Chapter 6: Elasticity Lecture Notes

Overview of Price Elasticity of Demand

• Definition: Price elasticity of demand measures how responsive consumers are to changes in the price of a specific product.

• Elastic Demand:

  • Occurs when consumers are highly sensitive to price changes.

  • Characterized by a relatively large change in the quantity demanded following a price change.

• Inelastic Demand:

  • Occurs when consumers are relatively insensitive to price changes.

  • Characterized by a relatively small change in the quantity demanded following a price change.

Formulas for Price Elasticity of Demand

• General Formula: Elasticity ($E_d$) is calculated as the percentage change in quantity demanded divided by the percentage change in price.

  • $E_d = \frac{\% \Delta Q_d}{\% \Delta P}$

• The Midpoint Formula: To ensure consistent results regardless of whether the price is increasing or decreasing, the midpoint formula is used. It averages the starting and ending points for both price and quantity.

  • $E_d = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\frac{P_2 - P_1}{(P_1 + P_2)/2}}$

• Unit-Free Measurement: Elasticity is expressed as a unit-free percentage. This allows for the comparison of responsiveness across different products (e.g., comparing the elasticity of shoes to the elasticity of gasoline).

• Elimination of Negative Signs: Because demand curves are downward sloping (price and quantity move in opposite directions), the result of the calculation is naturally negative. Economists typically ignore the minus sign and use the absolute value to make comparisons easier.

Interpretation of Demand Elasticity Coefficients

• Elastic (E_d > 1): The percentage change in quantity demanded is greater than the percentage change in price.

• Unit Elastic ($E_d = 1$): The percentage change in quantity demanded is exactly equal to the percentage change in price.

• Inelastic (E_d < 1): The percentage change in quantity demanded is less than the percentage change in price.

• Extreme Case - Perfectly Inelastic ($E_d = 0$): The quantity demanded does not change regardless of the price. On a graph, this is represented by a vertical demand curve ($D_1$).

• Extreme Case - Perfectly Elastic ($E_d = \infty$): A tiny change in price results in an infinitely large change in quantity demanded. On a graph, this is expressed as a horizontal demand curve ($D_2$).

The Total Revenue Test

• Total Revenue (TR) Calculation: $TR = P \times Q$.

• The Test Principle: The Total Revenue Test observes the relationship between a price change and the resulting change in total revenue to determine elasticity.

• Elastic Demand Relationship:

  • Price and Total Revenue move in opposite directions.

  • If price decreases, Total Revenue increases (the gain in revenue from selling more units exceeds the loss from the lower price).

  • If price increases, Total Revenue decreases.

• Inelastic Demand Relationship:

  • Price and Total Revenue move in the same direction.

  • If price decreases, Total Revenue decreases (the loss from the lower price per unit exceeds the gain from selling more units).

  • If price increases, Total Revenue increases.

• Unit-Elastic Demand Relationship:

  • Total Revenue remains unchanged when price changes.

  • The gain from selling more units exactly offsets the loss from the lower price.

Case Study: Movie Ticket Pricing and Revenue

• Detailed metrics for movie tickets illustrate how elasticity changes along a single demand curve:

  • Price $P = \$8$; Quantity $Q = 1,000$: $TR = \$8,000$; $E_d = 5.00$; Demand is Elastic.

  • Price $P = \$7$; Quantity $Q = 2,000$: $TR = \$14,000$; $E_d = 2.60$; Demand is Elastic.

  • Price $P = \$6$; Quantity $Q = 3,000$: $TR = \$18,000$; $E_d = 1.57$; Demand is Elastic.

  • Price $P = \$5$; Quantity $Q = 4,000$: $TR = \$20,000$; $E_d = 1.00$; Demand is Unit-elastic.

  • Price $P = \$4$; Quantity $Q = 5,000$: $TR = \$20,000$; $E_d = 0.64$; Demand is Inelastic.

  • Price $P = \$3$; Quantity $Q = 6,000$: $TR = \$18,000$; $E_d = 0.38$; Demand is Inelastic.

  • Price $P = \$2$; Quantity $Q = 7,000$: $TR = \$14,000$; $E_d = 0.20$; Demand is Inelastic.

  • Price $P = \$1$; Quantity $Q = 8,000$: $TR = \$8,000$; Demand is Inelastic.

Determinants of Price Elasticity of Demand

• Substitutability: The more substitute goods available, the more elastic the demand. Consumers can easily switch to another product if the price of one rises.

• Proportion of Income: Goods that consume a larger portion of a consumer's budget tend to have more elastic demand. Smaller items (like salt) usually have inelastic demand.

• Luxuries versus Necessities: Demand for luxury items (e.g., vacations) is generally more elastic than demand for necessities (e.g., medicine).

• Time: Demand is more elastic over longer time periods. Consumers need time to adjust their habits, find substitutes, or wait for existing products to wear out.

