Price Elasticity and Its Measurement: Demand, Supply, Income, Cross Elasticity

TAKEAWAYS:

• Price elasticity measures how much quantity demanded or supplied changes when price changes.
• Elasticity is classified into elastic, inelastic, and unitary elastic based on the magnitude of response.
• Income elasticity and cross elasticity help understand consumer behavior beyond price changes.
• Elasticity guides businesses in pricing strategies and governments in policy-making.
• Graphs and calculations are essential tools to determine elasticity.
• Real-world examples help visualize and apply elasticity concepts effectively.

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What is Price Elasticity?

Price elasticity measures how much the quantity demanded or supplied of a good changes when its price changes. It tells us whether consumers or producers are sensitive or insensitive to price changes.

Key Terms:

• Elastic Demand: Small price change → Big change in quantity demanded.
• Inelastic Demand: Small price change → Small change in quantity demanded.
• Unitary Elastic: Price change → Proportional change in quantity demanded.

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Price Elasticity of Demand (PED)

PED measures how much the quantity demanded changes when the price changes, keeping other factors constant.

Formula:

$$E_d=\frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Price}}$$

How to Calculate?

1. Find the initial price (P₁) and initial quantity (Q₁).
2. Find the new price (P₂) and new quantity (Q₂) after the change.
3. Calculate the percentage change in quantity and price.
4. Divide the two percentages to get E_d.

Example:

Suppose the price of a good increases from ₨100 to ₨120, and the quantity demanded decreases from 50 units to 40 units.

Initial Price (P₁) = ₨100
Initial Quantity (Q₁) = 50 units
New Price (P₂) = ₨120
New Quantity (Q₂) = 40 units

Step 1: Calculate % change in quantity demanded. $$\%\text{ Change in Q}=\frac{Q_2-Q_1}{Q_1}\times 100=\frac{40-50}{50}\times 100=-20\%$$

Step 2: Calculate % change in price. $$\%\text{ Change in P}=\frac{P_2-P_1}{P_1}\times 100=\frac{120-100}{100}\times 100=20\%$$

Step 3: Calculate PED. $$E_d=\frac{-20\%}{20\%}=-1$$

Interpretation: Since E_d = -1, demand is unitary elastic.

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Types of Price Elasticity of Demand

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Factors Affecting Price Elasticity of Demand

1. Availability of Substitutes: More substitutes → More elastic demand.
2. Necessity vs. Luxury: Necessities (e.g., salt) have inelastic demand; luxuries (e.g., yachts) have elastic demand.
3. Proportion of Income: If a good costs a large portion of income, demand is more elastic.
4. Time Period: In the short run, demand is inelastic; in the long run, it becomes elastic.
5. Addiction Habits: Addictive goods (e.g., cigarettes) have inelastic demand.

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Price Elasticity of Supply (PES)

PES measures how much the quantity supplied changes when the price changes, keeping other factors constant.

Formula:

$$E_s=\frac{\%\text{ Change in Quantity Supplied}}{\%\text{ Change in Price}}$$

Example:

Suppose the price of a good increases from ₨50 to ₨70, and the quantity supplied increases from 30 units to 50 units.

Initial Price (P₁) = ₨50
Initial Quantity (Q₁) = 30 units
New Price (P₂) = ₨70
New Quantity (Q₂) = 50 units

Step 1: Calculate % change in quantity supplied. $$\%\text{ Change in Q}=\frac{50-30}{30}\times 100=66.67\%$$

Step 2: Calculate % change in price. $$\%\text{ Change in P}=\frac{70-50}{50}\times 100=40\%$$

Step 3: Calculate PES. $$E_s=\frac{66.67\%}{40\%}=1.67$$

Interpretation: Since E_s = 1.67, supply is elastic.

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Types of Price Elasticity of Supply

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Income Elasticity of Demand (YED)

YED measures how much the quantity demanded changes when income changes, keeping other factors constant.

Formula:

$$E_y=\frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Income}}$$

Types of Goods Based on YED

Example:

If income increases by 10% and quantity demanded of a good increases by 20%, then: $$E_y=\frac{20\%}{10\%}=2$$ This means the good is a luxury good.

