Unit 2: Microeconomics Part I - Elasticities
Understanding Market Responsiveness: PED, YED, and PES
Introduction: Why Elasticity Matters
Elasticity measures the responsiveness of one variable to changes in another. In economics, we use elasticity to understand how quantity demanded or supplied responds to changes in price, income, or other factors. This concept is crucial for businesses setting prices, governments implementing taxes, and economists predicting market behavior.
Three Key Elasticities in IB Economics SL
- Price Elasticity of Demand (PED): Responsiveness of quantity demanded to price changes
- Income Elasticity of Demand (YED): Responsiveness of quantity demanded to income changes
- Price Elasticity of Supply (PES): Responsiveness of quantity supplied to price changes
1. Price Elasticity of Demand (PED)
Definition
Price Elasticity of Demand (PED) measures the responsiveness of quantity demanded to a change in price, ceteris paribus.
It tells us by what percentage quantity demanded changes when price changes by 1%.
PED Formula
\[ PED = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}} \]Or more precisely:
\[ PED = \frac{\Delta Q_d / Q_d}{\Delta P / P} = \frac{\Delta Q_d}{\Delta P} \times \frac{P}{Q_d} \]Where:
- • \(\Delta Q_d\) = Change in quantity demanded
- • \(\Delta P\) = Change in price
- • \(Q_d\) = Original quantity demanded
- • \(P\) = Original price
Important Note
PED is always negative due to the law of demand (inverse relationship between price and quantity demanded). However, economists typically discuss PED in absolute value terms.
When we say PED = 2, we mean |PED| = 2 (or technically PED = -2).
Calculating PED: Step-by-Step Example
Example 1: Basic PED Calculation
Scenario: Coffee shop reduces coffee price from $5 to $4. Sales increase from 100 cups to 140 cups per day.
Step 1: Calculate percentage change in quantity demanded
\[ \% \Delta Q_d = \frac{140 - 100}{100} \times 100\% = \frac{40}{100} \times 100\% = 40\% \]Step 2: Calculate percentage change in price
\[ \% \Delta P = \frac{4 - 5}{5} \times 100\% = \frac{-1}{5} \times 100\% = -20\% \]Step 3: Calculate PED
\[ PED = \frac{40\%}{-20\%} = -2 \]Interpretation: |PED| = 2 means a 1% decrease in price leads to a 2% increase in quantity demanded. Demand is price elastic.
Classifications of PED
| Type | Value | Meaning | Diagram |
|---|---|---|---|
| Perfectly Inelastic | |PED| = 0 | Quantity demanded does not change when price changes | Vertical demand curve |
| Inelastic | 0 < |PED| < 1 | Quantity demanded changes by a smaller percentage than price | Steep demand curve |
| Unit Elastic | |PED| = 1 | Quantity demanded changes by the same percentage as price | Rectangular hyperbola |
| Elastic | |PED| > 1 | Quantity demanded changes by a larger percentage than price | Flat demand curve |
| Perfectly Elastic | |PED| = ∞ | Any price change leads to infinite change in quantity (or zero quantity) | Horizontal demand curve |
📊 PED CLASSIFICATIONS
Perfectly Inelastic: Vertical line (P changes, Q constant)
Inelastic: Steep downward slope
Elastic: Flat downward slope
Perfectly Elastic: Horizontal line
Determinants of PED
1. Availability of Substitutes
- More substitutes → More elastic demand
- If many alternatives exist, consumers easily switch when price rises
- Example: Brand-name soft drinks (Coke vs. Pepsi) have elastic demand
- Example: Gasoline has inelastic demand (few substitutes for car travel)
2. Necessity vs. Luxury
- Necessities → Inelastic demand
- Luxuries → Elastic demand
- People will buy necessities regardless of price changes
- Example: Life-saving medications (inelastic)
- Example: Designer handbags (elastic)
3. Proportion of Income Spent
- Small proportion of income → Inelastic demand
- Large proportion of income → Elastic demand
- Example: Salt (small expense, inelastic)
- Example: Cars, houses (large expense, elastic)
4. Time Period
- Short run → More inelastic
- Long run → More elastic
- Consumers need time to find alternatives and adjust behavior
- Example: Gasoline price increase has small short-run effect but larger long-run effect as people buy fuel-efficient cars
5. Habit-Forming/Addictive Goods
- Addictive goods → Very inelastic demand
- Example: Cigarettes, alcohol have inelastic demand
- Consumers continue buying despite price increases
6. Breadth of Market Definition
- Narrowly defined goods → More elastic
- Broadly defined goods → More inelastic
- Example: "Food" in general (inelastic) vs. "organic strawberries" (elastic)
PED and Total Revenue
Total Revenue Calculation
\[ \text{Total Revenue (TR)} = \text{Price} \times \text{Quantity} \] \[ TR = P \times Q \]Understanding the relationship between PED and total revenue is crucial for business pricing decisions:
| Demand Type | Price Increase Effect on TR | Price Decrease Effect on TR |
|---|---|---|
| Elastic (|PED| > 1) | TR decreases | TR increases |
| Unit Elastic (|PED| = 1) | TR unchanged | TR unchanged |
| Inelastic (|PED| < 1) | TR increases | TR decreases |
Example 2: PED and Total Revenue
Scenario 1: Elastic Demand (|PED| = 2)
Current: Price = $10, Quantity = 100, TR = $1,000
Price increases to $11 (10% increase)
Quantity demanded falls to 80 (20% decrease, since |PED| = 2)
New TR = $11 × 80 = $880
Result: TR decreased. Price increase hurts revenue when demand is elastic.