Selected Values for Demand Elasticity

• Highly Inelastic ($E_d \leq 0.30$):

  • Newspapers ($0.10$)

  • Electricity for households ($0.13$)

  • Bread ($0.15$)

  • MLB Tickets ($0.23$)

  • Cigarettes ($0.25$)

  • Telephone service ($0.26$)

  • Sugar ($0.30$)

• Moderately Inelastic ($0.31 - 0.99$):

  • Medical Care ($0.31$)

  • Eggs ($0.32$)

  • Legal Services ($0.37$)

  • Automobile repair ($0.40$)

  • Clothing ($0.49$)

  • Gasoline ($0.60$)

  • Milk ($0.63$)

  • Household appliances ($0.63$)

  • Liquor ($0.70$)

  • Movies ($0.87$)

  • Beer ($0.90$)

  • Shoes ($0.91$)

• Elastic (E_d > 1.00):

  • Motor vehicles ($1.14$)

  • Beef ($1.27$)

  • China, glassware, tableware ($1.54$)

  • Residential land ($1.60$)

  • Restaurant meals ($2.27$)

  • Lamb and mutton ($2.65$)

  • Fresh peas ($2.83$)

Real-World Applications of Demand Elasticity

• Large Crop Yields: Farmers often face lower total revenue when there is a bumper crop because the demand for agricultural products is inelastic. The resulting drop in price is proportionately larger than the increase in sales volume.

• Excise Taxes: Governments often place excise taxes on products with inelastic demand (like cigarettes or alcohol) because it ensures a high amount of total revenue since consumption stays relatively steady despite higher prices.

• Decriminalization of Illegal Drugs: Since the demand for drugs is generally inelastic, shifting the legality may change market prices, but it will lead to more total revenue for the sellers due to the steady nature of addiction-driven demand.

Price Elasticity of Supply (PES)

• Definition: Measures how responsive producers/sellers are to changes in the price of a product.

• Elastic Supply: Producers are highly responsive to price changes (they can ramp up production easily).

• Inelastic Supply: Producers are not very responsive to price changes.

• Formula:

  • $E_s = \frac{\% \Delta Q_s}{\% \Delta P}$

• Interpretations:

  • E_s > 1: Supply is elastic.

  • $E_s = 1$: Supply is unit elastic.

  • E_s < 1: Supply is inelastic.

  • $E_s = 0$: Supply is perfectly inelastic (quantity supplied cannot change).

Determinants and Time Periods of Supply Elasticity

• Time as the Primary Determinant: The ability to adjust production depends on the time available to the producer.

• Immediate Market Period: Supply is perfectly inelastic ($S_m$). There is no time to adjust production; the amount of the product already in the market is fixed.

• Short Run: Plant capacity remains fixed, but firms can change the intensity of production (e.g., hiring more labor). Supply ($S_s$) is more elastic than the immediate market period.

• Long Run: Firms have enough time to change plant size and new firms can enter or exit the industry. Supply ($S_L$) is most elastic in the long run.

• Applications:

  • Antiques: Supply is highly inelastic because no more authentic antiques can be produced.

  • Reproductions: Supply is more elastic because modern factories can produce them on demand.

  • Gold: Prices are volatile because the supply of gold is relatively inelastic; it takes a long time to open new mines.

Cross Elasticity of Demand (XED)

• Definition: Measures the responsiveness of the quantity demanded of one good ($X$) to a change in the price of another good ($Y$).

• Formula:

  • $E_{xy} = \frac{\% \Delta Q_{dX}}{\% \Delta P_Y}$

• Interpretation of Coefficient Value:

  • Positive (Substitutes): If E_{wz} > 0, the goods are substitutes. An increase in the price of $Z$ leads to an increase in the demand for $W$.

  • Negative (Complements): If E_{xy} < 0, the goods are complements. An increase in the price of $Y$ leads to a decrease in the demand for $X$.

  • Zero (Independent Goods): No relationship between the price of one and the demand for the other.

• Strategic Applications: Businesses use cross elasticity to decide on pricing strategies. The government uses it to evaluate if a merger between two companies would create a monopoly by reducing competition among substitutes.

Income Elasticity of Demand (YED)

• Definition: Measures how responsive consumers are to changes in their income.

• Formula:

  • $E_i = \frac{\% \Delta Q_d}{\% \Delta Income}$

• Interpretation of Coefficient Value:

  • Positive (Normal/Superior Goods): Demand increases as income increases (E_i > 0).

  • Negative (Inferior Goods): Demand decreases as income increases (E_i < 0). Consumers switch to better alternatives as they become wealthier.

• Recession Insights:

  • Industries with high income elasticities (luxuries) are hit hardest by recessions.

  • Industries with low or negative income elasticities (necessities or inferior goods) are relatively resilient during economic downturns.

Elasticity and Pricing Power

• Companies can use price elasticity insights to exercise pricing power by charging different prices to different buyers.

• Business Air Travelers: Charged higher prices because their demand is inelastic (they must travel for work regardless of price).

• Children Discounts: Businesses offer lower prices (discounts) to children because families are often more price-sensitive (higher elasticity).

• College Tuition: Colleges use financial aid to adjust the actual price paid by students based on their price sensitivity and ability to pay.