Comprehensive Study Notes on Supply and Demand Shifts, Price Elasticity, and Income Elasticity

Exam Review and Study Guidelines

• Course review materials include Canvas Quizzes 1 through 4, as well as the upcoming Quiz 5.

• Key preparation resources for exams consist of:

  • Canvas quizzes (Quizzes 1 through 5).

  • Practice exam problems.

  • Take-home exam materials.

  • Primary lecture notes (focused page reviews highlighting core test concepts).

Supply and Demand Analysis

• Supply and Demand Framework:

  • Graphical supply and demand diagrams provide a systematic method to analyze market shifts, equilibrium prices, and equilibrium quantities.

• Three-Step Approach for Analyzing Multi-Event Market Adjustments (Slide 62):

  • Step 1: Identify whether an event affects supply or demand. In standard single-event course problems, an event will not affect both supply and demand simultaneously.

  • Step 2: Determine the direction of the shift (rightward shift for an increase, leftward shift for a decrease).

  • Step 3: Plot the original and shifted curves on a supply and demand diagram to compare the initial equilibrium point to the new equilibrium point for price and quantity.

• Market Analysis Examples:

  • Complementary Goods Example (Coffee and Sugar):

  • Event: An increase in the price of coffee.

  • Relationship: Coffee and sugar are complementary goods, meaning they are consumed together.

  • Impact on Market: An increase in the price of coffee causes the demand curve for sugar to shift to the left (demand for sugar decreases).

  • Equilibrium Impact: The equilibrium price of sugar falls, and the equilibrium quantity sold decreases from $50\,\text{units}$ to $40\,\text{units}$.

  • Two Simultaneous Events Example (Apple Juice and Oranges):

  • Event 1: The price of apple juice falls.

  • Event 2: The price of oranges falls due to a large harvest.

  • Combined Impact: A large orange harvest increases orange supply, driving equilibrium price down, while the magnitude of quantity changes depends on the relative shift strengths.

  • Supply Shock Example (Egg Prices in Early 2025):

  • Observed Event: Egg prices experienced a substantial surge, rising to more than $\$6$ per thousand/unit in early 2025.

  • Primary Cause: A widespread bird flu outbreak reduced the supply curve of eggs.

  • Driver Classification: The price increase was driven by supply-side contraction rather than demand-side shifts.

  • Demand Shift Example (Gold Prices):

  • Observed Event: Substantial increase in gold prices over a one-year period, followed by subsequent sharp decreases in 2025.

  • Main Drivers: Demand-driven shift, primarily motivated by large-scale gold purchases by central banks.

  • Four Primary Determinants of Demand Shifts:

    1. Consumer income.

    2. Prices of related goods (substitutes and complements).

    3. Expectations about future prices.

    4. Number of buyers in the market.

Fundamentals of Elasticity

• Broad Definition:

  • Elasticity measures the degree of responsiveness or flexibility of one variable to changes in another variable.

  • Applied across disciplines, including physics, dermatology, corporate finance, and economics.

  • Heavily emphasized in corporate earnings calls post-COVID to gauge consumer spending reactions to price changes.

• Industry Applications:

  • U.S. Airline Industry: Evaluates travel demand elasticity to establish ticket pricing strategies without causing steep declines in passenger volume.

  • Luxury Goods Industry (Gucci): Adjusts product pricing strategies based on luxury item demand elasticity.

Price Elasticity of Demand and Calculation Methods

• Definition:

  • Price Elasticity of Demand ($\epsilon_d$) measures the responsiveness of quantity demanded ($Q_d$) to a change in the product's price ($P$).

• Mathematical Formula:

  • $\epsilon_d = \frac{\%\,\Delta Q_d}{\%\,\Delta P}$

• Sign of Price Elasticity of Demand:

  • According to the Law of Demand, price ($P$) and quantity demanded ($Q_d$) move in opposite directions.

  • Because numerator and denominator always have opposite signs, price elasticity of demand is mathematically negative.

• The Midpoint Method:

  • Used to calculate percentage changes cleanly, ensuring that elasticity values remain identical regardless of the direction of movement between two points.

  • Formula:

  • $\text{Percentage Change} = \frac{\text{End Value} - \text{Start Value}}{\text{Midpoint}} \times 100\%$

  • $\text{Midpoint} = \frac{\text{Start Value} + \text{End Value}}{2}$

• Calculation Step-by-Step Example 1 (Point A to Point B):

  • Given Data:

  • Point A: $Q_1 = 12$, $P_1 = \$200$

  • Point B: $Q_2 = 8$, $P_2 = \$250$

  • Numerator Calculation ($\%\,\Delta Q_d$):

  • $\text{Midpoint } Q = \frac{12 + 8}{2} = 10$

  • $\%\,\Delta Q_d = \frac{8 - 12}{10} = \frac{-4}{10} = -0.40 \quad (-40\%$

  • Denominator Calculation ($\%\,\Delta P$):

  • $\text{Midpoint } P = \frac{200 + 250}{2} = 225$

  • $\%\,\Delta P = \frac{250 - 200}{225} = \frac{50}{225} \approx 0.2222 \quad (22.22\%$

  • Elasticity Calculation:

  • $\epsilon_d = \frac{-0.40}{\frac{50}{225}} = -1.8$

• Calculation Step-by-Step Example 2 (Exam Practice Problem):

  • Given Data: Price elasticity of demand = $-0.75$. A scenario asks which event corresponds to a $10\%$ decrease in quantity demanded.

