Lecture 5: Elasticities and Child Labour Application

Course Overview and Schedule

  • Course Identity: Introductory Microeconomics (Economics 10004), Semester 1, 2026, Department of Economics, University of Melbourne.

  • Lecturer: A/Prof Laura Panza.

  • Topics and Important Dates (Weeks 3-6):

    • Week 3 (Starts 16 Mar): Elasticities (GKBM Chapter 5) and Welfare in Perfectly Competitive Markets (GKBM Chapter 7).

    • Week 4 (Starts 23 Mar): Government Intervention (GKBM Chapters 6 and 8).

    • Week 5 (Starts 30 Mar): International Trade (GKBM Chapter 9) and Market Failures: Externalities (GKBM Chapter 10).

    • Non-teaching Period: 6–12 April.

    • Week 6 (Starts 13 Apr): Midterm test on 13 April (Time TBD); No class on 14 April; Common Resources and Public Goods (GKBM Chapter 11).

Introduction to Elasticity

  • Definition: Elasticity measures the responsiveness of quantity demanded (QDQD) or quantity supplied (QSQS) to its determinants.

  • Purpose and Analysis:

    • It helps analyze how buyers and sellers respond to specific changes in market conditions.

    • It enables precise statements regarding the magnitude of changes in market prices and quantities, rather than just the direction.

  • Measurement Properties:

    • It is a units-free measure, which allows for comparisons across different products with varying attributes.

    • Interpretation: It can be viewed as the percentage change in quantity demanded in response to a 1%1\% change in price.

Price Elasticity of Demand (ϵD\epsilon_D)

  • Conceptual Definition: Measures the responsiveness of quantity demanded to a change in price. It is expressed as the percentage change in quantity demanded per percent change in price.

  • Basic Formula:     ϵD=∣ΔQD/QDΔP/P∣\epsilon_D = \left| \frac{\Delta QD/QD}{\Delta P/P} \right|

    • ΔQD\Delta QD: Change in quantity demanded (movement along the demand curve).

    • ΔQD/QD\Delta QD/QD: Percentage change in quantity demanded.

    • ΔP\Delta P: Change in price.

    • ΔP/P\Delta P/P: Percentage change in price.

  • Arc Elasticity:

    • Calculated between two distinct points on a curve.

    • Example:

      • Point A: P1=15P_1 = 15, QD1=100QD_1 = 100

      • Point B: P2=25P_2 = 25, QD2=50QD_2 = 50

  • Point Elasticity (Using Calculus):

    • Measures elasticity at a specific point rather than an interval.

    • Formula: ϵD=∣dQDdP×PQD∣\epsilon_D = \left| \frac{dQD}{dP} \times \frac{P}{QD} \right|

    • By convention, the elasticity of demand is reported as a positive number (absolute value).

  • Mathematical Example:

    • Demand function: QD=120−20PQD = 120 - 20P

    • Calculation at QD=20QD = 20:

      • Find PP: 20=120−20P→20P=100→P=520 = 120 - 20P \rightarrow 20P = 100 \rightarrow P = 5

      • Derive: dQDdP=−20\frac{dQD}{dP} = -20

      • Elasticity: ∣−20×520∣=5\left| -20 \times \frac{5}{20} \right| = 5

    • Calculation at QD=100QD = 100:

      • Find PP: 100=120−20P→20P=20→P=1100 = 120 - 20P \rightarrow 20P = 20 \rightarrow P = 1

      • Elasticity: ∣−20×1100∣=15=0.2\left| -20 \times \frac{1}{100} \right| = \frac{1}{5} = 0.2

Range of Price Elasticities of Demand

  • Perfectly Inelastic: ∣ϵD∣=0|\epsilon_D| = 0. The curve is vertical; quantity does not change regardless of price.

  • Inelastic: 0 < |\epsilon_D| < 1. The quantity changes by a smaller percentage than the price; the curve is relatively steep.

  • Unit Elastic: ∣ϵD∣=1|\epsilon_D| = 1. The quantity changes by the exact same percentage as the price.