Scenario 2: Inelastic Demand (|PED| = 0.5)
Current: Price = $10, Quantity = 100, TR = $1,000
Price increases to $11 (10% increase)
Quantity demanded falls to 95 (5% decrease, since |PED| = 0.5)
New TR = $11 × 95 = $1,045
Result: TR increased. Price increase helps revenue when demand is inelastic.
Business Applications of PED
- If demand is elastic: Lower prices to increase total revenue
- If demand is inelastic: Raise prices to increase total revenue
- Pricing strategy: Firms try to make demand inelastic through branding, customer loyalty
- Sales and discounts: Effective when demand is elastic
PED and Indirect Taxes
Tax Incidence: How the burden of a tax is shared between consumers and producers
- Inelastic demand: Consumers bear most of the tax burden
- Elastic demand: Producers bear most of the tax burden
Example 3: Tax Incidence
Cigarettes (Inelastic Demand, |PED| = 0.4):
- Government imposes $2 tax per pack
- Price rises from $8 to $9.80 (consumers pay $1.80 more)
- Producers receive $7.80 (bear $0.20 of tax)
- Consumer burden: 90%, Producer burden: 10%
- Quantity decreases slightly
Restaurant Meals (Elastic Demand, |PED| = 2):
- Government imposes $2 tax per meal
- Price rises from $20 to $20.60 (consumers pay $0.60 more)
- Producers receive $18.60 (bear $1.40 of tax)
- Consumer burden: 30%, Producer burden: 70%
- Quantity decreases significantly
2. Income Elasticity of Demand (YED)
Definition
Income Elasticity of Demand (YED) measures the responsiveness of quantity demanded to a change in consumer income, ceteris paribus.
It tells us by what percentage quantity demanded changes when income changes by 1%.
YED Formula
\[ YED = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in income}} \]Or more precisely:
\[ YED = \frac{\Delta Q_d / Q_d}{\Delta Y / Y} = \frac{\Delta Q_d}{\Delta Y} \times \frac{Y}{Q_d} \]Where:
- • \(\Delta Q_d\) = Change in quantity demanded
- • \(\Delta Y\) = Change in income
- • \(Q_d\) = Original quantity demanded
- • \(Y\) = Original income
Example 4: YED Calculation
Scenario: Consumer's income increases from $3,000 to $3,600 per month. Their demand for restaurant meals increases from 10 to 14 per month.
Step 1: Calculate percentage change in quantity demanded
\[ \% \Delta Q_d = \frac{14 - 10}{10} \times 100\% = 40\% \]Step 2: Calculate percentage change in income
\[ \% \Delta Y = \frac{3600 - 3000}{3000} \times 100\% = 20\% \]Step 3: Calculate YED
\[ YED = \frac{40\%}{20\%} = 2 \]Interpretation: YED = 2 means a 1% increase in income leads to a 2% increase in quantity demanded. Restaurant meals are a luxury good (income elastic).
