gross 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)

Money multiplier = 1 ÷ required reserve ratio | Δmoney supply = money multiplier × excess reserves

M × V = P × Q (quantity theory of money), so V = (P × Q) ÷ M = nominal GDP ÷ money supply

Required reserves = required reserve ratio × checkable deposits

Excess reserves = total reserves − required reserves | required reserves = required reserve ratio × checkable deposits

Maximum deposit expansion = excess reserves × (1 ÷ required reserve ratio)

Nominal interest rate ≈ real interest rate + expected inflation rate

Nominal ≈ real + expected inflation | real ≈ nominal − expected inflation | expected inflation ≈ nominal − real

M × V = P × Q (P × Q = nominal GDP) | growth form: %ΔM + %ΔV ≈ %ΔP + %ΔQ

M1 = currency in circulation + checkable deposits + traveler's checks | M2 = M1 + savings deposits + small time deposits + retail money market funds

Monetary 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 ratio

Real money balances = M ÷ P | with a price index based at 100: real balances = (M ÷ price index) × 100

i = r* + π + 0.5(π − π*) + 0.5(output gap) | r* is the neutral real rate, π* is the inflation target

(1 + long rate)ⁿ = (1 + r₁) × (1 + r₂) × ... × (1 + rₙ) | n-year yield = [(1 + r₁)(1 + r₂)...(1 + rₙ)]^(1 ÷ n) − 1

Real seigniorage = (change in the monetary base ÷ price index) × 100 | Inflation tax = inflation rate × real money balances

Real interest rate ≈ Nominal interest rate − Inflation rate

Private saving = Disposable income − Consumption = Y − T − C | Public saving = T − G | National saving = Private saving + Public saving = Y − C − G

(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 − I

Approximate 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 price

Default risk premium = Risky bond yield − Risk-free yield (same maturity) | Break-even default rate = Premium ÷ (1 − Recovery rate)

Management fee = management fee rate × assets | Performance fee = performance fee rate × gross gain | Investor's net gain = gross gain − management fee − performance fee

Total 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) × 100

Taxable profit = revenue − deductible costs (wages, materials, interest, depreciation) | Tax owed = statutory rate × taxable profit | After-tax profit = taxable profit − tax owed

Labor productivity = Real output ÷ Labor hours

Gains from trade = Consumption with trade − Production without trade (computed per good, per country)

Lower 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)

End 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 1

FV = PV × (1 + r)ⁿ where r = interest rate as a decimal, n = number of years

Expected value = Σ (probability of an outcome × payoff of that outcome), where the probabilities must sum to 1

%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)

Skilled 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 rate

Years 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 decimal

Unit labor cost = Wage per hour ÷ Output per hour | Output per hour = Total output ÷ Total hours worked

Domestic 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 consumption

Net 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 price

Amount 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 reciprocal

Appreciation % = [(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 depreciation

Depreciation % = [(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 fall

PPP 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 × 100

Real 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 expensive

Current 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 sent

Terms 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 × 100

Marshall-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)

Arbitrage profit = (selling price − buying price) × quantity − transaction costs Break-even quantity = transaction costs ÷ (selling price − buying price)

GDP per capita = Real GDP ÷ Population

Growth rate (%) = ((Real GDP in year 2 − Real GDP in year 1) ÷ Real GDP in year 1) × 100

Gini = 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)

Consumer 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 change = ((New value − Old value) ÷ Old value) × 100

Balanced budget multiplier = spending multiplier + tax multiplier = 1 ÷ (1 − MPC) + (−MPC ÷ (1 − MPC)) = (1 − MPC) ÷ (1 − MPC) = 1 | ΔGDP = 1 × Δspending (when Δspending = Δtaxes)

PV = FV ÷ (1 + r)ⁿ where r = interest (discount) rate as a decimal, n = number of years

HHI = (s₁)² + (s₂)² + ... + (sₙ)² = Σ (share%)² where each share is a whole-number percent (0 to 100)

Excess 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 ATC

Market cap = share price × shares outstanding | Percent change in market cap = percent change in share price, when the share count is unchanged

Capital gain = selling price − purchase price (cost basis) | Percent return = (gain ÷ purchase price) × 100 | After-tax gain = gain × (1 − tax rate)

P/E ratio = share price ÷ earnings per share (EPS) | EPS = net income ÷ shares outstanding | Earnings yield = (EPS ÷ share price) × 100

q_leader = (a − c) ÷ (2b) | q_follower = (a − c) ÷ (4b) | P = a − b × (q_leader + q_follower) | Profit = (P − c) × q

q per firm = (a − c) ÷ [(n + 1) × b] | Q = n × q | P = a − bQ = (a + n × c) ÷ (n + 1) | Profit per firm = (P − c) × q

Let 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 payoffs

Cooperating = 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)

Poverty 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 size

Headcount 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 shortfall

Relative 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 × 100

Change in HHI = 2 × share A × share B | Post-merger HHI = pre-merger HHI + change | Pre-merger HHI = sum of every firm's squared percent share

Limit 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 price

Taxable estate = gross estate − exemption − deductions | Estate tax owed = tax rate × taxable estate | Effective rate = tax owed ÷ gross estate