Elasticity Lectures 1 and 2 - notes and flashcards.

Introduction to Elasticity

• Definition of Elasticity: Elasticity is a measure of responsiveness to a change in market conditions. It quantifies how one variable (such as quantity) responds to a change in another variable (such as price).

• Applicability: Elasticity applies to both supply and demand. Common types include:

  • Price elasticity of demand.

  • Price elasticity of supply.

  • Cross-price elasticity.

  • Income elasticity.

• The Law of Demand and Elasticity: The law of demand states that, all other things equal, a lower price leads to a higher quantity demanded, while a higher price leads to a lower quantity demanded. Elasticity quantifies this law by answering the question: "How much?"

• Price Sensitivity: Elasticity essentially measures price sensitivity. When thinking about elasticity, one can conceptually replace the term with "sensitivity."

Price Elasticity of Demand (PED)

• Definition: Price elasticity of demand measures the magnitude of the change in quantity demanded resulting from a change in the price of that specific good.

• Sensitivity Spectrum:

  • Elastic (High Sensitivity): A good is considered very elastic if a small increase in price causes a large number of people to stop buying it. Examples include goods with many substitutes or non-essential luxury items.

  • Inelastic (Low Sensitivity): A good is considered inelastic if people continue to buy it in similar quantities even if the price increases significantly. Examples include necessities like insulin or rent.

• Categories of Elasticity:

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

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

  • Unit Elastic: There is a one-to-one correspondence between the percentage change in price and the percentage change in quantity demanded ($Elasticity = 1$).

Factors Determining Demand Elasticity

• Availability of Substitutes: When two products are very similar, consumers are more likely to default to a substitute if the price of their preferred brand increases.

  • Example: If Lindor dark chocolate truffles increase in price, a consumer might switch to milk chocolate truffles or a different brand like Sora chocolate chip cookies.

• Degree of Necessity: Necessity items are highly inelastic because consumers literally cannot go without them.

  • Examples: Gasoline (needed for commuting), insulin, or other vital medications.

• Cost Relative to Income:

  • If a good represents a very small portion of a consumer's income, they are less likely to notice or respond to a price change, making it more inelastic.

  • Example: A can of beans increasing from $0.80$ to $1.00$ is a large percentage increase, but because the absolute increase is small relative to total income, demand remains inelastic. Conversely, a $20\%$ increase on a $100$ item ($120$) might trigger a greater reduction in demand.

• Adjustment Time:

  • Short Term: Goods are generally more inelastic because consumers have less time to find alternatives.

  • Long Term: Goods become more elastic as consumers have time to adjust, such as switching to an electric car in response to long-term high gas prices.

• Scope of the Market: This refers to how broadly or narrowly a market is defined.

  • Narrow Scope: Demand is more elastic for a specific item (e.g., apple juice) because consumers can easily switch to a different item in the same category (e.g., orange juice or cranberry juice).

  • Broad Scope: Demand is more inelastic for an entire category (e.g., fruit or gas in an entire city) because there are fewer available alternatives for the category as a whole.

Calculating Elasticity: The Midpoint Method

• The Issue with Standard Percentage Change: Using standard percentage change ($\frac{Q_2 - Q_1}{Q_1}$) results in different elasticity values depending on the direction of the change (e.g., moving from point A to B vs. B to A).

• The Midpoint Method Formula: This formula provides a consistent metric regardless of the direction of change. Though the result is typically negative due to the law of demand, economists often discuss the absolute value.

  • $\text{Price Elasticity of Demand} = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2) / 2}}{\frac{P_2 - P_1}{(P_1 + P_2) / 2}}$

• Calculation Example:

  • Scenario: Price increases from $4$ to $6$. Quantity demanded decreases from $20$ to $15$.

  • $\% \Delta Q = \frac{15 - 20}{(20 + 15) / 2} = \frac{-5}{17.5} \approx -0.2857$

  • $\% \Delta P = \frac{6 - 4}{(4 + 6) / 2} = \frac{2}{5} = 0.4$

  • $\text{Elasticity} = \frac{-0.2857}{0.4} = -0.714$

  • Interpretation: Since 0.714 < 1, the good is inelastic.

Graphing Elasticity

• Axial Relationship: On a standard plot, Quantity ($Q$) is on the x-axis and Price ($P$) is on the y-axis.

• Slope vs. Elasticity:

  • The slope of a line is "rise over run" ($\Delta P / \Delta Q$).

  • Elasticity is $\Delta Q / \Delta P$.