Classifications of YED
| Type | YED Value | Meaning | Examples |
|---|---|---|---|
| Inferior Goods | YED < 0 (negative) | Demand decreases as income increases | Instant noodles, second-hand clothes, public buses (for some consumers) |
| Normal Goods - Necessities | 0 < YED < 1 | Demand increases as income increases, but less than proportionally | Food, clothing, utilities, basic healthcare |
| Normal Goods - Luxuries | YED > 1 | Demand increases as income increases, more than proportionally | Jewelry, vacations, fine dining, sports cars, designer brands |
Key Insight: Normal vs. Inferior Goods
Normal Goods (YED > 0):
- As income rises, demand increases
- Most goods fall into this category
- Includes both necessities (0 < YED < 1) and luxuries (YED > 1)
Inferior Goods (YED < 0):
- As income rises, demand decreases
- Consumers switch to higher-quality alternatives
- Examples: Generic brands, low-quality goods, cheap substitutes
Real-World Examples of YED
Income Elasticity in Different Income Brackets
Low-Income Consumer:
- Rice and bread: YED ≈ 0.3 (necessity)
- Fast food: YED ≈ 1.2 (becomes luxury)
Middle-Income Consumer:
- Rice and bread: YED ≈ 0.1 (saturated demand)
- Restaurant meals: YED ≈ 1.5 (luxury)
- International travel: YED ≈ 2.5 (high luxury)
High-Income Consumer:
- Public transportation: YED < 0 (inferior, switches to private cars)
- Basic goods: YED ≈ 0 (no longer responsive)
- Luxury cars: YED ≈ 3 (very income elastic)
Applications of YED
Business Strategy Based on YED
For Luxury Goods Producers (YED > 1):
- Sales highly sensitive to economic cycles
- Boom periods: Rapid sales growth
- Recession periods: Sharp sales decline
- Strategy: Target high-income segments, maintain premium positioning
For Necessity Producers (0 < YED < 1):
- Stable demand regardless of economic conditions
- Recession-resistant
- Strategy: High volume, low margins, mass market appeal
For Inferior Goods Producers (YED < 0):
- Counter-cyclical business
- Sales increase during recessions
- Strategy: Budget positioning, value emphasis
Government and Policy Applications
- Economic Development: As countries develop, demand shifts from necessities to luxuries
- Sectoral Changes: Agriculture (low YED) declines relative to services (high YED)
- Tax Policy: Luxury taxes on high YED goods generate revenue without harming necessities
- Welfare Programs: Focus on goods with low YED (basic needs)
3. Price Elasticity of Supply (PES)
Definition
Price Elasticity of Supply (PES) measures the responsiveness of quantity supplied to a change in price, ceteris paribus.
It tells us by what percentage quantity supplied changes when price changes by 1%.
PES Formula
\[ PES = \frac{\% \text{ change in quantity supplied}}{\% \text{ change in price}} \]Or more precisely:
\[ PES = \frac{\Delta Q_s / Q_s}{\Delta P / P} = \frac{\Delta Q_s}{\Delta P} \times \frac{P}{Q_s} \]Where:
- • \(\Delta Q_s\) = Change in quantity supplied
- • \(\Delta P\) = Change in price
- • \(Q_s\) = Original quantity supplied
- • \(P\) = Original price
Important Note
PES is always positive due to the law of supply (direct relationship between price and quantity supplied).
Example 5: PES Calculation
Scenario: Price of wheat increases from $200 to $240 per ton. Farmers increase supply from 5,000 to 5,800 tons.
Step 1: Calculate percentage change in quantity supplied
\[ \% \Delta Q_s = \frac{5800 - 5000}{5000} \times 100\% = 16\% \]Step 2: Calculate percentage change in price
\[ \% \Delta P = \frac{240 - 200}{200} \times 100\% = 20\% \]Step 3: Calculate PES
\[ PES = \frac{16\%}{20\%} = 0.8 \]Interpretation: PES = 0.8 means a 1% increase in price leads to a 0.8% increase in quantity supplied. Supply is price inelastic (short-run agricultural response).