  • Setup using formula:

  • $\epsilon_d = \frac{\%\,\Delta Q_d}{\%\,\Delta P}$

  • $-0.75 = \frac{-10\%}{\%\,\Delta P}$

  • Rearranging to solve for unknown denominator:

  • $\%\,\Delta P = \frac{-10\%}{-0.75} = +13.33\%$

  • Result: A $13.33\%$ increase in price leads to a $10\%$ decrease in quantity demanded.

Categorization and Shapes of Demand Curves

• Elasticity Categories (Based on Magnitude/Absolute Value):

  • Inelastic Demand ($|\epsilon_d| < 1$):

  • Percentage change in price is greater than percentage change in quantity demanded.

  • Extreme Case — Perfectly Inelastic Demand ($\epsilon_d = 0$):

    • Numerator is zero; quantity demanded does not respond to price changes at all.

    • Graph Shape: A vertical line at a fixed quantity ($Q_1$).

    • Example: Life-saving medications or mandatory daily habits (e.g., a smoker who buys exactly $1$ pack of cigarettes per day regardless of price).

  • Unit Elastic Demand ($|\epsilon_d| = 1$):

  • Percentage change in price exactly equals percentage change in quantity demanded.

  • Elastic Demand ($|\epsilon_d| > 1$):

  • Percentage change in quantity demanded exceeds percentage change in price.

  • Extreme Case — Perfectly Elastic Demand ($\epsilon_d = -\infty$):

    • Graph Shape: A horizontal line at price $P_1$

    • Explanation: At price $P_1$, buyers will purchase any quantity supplied. At any price above $P_1$, quantity demanded falls to zero because perfect substitutes exist.

    • Example: An individual farmer selling standardized agricultural commodities in a competitive market.

• Linear Demand Curves vs. Elasticity:

  • Statement: "If demand is unit elastic, the demand curve must be a straight line." $\rightarrow$ False.

  • While a linear demand curve has a constant slope, elasticity varies along the curve:

  • High-Price / Low-Quantity Region (e.g., $P$ changes from$\$8$ to $\$9$, $Q$ changes from $2$ to $1$): Elasticity is $-5.7$ (Elastic).

  • Mid-Region: Elasticity equals $-1.0$ (Unit Elastic).

  • Low-Price / High-Quantity Region (e.g., $P$ changes from $\$2$ to $\$1$): Elasticity is $-0.18$ (Inelastic).

• Demand Curve Slope Rule:

  • For a given point $(P_1, Q_1)$, a flatter demand curve indicates a higher price elasticity of demand.

Determinants of Price Elasticity of Demand

• Necessities vs. Luxuries:

  • Water vs. Cell Phone: Cell phones have higher price elasticity than water because water is essential for survival.

  • Rule: Luxuries have higher price elasticity; necessities have lower price elasticity.

• Availability of Close Substitutes:

  • Chili Peppers vs. Soy Sauce: Chili peppers have higher price elasticity because more close substitutes exist.

  • Rule: Goods with more substitutes have higher price elasticity.

• Market Definition (Broad vs. Narrow):

  • All Coffee vs. Starbucks Frappuccinos: Starbucks Frappuccinos have higher price elasticity because a narrowly defined market has many close substitutes.

  • Rule: Narrowly defined markets have higher price elasticity than broadly defined markets.

• Time Horizon:

  • Gasoline in the Short Run vs. Long Run: Gasoline in the long run has higher price elasticity because consumers have time to adapt behavior (e.g., purchasing fuel-efficient vehicles).

  • Rule: Elasticity is higher in longer time horizons.

Price Elasticity and Total Revenue

• Total Revenue Formula:

  • $\text{Total Revenue } (TR) = P \times Q$

  • Example: Selling $400\,\text{units}$ at $\$4$ per unit yields $TR = \$1{,}600$

• Opposing Effects of a Price Increase:

  1. Price Effect: Higher price increases revenue collected per unit sold.

  2. Quantity Effect: Higher price reduces total units sold ($Q$ drops).

• Revenue Relationships Based on Elasticity:

  • Elastic Demand ($|\epsilon_d| > 1$):

  • Quantity effect dominates price effect.

  • Raising price decreases Total Revenue.

  • Lowering price increases Total Revenue.

  • Price and Total Revenue move in opposite directions.

  • Inelastic Demand ($|\epsilon_d| < 1$):

  • Price effect dominates quantity effect.

  • Raising price increases Total Revenue.

  • Lowering price decreases Total Revenue.

  • Price and Total Revenue move in the same direction.

• Application Example (Luxury Cruise Fare War):

  • Event: Price of a luxury cruise falls by $20\%$

  • Analysis: Luxury cruises have elastic demand ($|\epsilon_d| > 1$). For elastic goods, price cuts lead to revenue gains.

  • Outcome: The cruise industry's Total Revenue increases.

Income Elasticity of Demand

• Definition:

  • Income Elasticity of Demand ($\epsilon_I$) measures how quantity demanded responds to changes in consumer income.

• Mathematical Formula:

  • $\epsilon_I = \frac{\%\,\Delta Q_d}{\%\,\Delta \text{Income}}$

• Good Classification based on Sign:

  • Normal Good ($\epsilon_I > 0$):

  • Income and quantity demanded move in the same direction.

  • Example: Jim's sporting event tickets yield an income elasticity of $+2.3$, indicating it is a normal good.

  • Inferior Good ($\epsilon_I < 0$):

  • Income and quantity demanded move in opposite directions.

Classroom Discussion and Student Q&A

• Denominator of Elasticity Formula:

  • Question: What term goes in the denominator of the price elasticity of demand formula?

  • Response: Percentage change in price (Option C).