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IB DP Economics HL Formula Sheet (2022-2027)

For the IB DP Economics syllabus, first examinations 2022. Build IB DP Economics HL quantitative skills for Paper 3 and AO4 calculations. This reference brings together all SL formulas and HL extensions across Introduction to economics, Microeconomics, Macroeconomics and The Global Economy. Revise elasticities, costs and revenues, national accounting identities, inflation rates, weighted price indices, taxation, the Keynesian multiplier, exchange rates and balance of payments.

Unofficial revision resource. This is not an official IB formula sheet. IB Economics exams do not provide formula sheets. This resource is for revision purposes only; students must be familiar with all required formulas before the exam.

Download HL formula sheet (A3 PDF)

58 SL + HL formulas

Unit 1: Introduction to economics

Formulas

Opportunity cost of 1 unit of XThe next best alternative foregone when an economic decision is made.
Opportunity cost of 1 unit of X=Units of Y forgoneUnits of X gained\text{Opportunity cost of 1 unit of X} = \frac{\text{Units of Y forgone}}{\text{Units of X gained}}

Unit 2: Microeconomics

Competitive markets

Allocative efficiencyResources are allocated to produce the socially optimum quantity, where marginal social benefit equals marginal social cost.
MSB=MSC\mathrm{MSB} = \mathrm{MSC}

Where:

  • MSC = MPC + MEC: marginal social, private and external cost.
  • MSB = MPB + MEB: marginal social, private and external benefit.
Social costThe total cost to society of an economic activity, including private costs and external costs.
Private cost+External cost\text{Private cost} + \text{External cost}
Social benefitThe total benefit to society of an economic activity, including private benefits and external benefits.
Private benefit+External benefit\text{Private benefit} + \text{External benefit}
Area of a triangleThe amount of space inside a triangle, measured in square units.
A=12bhA = \frac{1}{2}bh

Where:

  • b = base
  • h = perpendicular height

Elasticities

Price elasticity of demandA measure of the responsiveness of the quantity demanded of a good or service when there is a change in its price.
PED=% Δ Quantity demanded% Δ Price\mathrm{PED} = \frac{\%\,\Delta\,\text{Quantity demanded}}{\%\,\Delta\,\text{Price}}
Price elasticity of supplyA measure of the responsiveness of the quantity supplied of a good or service when there is a change in its price.
PES=% Δ Quantity supplied% Δ Price\mathrm{PES} = \frac{\%\,\Delta\,\text{Quantity supplied}}{\%\,\Delta\,\text{Price}}
Income elasticity of demandA measure of the responsiveness of the demand for a good or service to a change in income.
YED=% Δ Quantity demanded% Δ Income\mathrm{YED} = \frac{\%\,\Delta\,\text{Quantity demanded}}{\%\,\Delta\,\text{Income}}
Percentage changeThe change in a value expressed as a percentage of its original value.
New value−Original valueOriginal value×100\frac{\text{New value} - \text{Original value}}{\text{Original value}} \times 100
Total revenueThe aggregate revenue gained by a firm from the sale of a particular quantity of output (equal to price times quantity sold).
TR=Price×Quantity\mathrm{TR} = \text{Price} \times \text{Quantity}

Market structures HL only

Average costThe total cost of production divided by the quantity of output produced.
AC=Total costQuantity\mathrm{AC} = \frac{\text{Total cost}}{\text{Quantity}}
Marginal costThe additional total cost of producing one more unit of output.
MC=Δ Total costΔ Quantity\mathrm{MC} = \frac{\Delta\,\text{Total cost}}{\Delta\,\text{Quantity}}
Total revenueThe aggregate revenue gained by a firm from the sale of a particular quantity of output (equal to price times quantity sold).
TR=Price×Quantity\mathrm{TR} = \text{Price} \times \text{Quantity}
Average revenueRevenue received per unit of output sold, equal to total revenue divided by quantity.
AR=Total revenueQuantity=Price\mathrm{AR} = \frac{\text{Total revenue}}{\text{Quantity}} = \text{Price}
Marginal revenueThe additional revenue received from selling one more unit of output.
MR=Δ Total revenueΔ Quantity\mathrm{MR} = \frac{\Delta\,\text{Total revenue}}{\Delta\,\text{Quantity}}
ProfitTotal revenue less total economic cost, including opportunity costs.
Total revenue−Total cost\text{Total revenue} - \text{Total cost}

Where:

  • Total cost includes opportunity cost.
Abnormal profitEconomic profit earned when total revenue exceeds total economic cost; average revenue is greater than average cost.
AR>AC\mathrm{AR} > \mathrm{AC}
Normal profitThe minimum return needed to keep an entrepreneur in the current activity. It is included in economic cost, so economic profit is zero.
AR=AC\mathrm{AR} = \mathrm{AC}
LossA situation in which total revenue is less than total economic cost; average revenue is below average cost.
AR<AC\mathrm{AR} < \mathrm{AC}
Profit maximisationProducing the quantity of output that gives the greatest economic profit. At an interior maximum, marginal cost equals marginal revenue and crosses it from below.
MR=MC\mathrm{MR} = \mathrm{MC}

Unit 3: Macroeconomics

National accounting

GDPThe total money value of all final goods and services produced in an economy in a given time period, usually one year.