Classifications of PES
| Type | Value | Meaning | Diagram |
|---|---|---|---|
| Perfectly Inelastic | PES = 0 | Quantity supplied does not change when price changes | Vertical supply curve |
| Inelastic | 0 < PES < 1 | Quantity supplied changes by a smaller percentage than price | Steep supply curve |
| Unit Elastic | PES = 1 | Quantity supplied changes by the same percentage as price | 45-degree supply curve from origin |
| Elastic | PES > 1 | Quantity supplied changes by a larger percentage than price | Flat supply curve |
| Perfectly Elastic | PES = ∞ | Any price decrease leads to zero supply; any price increase leads to infinite supply | Horizontal supply curve |
📊 PES CLASSIFICATIONS
Perfectly Inelastic: Vertical line (P changes, Q constant)
Inelastic: Steep upward slope
Elastic: Flat upward slope
Perfectly Elastic: Horizontal line
Determinants of PES
1. Time Period
Most Important Determinant
- Momentary/Market Period: PES ≈ 0 (perfectly inelastic)
- Fixed supply, no time to produce more
- Example: Fresh fish at morning market, concert tickets for tonight
- Short Run: PES < 1 (inelastic)
- Can increase output with existing capacity
- Example: Factory runs extra shifts, farmers harvest earlier
- Long Run: PES > 1 (elastic)
- Can build new capacity, new firms enter
- Example: Build new factories, plant more crops, train workers
2. Spare Productive Capacity
- Excess capacity → More elastic supply
- Can quickly increase output without new investment
- Full capacity → More inelastic supply
- Must invest in new capacity to increase supply
- Example: Hotel with 50% occupancy can easily accommodate more guests (elastic)
3. Mobility of Factors of Production
- Mobile factors → More elastic supply
- Resources can be easily switched between uses
- Immobile factors → More inelastic supply
- Example: Retail workers are mobile (elastic supply)
- Example: Specialized medical equipment is immobile (inelastic supply)
4. Ability to Store Stock/Inventory
- Storable goods → More elastic supply
- Can release inventory when prices rise
- Non-storable goods → More inelastic supply
- Example: Canned goods (storable, elastic)
- Example: Fresh produce (perishable, inelastic)
- Example: Services (non-storable, inelastic)
5. Production Lag/Gestation Period
- Short production time → More elastic supply
- Long production time → More inelastic supply
- Example: T-shirts (days to produce, elastic)
- Example: Wine (years to mature, inelastic)
- Example: Skyscrapers (years to build, very inelastic)
6. Ease of Entry to the Market
- Low barriers → More elastic supply
- New firms can enter easily when prices rise
- High barriers → More inelastic supply
- Example: Food trucks (low barriers, elastic)
- Example: Pharmaceutical manufacturing (high barriers, inelastic)
Real-World Examples of PES
Example 6: Agricultural Products
Coffee (Short Run):
- Takes 3-4 years for coffee trees to mature
- Short-run PES ≈ 0.1-0.2 (very inelastic)
- Price spike → Cannot increase supply immediately
- Result: Large price fluctuations
Coffee (Long Run):
- Farmers can plant more trees, new farms established
- Long-run PES ≈ 1.5-2.0 (elastic)
- High prices → Eventually leads to increased supply
Example 7: Service Industries
Restaurant Meals (Evening):
- Fixed number of tables and staff
- Momentary PES ≈ 0 (perfectly inelastic)
- Cannot serve more customers than capacity
Restaurant Meals (Long Run):
- Can hire more staff, extend hours, open new locations
- Long-run PES ≈ 2-3 (elastic)
- High demand → Eventually leads to more restaurants
PES and Tax Incidence
Tax Burden Distribution: The combination of PED and PES determines who bears the tax burden.
