Elasticity Fundamentals: Demand, Supply, and Applications

Elasticity: Demand and Supply

  • Overview

    • Elasticity measures how much quantity responds to price changes.
    • For demand, the elasticity of demand is typically negative because price and quantity move in opposite directions.
    • Magnitude is often interpreted using the absolute value: |\varepsilon_D| measures responsiveness; the sign is kept or discarded depending on convention.
    • For supply, the elasticity is typically positive (quantity responds to price in the same direction).

  • Key definitions and formulas

    • Elasticity of demand:
    • \varepsilon_D = \frac{\%\Delta Q}{\%\Delta P} = \frac{\Delta Q / Q}{\Delta P / P}
    • In practice, the value is negative due to the inverse relationship between price and quantity demanded.
    • Elasticity of supply:
    • \varepsilon_S = \frac{\%\Delta Q}{\%\Delta P} = \frac{\Delta Q / Q}{\Delta P / P}
    • The value is typically positive since price and quantity supplied move together.
    • For small changes, the percent changes approximate linearly:
    • \Delta QD / Q \approx \varepsilonD \; (\Delta P / P)
    • \Delta QS / Q \approx \varepsilonS \; (\Delta P / P)
    • Interpreting signs and magnitudes
    • If the calculated \varepsilon_D is negative, take the absolute value to discuss magnitude of responsiveness.
    • If price and quantity happen to move in the same direction in a calculation, you may be looking at a scenario where the model convention or a specific context implies a positive interpretation; typically for demand, the direction is opposite.

  • Time horizon and elasticity of supply

    • Time horizon is a major determinant of elasticity of supply.
    • Short run (limited ability to adjust capacity):
    • Production can be increased only modestly (e.g., more hours, more workers, existing facilities).
    • Supply is less elastic in the short run.
    • Long run (capacity can be expanded):
    • Firms can invest in new wells, new factories, or new machinery.
    • Supply is more elastic in the long run.
    • Practical questions used to assess elasticity:
    • How costly is it to expand per unit production?
    • Does increasing capacity require new inputs or technology?
    • How long does setup or construction take (e.g., drilling a new well vs expanding a factory)?
    • What are the implications for input markets (e.g., lumber, oil inputs, etc.)?

  • Cost structure and production flexibility

    • Per-unit costs can rise when pushing capacity beyond existing limits (deeper drilling, specialized processes).
    • In some industries, manufacturing processes are easier to expand (e.g., adding shifts or hours) than to scale up capacity in natural-resource extraction.
    • In the short run, capacity limits constrain output growth and dampen price responsiveness.
    • In the long run, sustainable price increases may encourage expanding capacity (e.g., drilling new wells, building new cars or factories).

  • Industry examples and intuitive explanations

    • Input markets (e.g., lumber vs housing):
    • Different uses of inputs lead to different elasticities in the market for the input.
    • When demand for a broad class of building inputs increases (e.g., lumber), the per-unit cost and availability shape how quickly supply can respond.
    • Policy implications and market structure:
    • Open-access vs. closed-access policies create different elasticities of supply.
    • Cities with restrictive construction policies (e.g., New York, San Francisco) have more inelastic supply in the short run due to zoning and permitting frictions.
    • Open-access regions (e.g., Atlanta) tend to have more elastic supply as building can respond more readily to price signals.
    • Geography and elasticity:
    • Elasticity of supply can vary by location due to policy constraints and geographic factors.
    • A city’s policy environment can amplify or dampen price changes in response to demand shocks.

  • Gun buyback programs as a policy example

    • Gun buyback programs are typically administered by police departments and aim to pull guns off the street.
    • In discussions, a “perfectly elastic” or horizontal supply curve is sometimes described in relation to these programs: the program is willing to purchase any quantity at a fixed price, which affects the observed market dynamics.
    • Implication: The policy intention is to reduce the number of guns, but the pricing mechanism and quantity of guns turned in depend on the interaction of the fixed buyback price with gun availability and safety considerations.
    • Analytical takeaway: The elasticity of supply in this context reflects how responsive the quantity of guns offered for buyback is to the price offered by the program.

  • Elasticity and price prediction: two standard formulas

    • If a change in price is caused by a shift in demand, you can infer the size of the demand shift from the price change, using:
    • \Delta Q / Q \approx \varepsilon_D \; (\Delta P / P)
    • If a change in price is caused by a shift in supply, you can infer the size of the supply shift from the price change, using:
    • \Delta Q / Q \approx \varepsilon_S \; (\Delta P / P)
    • In practice, you also account for the sign conventions: a rightward shift of the supply curve (more supply at each price) tends to lower price, all else equal.

  • Real-world data and qualitative observations

    • Housing prices over time (1950–2020) show geographic variation in elasticity due to policy and geographic factors.
    • Closed-access cities with restraining policies exert less responsive supply to price changes, leading to larger price movements for a given demand shock.
    • Open-access regions exhibit more elastic supply, dampening price changes in response to demand fluctuations.

  • War on drugs example and broader implications

    • A policy that reduces drug supply (restrictive enforcement) can raise prices, potentially reducing consumption but may not strongly deter sellers if demand is inelastic.
    • This highlights how elasticity interacts with policy goals: price signals depend on the relative elasticities of demand and supply.

  • A quick practice exercise (conceptual)

    • People often categorize elasticity by scenario: short run is typically least elastic; long run is most elastic.
    • Example result from a quick in-class exercise: the least elastic option tends to be the short-run scenario; the most elastic tends to be the long-run scenario.

  • Supporting logistics and study help

    • Instructor and TA office hours (examples from the transcript):
    • TAs: 2:00–7:00 PM on today and Wednesday.
    • Instructor: 1:30–2:30 PM today and Wednesday.
    • Additional locations: Arts and Sciences building (2:00–5:00 PM) and Middlebush (5:00–7:00 PM);
      check the syllabus for exact locations.
    • Encouragement to seek help and use available resources to prepare for the exam.

  • Quick recap of key takeaways

    • Demand elasticity is negative; use absolute value for magnitude interpretation.
    • Supply elasticity is typically positive; time horizon increases elasticity.
    • Short run vs long run differences are central to production decisions and price responsiveness.
    • Policy interventions (e.g., gun buybacks, drug enforcement) interact with elasticities to determine outcomes.
    • Simple linear approximations:
    • \Delta QD / Q \approx \varepsilonD \; (\Delta P / P)
    • \Delta QS / Q \approx \varepsilonS \; (\Delta P / P)
    • For shifts, use the sign and magnitude of elasticities to reason about direction and intensity of price changes.