  • Therefore, $\text{Slope} = \frac{1}{\text{Elasticity}}$.

• Visual Cues:

  • Flatter Line: Indicates higher elasticity (more elastic). A small change in price leads to a large change in quantity.

  • Steeper Line: Indicates lower elasticity (more inelastic). A large change in price leads to a small change in quantity.

• Extremes:

  • Perfectly Elastic: A perfectly horizontal line. Any price change causes quantity demanded to drop to zero.

  • Perfectly Inelastic: A perfectly vertical line. Quantity demanded remains the same regardless of the price (e.g., a lifesaving drug with no substitutes).

• Linear Demand Curve: Elasticity changes along a linear demand curve:

  • Higher Price Points: The upper portion of the curve is elastic because the percentage change in price is relatively small compared to the large percentage change in quantity.

  • Midpoint: Unit elastic.

  • Lower Price Points: The bottom portion of the curve is inelastic.

Elasticity and Total Revenue

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

• The Dual Effects of Price Increases:

  • Price Effect: After a price increase, each unit sold earns more revenue.

  • Quantity Effect: After a price increase, fewer units are sold due to the law of demand.

• Revenue Outcomes:

  • Inelastic Demand: The price effect outweighs the quantity effect. A price increase leads to an increase in total revenue. Price and total revenue move in the same direction.

  • Elastic Demand: The quantity effect outweighs the price effect. A price increase leads to a decrease in total revenue. Price and total revenue move in opposite directions.

• Business Application (Disney/Netflix Example): Managers use elasticity to determine if they can "jack up" prices without losing too many customers. For example, if a streaming service like Disney+ or Netflix increases subscription prices, they calculate if the extra revenue per remaining subscriber covers the loss of customers who cancel their service.

Other Types of Elasticity

Cross-Price Elasticity of Demand

• Definition: Measures how the quantity demanded of Good A changes in response to a change in the price of Good B.

• Formula: $\frac{\% \Delta Q_A}{\% \Delta P_B}$

• Substitutes (Positive Elasticity): If the price of Good B (e.g., Queso) increases, the demand for Good A (e.g., Guacamole) increases.

  • Note: Closely related substitutes (e.g., Coke and Pepsi) have higher cross-price elasticity than less related substitutes (e.g., Coke and Lacroix).

• Complements (Negative Elasticity): If the price of Good B (e.g., Chips) increases, the demand for Good A (e.g., Salsa) decreases.

Income Elasticity of Demand

• Definition: Measures how quantity demanded changes in response to a change in consumer income.

• Normal Goods (Elasticity > 0): Demand increases as income increases.

  • Necessities: Elasticity is between $0$ and $1$. Demand increases moderately (e.g., T-shirts).

  • Luxuries: Elasticity is greater than $1$. Demand increases significantly in proportion to income (e.g., concert tickets).

• Inferior Goods (Elasticity < 0): Demand decreases as income increases (e.g., ramen noodles or potatoes), as consumers substitute toward higher quality goods.

Price Elasticity of Supply (PES)

• Definition: Measures the responsiveness of quantity supplied to a change in price.

• Law of Supply: PES is always positive because producers want to sell more as prices rise.

• Factors Influencing Supply Elasticity:

  • Availability of Inputs: If inputs are readily available, supply is more elastic.

  • Flexibility of Production: If a process can easily scale up or down, supply is more elastic.

  • Adjustment Time: Supply is more elastic in the long run than the short run as producers can build new factories or plant more trees (e.g., apple orchards over a decade).

  • Scope: It is easier to change the supply of a specific item (breakfast cereal) than the total supply of a broad category (food).

Practice Problems and Mathematical Applications

• Problem 1: Netflix PED:

  • Price increases from $8$ to $16$. Subscribers fall from $60\text{ million}$ to $40\text{ million}$.

  • $\% \Delta Q = \frac{40 - 60}{(60 + 40) / 2} = -0.4$

  • $\% \Delta P = \frac{16 - 8}{(8 + 16) / 2} = \frac{8}{12} \approx 0.667$

  • $\text{Elasticity} = \frac{-0.4}{0.667} = -0.6$

  • Result: Inelastic (less than $1$). Netflix increases revenue because the price effect dominates.

• Problem 2: Cupcake PED:

  • Quantity changes from $12$ to $2$. Price changes from $6$ to $2$.

  • Result: $\text{Elasticity} = -0.5$ (Inelastic).

  • Total revenue will decrease because for an inelastic good, revenue moves in the same direction as price (price decreased, so revenue decreased).