Expenditure approach

C+I+G+(X−M)C + I + G + (X - M)

Where:

  • C = consumption; I = investment; G = government spending.
  • X = exports; M = imports

Income approach

Wages and salaries+Rent+Interest+Profit\text{Wages and salaries} + \text{Rent} + \text{Interest} + \text{Profit}

Output approach

Sum of all goods and services produced in an economy\text{Sum of all goods and services produced in an economy}
Nominal GDPThe value of final goods and services produced in an economy, measured at current prices without adjusting for inflation.
Quantity of goods and services produced×Current prices\text{Quantity of goods and services produced} \times \text{Current prices}
Real GDPThe total money value of all final goods and services produced in an economy in a given time period, usually one year, adjusted for inflation.
Quantity produced×constant prices\text{Quantity produced} \times \text{constant prices}

Or

Nominal GDPPrice index*×100\frac{\text{Nominal GDP}}{\text{Price index*}} \times 100

Any price index: CPI, GDP deflator

GDP deflatorA price index measuring the prices of domestically produced final goods and services, relative to a base year.
Nominal GDPReal GDP×100\frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100
GNIThe total money value of all final goods and services produced in an economy in one year, plus net property income from abroad (interest, rent, dividends and profit).
GNI=GDP+Net factor income\mathrm{GNI} = \mathrm{GDP} + \text{Net factor income}
Real GNIGross national income adjusted for changes in the price level.
Nominal GNIPrice deflator×100\frac{\text{Nominal GNI}}{\text{Price deflator}} \times 100
GDP per capitaGross domestic product divided by the total population: average output per person.
GDPTotal population\frac{\mathrm{GDP}}{\text{Total population}}
GNI per capitaGross national income divided by the total population: average income per person.
GNITotal population\frac{\mathrm{GNI}}{\text{Total population}}
Aggregate demandThe total spending in an economy consisting of consumption, investment, government expenditure and net exports.
C+I+G+(X−M)C + I + G + (X - M)

Where:

  • C = consumption; I = investment; G = government spending.
  • X = exports; M = imports;

Growth employment prices and inequality

Economic growth rateThe percentage increase in real output over time, usually measured using real GDP.
New real GDP−Old real GDPOld real GDP×100\frac{\text{New real GDP} - \text{Old real GDP}}{\text{Old real GDP}} \times 100
Unemployment rateThe number of unemployed workers expressed as a percentage of the total workforce.
UnemployedLabour force×100\frac{\text{Unemployed}}{\text{Labour force}} \times 100

Where:

  • Labour force = employed + unemployed actively seeking work.
Index numberA measure showing the value of a variable relative to a base period, usually set equal to 100.
Current valueBase-year value×100\frac{\text{Current value}}{\text{Base-year value}} \times 100
Inflation rateThe percentage change of a price index over a certain time period.
New CPI−Old CPIOld CPI×100\frac{\text{New CPI} - \text{Old CPI}}{\text{Old CPI}} \times 100

Where:

  • CPI = consumer price index.
Gini coefficientA measure of inequality based on the Lorenz curve. A coefficient of 0 represents perfect equality; 1 represents maximum inequality.
AA+B\frac{A}{A + B}

Where:

  • A = area between equality line and Lorenz curve; B = area below Lorenz curve.
  • Coefficient: 0 to 1. Index: coefficient × 100.
Real interest rate (approx.)The interest rate adjusted for inflation, approximated by the nominal interest rate minus the inflation rate.
Nominal rate−Inflation rate\text{Nominal rate} - \text{Inflation rate}

Weighted price indices HL only

Weighted average of item price indicesAn average of item price indices that gives greater influence to items with larger expenditure weights.
Weighted price index=Total of (each item’s price index×its weight)Total weights\text{Weighted price index} = \frac{\text{Total of (each item’s price index} \times \text{its weight)}}{\text{Total weights}}

Use the expenditure weights or spending shares provided; do not multiply by 100 again.

Item price indexThe price of one item expressed relative to its price in a base year, with the base-year index set to 100.
Item price index=Current price of the itemBase-year price of the item×100\text{Item price index} = \frac{\text{Current price of the item}}{\text{Base-year price of the item}} \times 100

The base-year index is 100.

