Comprehensive Study Notes on Price Elasticity of Supply, Market Applications, and Demand Elasticities

Price Elasticity of Supply Fundamentals

• Definition of Price Elasticity of Supply:

  • Also referred to as supply elasticity or elasticity of supply.

  • Measures the sensitivity or responsiveness of sellers to changes in price.

  • Quantifies price sensitivity on the supply side of the market.

• Mathematical Calculation (Midpoint Formula):

  • Uses the exact same mathematical structure as the price elasticity of demand, substituting quantity supplied for quantity demanded.

  • Formula:         $E_s = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_2 + P_1}{Q_2 + Q_1}$

  • $Q_1$ and $Q_2$ represent the initial and secondary quantities supplied.

  • $P_1$ and $P_2$ represent the initial and secondary prices.

• Sign of Supply Elasticity:

  • The sign of the price elasticity of supply is always positive ($E_s > 0$).

  • This positive relationship reflects the Law of Supply: price and quantity supplied move in the same direction.

• Relationship to the Slope of the Supply Curve:

  • The term $\frac{Q_2 - Q_1}{P_2 - P_1}$ in the elasticity equation represents the inverse of the slope ($\frac{1}{\text{slope}}$).

  • Steep Supply Curve: Represents a less elastic or highly inelastic supply curve. Sellers are less sensitive to price changes.

  • Flat Supply Curve: Represents a more elastic supply curve. Sellers are highly sensitive to price changes.

Classification of Supply Curves

• 1. Perfectly Inelastic Supply:

  • Graphical Representation: A perfectly vertical line.

  • Numerical Value: $E_s = 0$

  • Behavior: If price increases by $10\%$, the percentage change in quantity supplied is exactly $0\%$ ($\frac{0\%}{10\%} = 0$).

  • Real-World Example: The supply of original Pablo Picasso paintings. Because Picasso is deceased, the physical stock of his paintings is permanently fixed. Price fluctuations do not change the existing quantity of paintings available.

• 2. Inelastic Supply:

  • Graphical Representation: A relatively steep line.

  • Numerical Value: $0 < E_s < 1$

  • Behavior: If the price rises by $10\%$, the quantity supplied increases by less than $10\%$, making the elasticity ratio less than $1$

• 3. Unit Elastic Supply:

  • Graphical Representation: A linear supply curve passing through the origin.

  • Numerical Value: $E_s = 1$

  • Behavior: The percentage change in quantity supplied is equal in magnitude to the percentage change in price ($\frac{\text{\% change in } Q_s}{\text{\% change in } P} = 1$).

• 4. Elastic Supply:

  • Graphical Representation: A relatively flat line.

  • Numerical Value: $E_s > 1$

  • Behavior: If the price increases by $10\%$, the quantity supplied increases by more than $10\%$, yielding an elasticity ratio greater than $1$

• 5. Perfectly Elastic Supply:

  • Graphical Representation: A perfectly horizontal line.

  • Numerical Value: $E_s = \infty$

  • Behavior: At a fixed price, the quantity supplied can change by an infinite percentage ($\frac{\text{any \%}}{0\%} = \infty$).

  • Application: Represents the long-run market supply curve in competitive markets under specific baseline assumptions.

Determinants of Supply Elasticity

• Ease of Seller Adjustment:

  • Supply elasticity depends on how easily sellers can alter production levels or exit/enter a market in response to price changes.

  • If sellers can easily alter production plans or leave a market, supply is elastic. If sellers are constrained, supply is inelastic.

• Industry Comparisons:

  • Housing / Real Estate Market: Highly inelastic supply. A home builder currently constructing houses cannot easily destroy or cease mid-construction projects due to a price drop; projects must be completed, rendering current supply insensitive to immediate price changes.

  • Automotive / Food Manufacturing: Highly elastic supply. Car manufacturers and food producers can rapidly alter manufacturing schedules and reallocate resources following industry price movements.

• Time Horizon:

  • Supply is significantly more elastic in the long run than in the short run.

