IGCSE Economics Formula Practice
Worked Examples by Topic | Cambridge IGCSE Economics (0455)
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Price Elasticity of Demand
PED = % Change in Qd ÷ % Change in Price
How to Use This Guide
- Read the formula and understand what each variable means
- Study the example - note how values are substituted
- Try the practice problem before looking at the answer
- Show your working - set out each step with its units ($, %, millions) so your method is clear
1. Percentage Change Calculations
The foundation of most economics calculations. You'll need this for PED, PES, GDP growth, and inflation. Master this first!
Basic Percentage Change
Measures how much a value has increased or decreased relative to its original value. Used whenever exam questions ask "calculate the percentage change in..."
% Change = ((New Value - Old Value) ÷ Old Value) × 100
% = ((N - O) / O) × 100
Worked Example:
The price of a smartphone increases from $800 to $920. Calculate the percentage change.
Step 1: Identify values
Old = $800, New = $920
Step 2: Apply the formula
% change = ((920 - 800) / 800) × 100
% change = (120 / 800) × 100
% change = +15%
Practice Problem:
A country's GDP falls from $500 billion to $475 billion. Calculate the percentage change.
Show Answer
% change = ((475 - 500) / 500) × 100
= (-25 / 500) × 100
= -5%
Finding Original Value from Percentage Change
Works backwards from a final value when you know the percentage change. Useful when questions give you the result after a change and ask for the starting value. This is a maths skill rather than a named 0455 syllabus item.
Original = New Value ÷ (1 + % change/100)
O = N ÷ (1 + %/100)
Worked Example:
After a 20% increase, wages are now $36,000. What were wages before the increase?
Step 1: Set up equation
Original × 1.20 = $36,000
Step 2: Solve for original
Original = $36,000 ÷ 1.20
Original = $30,000
Practice Problem:
After a 15% decrease, the price of oil is $85 per barrel. What was the original price?
Show Answer
Original × 0.85 = $85
Original = $85 ÷ 0.85
= $100 per barrel
2. Price Elasticity of Demand (PED)
Measures how sensitive consumers are to price changes. Helps businesses decide whether raising prices will increase or decrease their revenue.
Calculating PED
The core elasticity formula. Shows how much quantity demanded changes when price changes. A high value means consumers are very responsive to price.
PED = % Change in Quantity Demanded ÷ % Change in Price
PED = %ΔQd / %ΔP
PED is usually negative (ignore the sign for interpretation)
⚠️ Watch out:
Don't invert the formula! It's % change in quantity divided by % change in price, not the other way around.
Worked Example:
When the price of coffee rises from $3 to $3.60, quantity demanded falls from 100 cups to 80 cups per day. Calculate PED.
Step 1: Calculate % change in price
%ΔP = ((3.60 - 3) / 3) × 100 = 20%
Step 2: Calculate % change in Qd
%ΔQd = ((80 - 100) / 100) × 100 = -20%
Step 3: Calculate PED
PED = -20% / 20%
PED = -1 (unitary elastic)
Practice Problem:
The price of cinema tickets rises from $10 to $12. Ticket sales fall from 500 to 350 per week. Calculate PED and state if demand is elastic or inelastic.
Show Answer
%ΔP = ((12-10)/10) × 100 = 20%
%ΔQd = ((350-500)/500) × 100 = -30%
PED = -30/20 = -1.5 (elastic)
|PED| > 1, so demand is elastic
Interpreting PED Values
After calculating PED, you need to interpret what the number means. The size of PED tells you whether demand is elastic (responsive) or inelastic (unresponsive) to price changes.
Revenue Impact:
Elastic demand (|PED| > 1): Price ↑ → Revenue ↓ (lose more customers)
Inelastic demand (|PED| < 1): Price ↑ → Revenue ↑ (keep most customers)
Practice Problem:
A firm's PED is -0.4. If they increase prices by 25%, what will happen to their revenue? Explain why.
Show Answer
%ΔQd = PED × %ΔP = -0.4 × 25% = -10%
Revenue will increase because demand is inelastic (|PED| < 1).
The 25% price rise outweighs the 10% fall in quantity.
Calculating Total Revenue
The total money a firm receives from selling its products. This links to PED because elasticity determines whether a price change increases or decreases revenue.
Total Revenue = Price × Quantity
TR = P × Q
Worked Example:
A shop sells 200 items at $15 each. After raising the price to $18, sales fall to 160. Calculate the change in revenue.