CPI using a fixed basketAn index comparing the cost of the same fixed quantities of goods and services at current prices with their cost at base-year prices.
CPI=Cost of the fixed basket at current pricesCost of the same basket at base-year prices×100\mathrm{CPI} = \frac{\text{Cost of the fixed basket at current prices}}{\text{Cost of the same basket at base-year prices}} \times 100

Keep quantities fixed; each basket cost is the total of each item’s price × its quantity.

Taxation HL only

Indirect tax paidThe amount of tax paid on expenditure on goods and services, calculated using the stated tax rate.

Tax-exclusive* expenditure

Tax=E×t\text{Tax} = E \times t

Tax-inclusive* expenditure

Tax=E×t1+t\text{Tax} = E \times \frac{t}{1+t}

Where:

  • E = expenditure; t = tax rate as a decimal (20% = 0.20).

* Tax-exclusive: expenditure excludes tax. Tax-inclusive: expenditure already includes tax.

Taxable incomeIncome remaining subject to income tax after subtracting the tax-free allowance.
Total income−Tax-free allowance\text{Total income} - \text{Tax-free allowance}
Total income taxThe total tax payable on income after applying the relevant tax rate to the income within each tax band.
∑ (Income in each band×Band rate)\sum\, (\text{Income in each band} \times \text{Band rate})

Where:

  • Σ = sum. Apply each rate only within its band; a tax-free band has rate 0%.
Average tax rateTotal income tax paid expressed as a percentage of total income.
Total income tax paidTotal income×100\frac{\text{Total income tax paid}}{\text{Total income}} \times 100
Marginal tax rateThe percentage of additional income paid in additional income tax.
Δ Total income tax paidΔ Total income×100\frac{\Delta\,\text{Total income tax paid}}{\Delta\,\text{Total income}} \times 100

Keynesian multiplier HL only

MultiplierThe ratio of the change in equilibrium national income to the initial change in autonomous expenditure.
k=11−MPC=1MPWk = \frac{1}{1-\mathrm{MPC}} = \frac{1}{\mathrm{MPW}}
MPW=MPS+MPT+MPM\mathrm{MPW} = \mathrm{MPS} + \mathrm{MPT} + \mathrm{MPM}

Where:

  • MPC = marginal propensity to consume; MPW = marginal propensity to withdraw.
  • MPS, MPT, MPM = marginal propensities to save, tax and import.
Change in GDPThe change in national output resulting from a change in an autonomous injection multiplied through the economy.
ΔY=k×ΔJ\Delta Y = k \times \Delta J

Where:

  • Y = GDP; J = autonomous injection (I, G or X).
Marginal propensityThe proportion of a change in income that is consumed, saved, paid in tax or spent on imports.
MPZ=ΔZΔY\mathrm{MPZ} = \frac{\Delta Z}{\Delta Y}

Where:

  • Z = C, S, T or M: consumption, saving, tax or imports; Y = income.

Other relationships HL only

Debt to GDP ratioGovernment debt expressed as a percentage of gross domestic product.
Government debtGDP×100\frac{\text{Government debt}}{\mathrm{GDP}} \times 100

Unit 4: The Global Economy

Exchange rates

Currency conversionExpressing an amount of one currency in another currency using the exchange rate.
Amount B=Amount A×e\text{Amount B} = \text{Amount A} \times e

Where

  • e = units of currency B per 1 unit of A.
Currency changeThe percentage change in an exchange-rate quote between two periods.
Et−Et−1Et−1×100\frac{E_t - E_{t-1}}{E_{t-1}} \times 100

Where:

  • t = current period; t−1 = previous period.

A rise in this quote means A appreciates; a fall means A depreciates.

Trade relationships HL only

Marshall Lerner conditionThe condition that the absolute values of the price elasticities of demand for exports and imports sum to more than one, allowing depreciation to improve the trade balance, other things equal.
∣PEDX∣+∣PEDM∣>1|\mathrm{PED}_{X}| + |\mathrm{PED}_{M}| > 1

Where:

  • PEDₓ = PED of exports
  • PEDₘ = PED of imports

Depreciation improves the trade balance if this holds, other things equal.

Opportunity cost of XThe amount of one good forgone to produce one unit of another good. A lower opportunity cost indicates comparative advantage.
Units of Y forgoneUnits of X gained\frac{\text{Units of Y forgone}}{\text{Units of X gained}}

For the same resources; lower opportunity cost gives comparative advantage.