  • Given more time, firms can adjust plant size, build new facilities, or exit industries entirely.

Comparative Analysis and Real-World Market Applications

• Comparative Market Setup: Beachfront Property vs. New Cars:

  • Beachfront Property Market: Inelastic supply (steep supply curve) because supply is strictly limited and hard to vary.

  • New Car Market: Elastic supply (flat supply curve) because manufacturing output is easily scalable.

  • Exogenous Shock: Population growth causes the demand for both goods to double ($Q_d$ doubles at every price level, shifting the demand curve to the right).

  • Market Outcomes:

    • Equilibrium Quantity ($Q$): Changes the most in the market for new cars due to elastic supply.

    • Equilibrium Price ($P$): Changes the most in the market for beachfront properties due to inelastic supply.

• Case Study: Housing Boom in Fargo, North Dakota:

  • Background: Hydraulic fracturing (fracking) technology led to a massive natural gas extraction boom in North Dakota.

  • Demand Shock: Thousands of workers and engineers earning salaries exceeding $\$100,000\,$ per year moved to Fargo, North Dakota, creating a massive rightward shift in housing demand.

  • Supply Dynamics: Short-run housing supply was extremely inelastic (steep curve) due to the multi-month time required to build housing units, compounded by restrictive local government urban policies.

  • Outcome: Housing prices skyrocketed exponentially while equilibrium quantity built increased only minimally in the short term. Workers earning over $\$100,000\,$ per year were forced to sleep in Walmart parking lots while waiting for housing construction to complete.

Case Study: Agriculture and Technological Advances

• Market Dynamics of Corn Production:

  • Corn is an agricultural commodity with a steep (inelastic) demand curve because it is a staple food item with few direct immediate substitutes at low price points.

  • Initial Market Equilibrium:

    • Equilibrium Price ($P_1$): $\$3\,$ per bushel.

    • Equilibrium Quantity ($Q_1$): $100\,$ million bushels annually in the United States.

    • Initial Farming Revenue:             \text{Revenue}_1 = P_1 \times Q_1 = \3 \times 100\text{ million} = \$300\text{ million}$

• Technological Shock (Monsanto Genetically Modified Seed):

  • Biotechnology firm Monsanto developed a genetically modified (GMO) crop engineered to resist plant pathogens and produce higher yields.

  • Adopting GMO seeds lowered costs for fertilizers and pesticides, reducing production expenditures.

  • Technological advancement acts as a positive supply shock, shifting the supply curve to the right ($S_1$ to $S_2$).

• Post-Innovation Market Equilibrium:

  • Due to inelastic demand, the rightward supply shift causes price to drop significantly to $P_2 = \$2\,$ per bushel.

  • Equilibrium quantity increases by only $10\,$ million bushels to $Q_2 = 110\,$ million bushels.

  • Post-Innovation Farming Revenue:         \text{Revenue}_2 = P_2 \times Q_2 = \2 \times 110\text{ million} = \$220\text{ million}$

• Economic Analysis ("Good News or Bad News for Farmers"):

  • Good News: Lower production costs and reduced chemical usage per acre.

  • Bad News: Aggregate farming revenue fell from $\$300\,$ million to $\$220\,$ million, resulting in a net revenue loss of $\$80\,$ million for the farming sector.

  • Takeaway: Technological advancements in markets with inelastic demand lead to a disproportionate drop in price relative to quantity expansion, lowering total producer revenue.

Case Study: Public Policy and Illegal Drug Markets

• Characteristics of Illegal Drug Demand:

  • The demand for illegal drugs (e.g., heroin epidemics in the 1980s, methamphetamine in the 1990s, opioid epidemics) is extremely inelastic (steep demand curve).

  • Addiction causes consumers to treat drugs as a necessity/medicine, leading users to commit severe crimes or theft to acquire funds for purchase regardless of price.

• Policy 1: Drug Interdiction (Supply-Side Enforcement):

  • Policy Action: Law enforcement targets drug dealers, cartel leaders (e.g., US operations in Colombia), and seizures of drug supplies.