Step 1: Calculate original revenue
TR₁ = 200 × $15 = $3,000
Step 2: Calculate new revenue
TR₂ = 160 × $18 = $2,880
Step 3: Calculate change
Change = $2,880 - $3,000
Revenue fell by $120
Practice Problem:
A bus company carries 1,000 passengers daily at $2 per fare. If they reduce the fare to $1.50 and passengers increase to 1,500, should they make this change?
Show Answer
TR₁ = 1,000 × $2 = $2,000
TR₂ = 1,500 × $1.50 = $2,250
Change = +$250
Revenue increases by $250/day, so on revenue alone the fare cut is worthwhile. The company should also check its costs, because profit = TR - TC.
3. Price Elasticity of Supply (PES)
Measures how quickly producers can respond to price changes. Important for understanding why some markets adjust faster than others.
Calculating PES
Similar to PED but measures producer response. Shows how much quantity supplied changes when price changes. Higher PES means producers can easily increase output.
PES = % Change in Quantity Supplied ÷ % Change in Price
PES = %ΔQs / %ΔP
PES is usually positive (supply rises with price)
Worked Example:
When the price of wheat rises from $200 to $250 per tonne, farmers increase supply from 1,000 to 1,200 tonnes. Calculate PES.
Step 1: Calculate % change in price
%ΔP = ((250 - 200) / 200) × 100 = 25%
Step 2: Calculate % change in Qs
%ΔQs = ((1200 - 1000) / 1000) × 100 = 20%
Step 3: Calculate PES
PES = 20% / 25%
PES = 0.8 (inelastic supply)
Practice Problem:
The price of handmade furniture rises from $500 to $600. A craftsman increases output from 10 to 11 units per month. Calculate PES and explain why it might be so low.
Show Answer
%ΔP = ((600-500)/500) × 100 = 20%
%ΔQs = ((11-10)/10) × 100 = 10%
PES = 10/20 = 0.5 (inelastic)
Supply is inelastic because handmade goods require skilled labor and time - production cannot easily be scaled up.
Factors Affecting PES
Understanding why some goods have elastic supply (easy to produce more) and others have inelastic supply (hard to increase production quickly).
Supply is MORE elastic when:
- Spare capacity available (can quickly increase output)
- Stocks/inventory held (can sell from storage)
- Short production time (can respond quickly)
- Easy to hire more workers or get resources
Supply is LESS elastic when:
- Operating at full capacity
- Long production time (e.g., crops, housing)
- Requires specialized skills or resources
- Limited raw materials available
4. Costs, Revenue and Profit
Essential calculations for understanding how firms operate. Used to analyse business decisions about pricing, output levels, and whether to continue production.
Types of Costs
Firms have two types of costs: fixed costs (paid regardless of output, like rent) and variable costs (change with output, like raw materials). Understanding the difference is crucial.
Fixed Costs (FC): Costs that don't change with output (rent, insurance, salaries)
Variable Costs (VC): Costs that change with output (raw materials, wages for workers)
Total Cost (TC): FC + VC
Total Cost = Fixed Cost + Variable Cost
TC = FC + VC
Worked Example:
A bakery has fixed costs of $2,000/month. Each loaf costs $1.50 in ingredients and labor. If they produce 1,000 loaves, what is the total cost?
FC = $2,000
VC = $1.50 × 1,000 = $1,500
TC = FC + VC = $2,000 + $1,500
TC = $3,500
Average Costs
Cost per unit produced. Firms need to know their average cost to set prices that cover their costs and make a profit. AFC falls as output rises (spreading fixed costs).
Average Fixed Cost = FC ÷ Quantity
Average Variable Cost = VC ÷ Quantity
Average Total Cost = TC ÷ Quantity
AFC = FC/Q AVC = VC/Q ATC = TC/Q
⚠️ Watch out:
Don't confuse Total Cost with Average Cost. If asked for AVC, you must divide variable costs by quantity!
Worked Example:
A firm has FC = $5,000, VC = $3,000 and produces 200 units. Calculate AFC, AVC and ATC.
AFC = $5,000 / 200 = $25
AVC = $3,000 / 200 = $15
TC = $5,000 + $3,000 = $8,000
ATC = $8,000 / 200 = $40
(Note: ATC = AFC + AVC = $25 + $15 = $40 ✓)
Practice Problem:
A factory's total cost is $12,000 when producing 400 units. Fixed costs are $4,000. Calculate AVC.
Show Answer
VC = TC - FC = $12,000 - $4,000 = $8,000
AVC = VC / Q = $8,000 / 400
= $20 per unit
Calculating Profit
The key measure of business success. Profit is what's left after paying all costs. Negative profit (loss) means the firm is losing money and may need to change strategy or close.