- Inelastic supply + Elastic demand: Producers bear most of the tax
- Elastic supply + Inelastic demand: Consumers bear most of the tax
Example 8: Tax Incidence Comparison
Labor Market (Inelastic Supply):
- Workers cannot easily reduce hours worked (PES ≈ 0.3)
- Income tax → Workers bear most of the burden
- Hard to shift tax burden to employers
Manufacturing (Elastic Supply):
- Firms can easily adjust production (PES ≈ 2.0)
- Production tax → Burden shifts to consumers via higher prices
- Producers reduce output rather than absorb tax
Applications of PES
Market Stability
- Inelastic supply: Price volatility (small demand changes cause large price swings)
- Elastic supply: Price stability (supply adjusts to demand changes)
- Example: Oil prices (inelastic short-run supply) vs. manufactured goods (elastic supply)
Government Policy
- Price controls: More effective with elastic supply (less shortage/surplus)
- Subsidies: More quantity increase with elastic supply
- Buffer stock schemes: Necessary for inelastic supply markets (agriculture)
Business Planning
- Short-run inelastic supply: Cannot capitalize on sudden demand spikes
- Building capacity: Investment to make supply more elastic in long run
- Inventory management: Stock storage increases PES
Comparing All Three Elasticities
| Aspect | PED | YED | PES |
|---|---|---|---|
| Measures | Responsiveness of Qd to price changes | Responsiveness of Qd to income changes | Responsiveness of Qs to price changes |
| Sign | Usually negative (use absolute value) | Positive (normal goods) or negative (inferior goods) | Always positive |
| Key Determinant | Availability of substitutes | Type of good (necessity vs. luxury) | Time period |
| Business Application | Pricing decisions, revenue maximization | Product positioning, economic forecasting | Production planning, capacity investment |
| Government Application | Tax policy, price controls | Welfare policy, development planning | Market intervention, agricultural policy |
Calculation Summary: Quick Reference
All Elasticity Formulas
Price Elasticity of Demand (PED):
\[ PED = \frac{\% \Delta Q_d}{\% \Delta P} = \frac{\Delta Q_d / Q_d}{\Delta P / P} \]Income Elasticity of Demand (YED):
\[ YED = \frac{\% \Delta Q_d}{\% \Delta Y} = \frac{\Delta Q_d / Q_d}{\Delta Y / Y} \]Price Elasticity of Supply (PES):
\[ PES = \frac{\% \Delta Q_s}{\% \Delta P} = \frac{\Delta Q_s / Q_s}{\Delta P / P} \]Percentage Change Formula:
\[ \% \text{ change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\% \]Common Exam Questions and Mistakes
Common Mistakes to Avoid
- Sign errors: Remember PED is negative, but we use absolute values; YED can be positive or negative
- Confusing elasticity with slope: Elasticity ≠ slope (elasticity varies along a linear curve)
- Wrong interpretation: "Elastic" means responsive, "inelastic" means unresponsive
- Forgetting time dimension: Always specify short-run vs. long-run for PES
- Calculation errors: Use correct base values (old values, not new values)
- Revenue confusion: Price increase raises revenue only if demand is inelastic
Exam Strategy Tips
- Define clearly: Always start by defining the elasticity concept
- Show calculations: Write out all steps, even if they seem obvious
- Include units: Always state units (%, dollars, quantity)
- Diagrams: Draw and label graphs accurately (elastic = flat, inelastic = steep)
- Real-world examples: Use specific examples to illustrate concepts
- Explain significance: Don't just calculate—explain what the number means
- Compare and contrast: Discuss differences between types of elasticity
- Evaluation: Consider limitations, assumptions, time periods
Practice Question
Comprehensive Elasticity Problem
Scenario: The market for organic vegetables:
- Current price: $5 per kg, Quantity: 1,000 kg per week
- After 20% price increase to $6, quantity demanded falls to 700 kg
- Average consumer income: $4,000 per month
- When income rises to $5,000, quantity demanded increases to 1,300 kg (at original price)
- Farmers can supply 1,000 kg currently; at $6, they supply 1,100 kg
Calculate:
1. PED
2. YED
3. PES
4. Interpret each result
Solutions:
1. PED:
\[ PED = \frac{(700-1000)/1000}{(6-5)/5} = \frac{-30\%}{20\%} = -1.5 \]|PED| = 1.5 (elastic demand—consumers are price-sensitive)
2. YED:
\[ YED = \frac{(1300-1000)/1000}{(5000-4000)/4000} = \frac{30\%}{25\%} = 1.2 \]YED = 1.2 > 1 (luxury good—income elastic)
3. PES:
\[ PES = \frac{(1100-1000)/1000}{(6-5)/5} = \frac{10\%}{20\%} = 0.5 \]PES = 0.5 < 1 (inelastic supply—short-run agricultural constraints)
4. Business Implications:
- Price increase reduces total revenue (elastic demand)
- Target higher-income consumers (luxury good)
- Supply cannot quickly adjust to demand (invest in capacity)
✓ Unit 2 Elasticities Checkpoint
You should now understand how to calculate and interpret PED, YED, and PES; recognize the determinants of each elasticity; apply elasticity concepts to real-world business and policy decisions; and analyze the relationship between elasticity, total revenue, and tax incidence. These concepts are essential for understanding market behavior and will be applied throughout your IB Economics SL course, especially in market failures, government intervention, and international trade topics.