  • Market Shift: Reduces drug availability, shifting the supply curve leftward ($S_1$ to $S_2$).

  • Market Impact:

    • Due to inelastic demand, equilibrium quantity consumed drops very little ($Q_1$ to $Q_2$).

    • Equilibrium price rises dramatically ($P_1$ to $P_2$).

  • Unintended Consequences:

    • Total revenue earned by surviving drug dealers increases significantly ($\text{Revenue} = P \times Q$ increases).

    • Higher drug prices make drug trafficking far more lucrative, incentivizing new drug dealers to enter the market despite law enforcement risks.

• Policy 2: Drug Education (Demand-Side Intervention):

  • Policy Action: Educational initiatives targeting youth regarding health risks, death, and social impacts (e.g., the "Montana Meth Project" implemented in Montana during the 1990s methamphetamine epidemic).

  • Market Shift: Reduces consumer desire for drugs, shifting the demand curve leftward ($D_1$ to $D_2$).

  • Market Impact:

    • Both equilibrium price and equilibrium quantity decrease substantially.

  • Economic Advantage: Lower drug prices drastically reduce overall drug market revenues, removing financial incentives for prospective drug dealers and systematically shrinking the market.

Income Elasticity of Demand

• Definition:

  • Measures the percentage change in quantity demanded resulting from a $1\%$ change in consumer income.

• Mathematical Formula (Midpoint Method):

  • Formula:         $E_I = \frac{Q_2 - Q_1}{I_2 - I_1} \times \frac{I_2 + I_1}{Q_2 + Q_1}$

  • $I_1$ and $I_2$ represent initial and secondary income levels.

  • $Q_1$ and $Q_2$ represent initial and secondary quantities demanded.

• Classification of Goods by Income Elasticity:

  • Inferior Goods ($E_I < 0$):

    • Income and quantity demanded move in opposite directions.

    • An increase in income causes a decrease in quantity demanded (e.g., lower-grade fast food hamburgers relative to steak).

  • Normal Goods ($E_I > 0$):

    • Income and quantity demanded move in the same direction.

    • An increase in income causes an increase in quantity demanded.

  • Superior / Luxury Goods ($E_I > 1$):

    • A subcategory of normal goods where quantity demanded increases proportionally more than the increase in income.

Cross-Price Elasticity of Demand

• Definition:

  • Measures the percentage change in quantity demanded of Good 1 ($Q_1$) relative to a $1\%$ change in the price of Good 2 ($P_2$).

• Mathematical Formula (Midpoint Method):

  • Formula:         $E_{1,2} = \frac{Q_{1,2} - Q_{1,1}}{P_{2,2} - P_{2,1}} \times \frac{P_{2,2} + P_{2,1}}{Q_{1,2} + Q_{1,1}}$

  • $Q_{1,1}$ and $Q_{1,2}$ represent quantities demanded for Good 1.

  • $P_{2,1}$ and $P_{2,2}$ represent prices for Good 2.

• Classification of Goods by Cross-Price Elasticity:

  • Complements ($E_{1,2} < 0$):

    • The price of Good 2 and quantity demanded of Good 1 move in opposite directions.

    • Example: An increase in the price of bacon leads to a decrease in the demand for eggs.

  • Substitutes ($E_{1,2} > 0$):

    • The price of Good 2 and quantity demanded of Good 1 move in the same direction.

    • Example: An increase in the price of Pepsi leads consumers to purchase less Pepsi and more Coca-Cola.

  • Unrelated Goods ($E_{1,2} = 0$):

    • Price changes in Good 2 have zero impact on the quantity demanded of Good 1.

Questions and Discussion

• Clarification on Elasticity Definitions:

  • Prompt/Question: A student asked for clarification regarding whether elasticity measures a percentage change in demand or a percentage change in price.

  • Response: Elasticity specifically measures the percentage change in quantity demanded (or quantity supplied) resulting from a $1\%$ change in price (or income). The terminology must strictly distinguish between percentage changes in quantity demanded versus changes in price.