Profit = Total Revenue - Total Cost
Profit = TR - TC
If negative, the firm makes a loss
Worked Example:
A firm sells 500 units at $20 each. Fixed costs are $3,000 and variable costs are $8 per unit. Calculate the profit.
Step 1: Calculate Total Revenue
TR = 500 × $20 = $10,000
Step 2: Calculate Total Cost
VC = 500 × $8 = $4,000
TC = FC + VC = $3,000 + $4,000 = $7,000
Step 3: Calculate Profit
Profit = TR - TC = $10,000 - $7,000
Profit = $3,000
Practice Problem:
A restaurant serves 200 meals at $25 each. Fixed costs are $2,500 and each meal costs $12 to prepare. Calculate the profit or loss.
Show Answer
TR = 200 × $25 = $5,000
VC = 200 × $12 = $2,400
TC = $2,500 + $2,400 = $4,900
Profit = $5,000 - $4,900 = $100 profit
5. GDP and Economic Growth
GDP measures the total value of goods and services produced in a country. It's the main indicator of economic size and is used to compare countries and track economic growth.
GDP per Capita
Average GDP per person. A better measure of living standards than total GDP because it accounts for population size. A small rich country can have higher GDP per capita than a large poor country.
GDP per capita = GDP ÷ Population
GDP per capita = GDP / Pop
Worked Example:
Country A has GDP of $200 billion and population of 25 million. Calculate GDP per capita.
GDP per capita = $200,000,000,000 / 25,000,000
GDP per capita = $8,000
Practice Problem:
Country B has GDP of $50 billion and population of 4 million. Country C has GDP of $120 billion and population of 12 million. Which has higher living standards based on GDP per capita?
Show Answer
Country B: 50bn / 4m = $12,500
Country C: 120bn / 12m = $10,000
Country B has higher GDP per capita ($12,500 vs $10,000)
Economic Growth Rate
Measures how fast the economy is growing (or shrinking). Positive growth means expansion; negative growth (two consecutive quarters) means recession.
Growth Rate = ((Real GDP this year - Real GDP last year) ÷ Real GDP last year) × 100
Growth = ((Y₂ - Y₁) / Y₁) × 100
Worked Example:
Real GDP was $400bn in 2024 and $412bn in 2025. Calculate the economic growth rate.
Growth = ((412 - 400) / 400) × 100
Growth = (12 / 400) × 100
Growth rate = 3%
Practice Problem:
A country's real GDP fell from $180bn to $171bn during a recession. Calculate the growth rate and identify this as recession or expansion.
Show Answer
Growth = ((171 - 180) / 180) × 100
= (-9 / 180) × 100 = -5%
Negative growth: real GDP is falling, which fits a recession (two consecutive quarters of negative growth), not an expansion
6. Unemployment Rate
A key indicator of economic health. High unemployment wastes human resources and reduces living standards. Governments aim to keep unemployment low.
Calculating Unemployment Rate
The percentage of the labour force without jobs but actively seeking work. Note: people who have stopped looking for work are not counted as unemployed.
Unemployment Rate = (Number Unemployed ÷ Labour Force) × 100
U rate = (U / LF) × 100
Labour Force = Employed + Unemployed (actively seeking work)
⚠️ Watch out:
Divide by the labour force (working population), NOT the total population!
Worked Example:
A country has 45 million employed and 5 million unemployed. Calculate the unemployment rate.
Step 1: Calculate labour force
LF = 45m + 5m = 50 million
Step 2: Calculate rate
U rate = (5 / 50) × 100
Unemployment rate = 10%
Practice Problem:
The labour force is 20 million. If the unemployment rate is 8%, how many people are employed?
Show Answer
Unemployed = 8% × 20m = 1.6 million
Employed = 20m - 1.6m = 18.4 million
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Frequently Asked Questions
How do I calculate Price Elasticity of Demand (PED)?
PED = Percentage change in quantity demanded ÷ Percentage change in price. Calculate each percentage change as (new - old)/old × 100, then divide. PED is usually negative but often expressed as an absolute value. |PED| greater than 1 is elastic, |PED| less than 1 is inelastic.
How do I calculate profit for a firm?
Profit = Total Revenue - Total Cost. Total Revenue = Price × Quantity sold. Total Cost = Fixed Costs + Variable Costs. If the result is positive, the firm makes a profit. If negative, the firm makes a loss.
How do I calculate unemployment rate?
Unemployment Rate = (Number of Unemployed ÷ Labour Force) × 100. The labour force includes both employed and unemployed people actively seeking work. Do not divide by the total population.
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