Balance of payments

Trade balanceThe difference between the value of exports and the value of imports over a given period.
Exports−Imports\text{Exports} - \text{Imports}
Current accountA measure of the flow of funds from trade in goods and services, plus net investment income flows (profit, interest, and dividends) and net transfers of money (foreign aid, grants, and remittances).
Goods balance+Services balance+Net income+Net current transfers\begin{gathered}\text{Goods balance} + \text{Services balance}\\ + \text{Net income} + \text{Net current transfers}\end{gathered}
Account balanceThe difference between the credits and debits recorded in a balance-of-payments account.
Credits−Debits\text{Credits} - \text{Debits}
Capital accountThe balance-of-payments account recording capital transfers and transactions in non-produced, non-financial assets.
Net capital transfers+Net non-produced asset transactions\text{Net capital transfers} + \text{Net non-produced asset transactions}
Financial accountThe balance-of-payments account recording cross-border transactions in financial assets and liabilities.
Net FDI+Net portfolio investment+Net reserves+Net borrowing\text{Net FDI} + \text{Net portfolio investment} + \text{Net reserves} + \text{Net borrowing}
Payments identityThe accounting relationship requiring the balance-of-payments accounts, including errors and omissions, to sum to zero under the stated sign convention.
CA+KA+FA+EO=0\mathrm{CA} + \mathrm{KA} + \mathrm{FA} + \mathrm{EO} = 0

where

  • CA = current account
  • KA = capital account
  • FA = Financial account
  • EO = errors/omissions.

Development Economics

Happy Planet IndexA measure of how efficiently environmental resources support long, happy lives. The displayed formula is a simplified approximation.
HPI≈Wellbeing×Life expectancyEcological footprint\mathrm{HPI} \approx \frac{\text{Wellbeing} \times \text{Life expectancy}}{\text{Ecological footprint}}

IB DP Economics HL formula sheet: revision FAQs

Connect formula recall with Paper 3 problem-solving, AO4 calculations and economic analysis in past papers, mock exams and trial exams.

Does the HL formula sheet include the SL formulas?

Yes. This IB DP Economics HL formula sheet includes the current SL formulas and adds HL extensions. Use it to revise national accounting identities, inflation rates and exchange rates alongside costs and revenues, market structures, weighted price indices, taxation, the Keynesian multiplier, debt-to-GDP ratios and the Marshall Lerner condition.

Is a formula sheet provided in IB Economics HL Paper 3?

No. IB Economics exams do not provide a formula sheet. This is an unofficial revision resource, and students must be familiar with the required formulas before the exam. Practise recalling each formula and choosing it from the data in a question, rather than relying on recognising it when the answer is visible.

How should I use this page with IB Economics Paper 3 past papers?

Work through a current-syllabus Paper 3 problem before checking the sheet. Identify the economic measure, select the data, show your calculation and explain the result where asked. Compare your method with the relevant IB Economics markscheme, including any method marks and follow-on calculations. Use older past papers selectively because syllabus coverage and paper formats can differ.

How can I prepare for HL mock exams and trial exams?

Use flashcard mode for recall, then practise mixed Paper 2 and Paper 3 calculations without the sheet. Include timed questions that combine several steps, such as finding a basket cost, calculating CPI and then calculating inflation. Before mock exams or trial exams, check your teacher’s coverage and review mistakes using the marking guidance supplied for that assessment.

What is the difference between AO2 analysis and AO4 quantitative skills?

AO4 covers the selection, use and application of appropriate skills, including calculations and economic diagrams. AO2 application and analysis requires you to connect economic theory to the situation described. A strong calculation answer uses the correct method; a strong explanation also interprets the result and develops the economic reasoning that the question asks for.

How do Paper 1, Paper 2 and Paper 3 assessment criteria differ?

Paper 1 rewards developed essay responses, including economic theory, diagrams and evaluation where required. Paper 2 combines data-response tasks with an extended response. HL Paper 3 combines shorter problem-solving tasks with a policy recommendation. Use the relevant assessment criteria or markbands for extended responses and the question-specific markscheme for individual calculations; one checklist cannot replace all three.

How do I choose between a weighted price index and a fixed-basket CPI calculation?

When a question gives item price indices and expenditure weights, multiply each index by its weight, add the results and divide by total weights. When it gives prices and fixed quantities, calculate the basket cost at current and base-year prices, then divide current cost by base-year cost and multiply by 100. Raw quantities are not interchangeable with expenditure weights.

What calculation errors should I check against the Paper 3 markscheme?

Check percentage versus decimal tax rates, tax-inclusive versus tax-exclusive expenditure, the base year of an index, exchange-rate quotation and the difference between CPI and annual inflation. Show numerical working, use appropriate units and follow rounding instructions. Keep intermediate values precise, and read the markscheme to see how the particular question allocates method and answer marks.

Which common HL Economics topics should I revise alongside the formulas?

Combine calculations with the concepts behind elasticities, market structures, externalities, national income, inflation, taxation, the multiplier, exchange rates and international trade. Practise explaining what a calculated value means, including its limitations where relevant. These are useful revision areas, not a prediction of future IB Economics exam questions or a substitute for covering the syllabus.

Continue your revision: SL formula sheetIB DP Economics glossaryPaper 1 model essaysPaper 1 assessment guidance

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