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Cross Elasticity of Demand (XED)

XED measures how much the quantity demanded of one good changes when the price of another good changes, keeping other factors constant.

Formula:

$$E_x=\frac{\%\text{ Change in Quantity Demanded of Good A}}{\%\text{ Change in Price of Good B}}$$

Types of Goods Based on XED

Example:

If the price of pepsi increases by 10% and the quantity demanded of coca-cola increases by 5%, then: $$E_x=\frac{5\%}{10\%}=0.5$$ This means pepsi and coca-cola are substitutes.

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Graphical Representation of Elasticity

1. Elastic Demand (E_d > 1)

![demand curve elastic](/media/3d1a1dd742c338a5d372.gif "A demand curve with a flatter slope, showing a large change in quantity for a small price change. (Image: Michael Anthony Howard, CC BY-SA 3.0, via Wikimedia Commons)")

• Key Feature: The curve is flatter because a small price change leads to a large quantity change.

2. Inelastic Demand (E_d < 1)

![demand curve inelastic](/media/290a68c239609a51e32b.gif "A demand curve with a steeper slope, showing a small change in quantity for a large price change. (Image: Michael Anthony Howard, CC BY-SA 3.0, via Wikimedia Commons)")

• Key Feature: The curve is steeper because a large price change leads to a small quantity change.

3. Unitary Elastic Demand (E_d = 1)

• Key Feature: The curve is rectangular hyperbola (a special shape where the slope changes proportionally).

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Applications of Elasticity

1. Pricing Strategies: Businesses use elasticity to set prices that maximize revenue.
2. Government Policies: Taxes on inelastic goods (e.g., cigarettes) raise more revenue.
3. Consumer Behavior: Helps understand how consumers respond to price changes.
4. Market Forecasting: Predicts demand and supply trends based on elasticity.

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Exam Tip

• Memorize Formulas: Always recall the elasticity formulas for demand, supply, income, and cross elasticity.
• Understand Graphs: Be able to draw and interpret demand and supply curves for different elasticity types.
• Real-World Examples: Use examples like salt (inelastic), luxury cars (elastic), and substitutes (pepsi and coca-cola) in answers.
• Calculate Carefully: Practice calculating elasticity with given data to avoid mistakes.
• Classify Goods: Know how to classify goods based on YED (normal, inferior, luxury) and XED (substitutes, complements).
• Time Management: Spend more time on numerical problems as they carry more marks in NEB exams.

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Practice Questions (NEB Board Style):

1. Calculate PED: If the price of a good falls from ₨200 to ₨150 and quantity demanded rises from 100 units to 150 units, what is the price elasticity of demand?

2. Interpret E_s: The price of a good increases by 20%, and the quantity supplied increases by 40%. Is the supply elastic or inelastic? Explain.

3. YED Classification: If income increases by 15% and the quantity demanded of a good decreases by 5%, classify the good as normal, inferior, or luxury.

4. XED Scenario: If the price of good X increases by 10% and the quantity demanded of good Y increases by 20%, are X and Y substitutes or complements?

5. Graphical Analysis: Draw a demand curve for a good with unitary elastic demand. Label the axes and explain why the curve has this shape.

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Solved Example (NEB Board Style):

Question: The price of a good decreases from ₨10 to ₨8, and the quantity demanded increases from 50 units to 60 units. Calculate the price elasticity of demand and interpret the result.

Solution:

• Initial Price (P₁) = ₨10
• Initial Quantity (Q₁) = 50 units
• New Price (P₂) = ₨8
• New Quantity (Q₂) = 60 units

Step 1: Calculate % change in quantity demanded. $$\%\text{ Change in Q}=\frac{60-50}{50}\times 100=20\%$$

Step 2: Calculate % change in price. $$\%\text{ Change in P}=\frac{8-10}{10}\times 100=-20\%$$

Step 3: Calculate PED. $$E_d=\frac{20\%}{-20\%}=-1$$

Interpretation: Since E_d = -1, the demand is unitary elastic. This means that a 1% decrease in price leads to a 1% increase in quantity demanded.

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Key Takeaway: Elasticity helps businesses and policymakers understand how sensitive consumers and producers are to price changes, allowing for better decision-making. Always practice calculations and graphical interpretations to master this topic!