  • Elastic: 1 < |\epsilon_D| < \infty. The quantity changes by a larger percentage than the price; the curve is relatively flat.

  • Perfectly Elastic: ∣ϵD∣=∞|\epsilon_D| = \infty. The curve is horizontal; at a specific price, buyers will purchase any quantity, but at any other price, quantity demanded drops to zero.

Determinants of Price Elasticity of Demand

  • Degree of Necessity: The more a good is considered a necessity, the less elastic its quantity demanded becomes.

  • Availability of Substitutes: The more substitutes that are available for a good, the more elastic its quantity demanded becomes.

  • Time Horizon: The longer the time horizon allowed for adjustment, the more elastic the quantity demanded becomes.

Elasticity and Total Revenue (TR)

  • Total Revenue Formula: TR=P×QDTR = P \times QD

  • Relationship Analysis: When price changes, quantity demanded moves in the opposite direction. The effect on total revenue depends on the relative size of the percentage change in price compared to the percentage change in quantity (own-price elasticity).

  • The Inelastic Case (|\epsilon_D| < 1):

    • 1\% \Uparrow P \Rightarrow < 1\% \Downarrow QD

    • Result: TR⇑TR \Uparrow.

  • The Elastic Case (|\epsilon_D| > 1):

    • 1\% \Uparrow P \Rightarrow > 1\% \Downarrow QD

    • Result: TR⇓TR \Downarrow.

  • The Unit Elastic Case (∣ϵD∣=1|\epsilon_D| = 1):

    • 1%⇑P⇒1%⇓QD1\% \Uparrow P \Rightarrow 1\% \Downarrow QD

    • Result: TRTR remains unchanged.

  • Application Example: Funding a highway extension via toll increments.

    • If current ϵD=0.8\epsilon_D = 0.8 (inelastic), a toll increase will successfully increase total revenue.

    • If ϵD=1.8\epsilon_D = 1.8 (elastic), a toll increase will lead to a decrease in total revenue.

Price Elasticity of Supply (ϵS\epsilon_S)

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

  • Formula (Point-Price Elasticity):     ϵS=dQS/QSdP/P=dQSdP×PQS\epsilon_S = \frac{dQS/QS}{dP/P} = \frac{dQS}{dP} \times \frac{P}{QS}

  • Range of Supply Elasticities:

    • Perfectly Inelastic: ϵS=0\epsilon_S = 0 (vertical line).

    • Inelastic: 0 < \epsilon_S < 1

    • Unit Elastic: ϵS=1\epsilon_S = 1

    • Elastic: 1 < \epsilon_S < \infty

    • Perfectly Elastic: ϵS=∞\epsilon_S = \infty (horizontal line).

Application Study: Child Labour

  • Global Statistics (UNICEF 2020):

    • Total children in child labour: Approximately 160 million (1 in 20).

    • Annual increase: Increased by 8.4 million in 2020.

    • Sector distribution: 70%70\% work in agriculture.

    • Regional/Economic distribution: Highest share is in Sub-Saharan Africa; more than half are located in middle-income countries.

  • Policy Analysis (JB Case Study 2.5):

    • Assumptions: Demand for child labour is relatively price-elastic (LDLD is flat); Supply of child labour is relatively price-inelastic (LSLS is steep).

    • Demand-side Policy (e.g., Ban on products using child labour):

      • This causes a decrease in LDLD (curve shifts left from LD1LD1 to LD2LD2).

      • The equilibrium shifts from point A to point B.

      • Outcome: The wage decreases significantly due to excess supply, but there is only a small reduction in the quantity of child labour used because supply is inelastic.

    • Supply-side Policy (e.g., Payments for children to remain in school):

      • This causes a decrease in LSLS (curve shifts left from LS1LS1 to LS2LS2).

      • The equilibrium shifts from point A to point B.

      • Outcome: The wage increases due to excess demand, and because demand is elastic, this leads to a large reduction in the quantity of child labour used.

  • Conclusion: Supply-side policies are more effective than demand-side policies when demand is wage-elastic and supply is wage-inelastic, resulting in a larger reduction in the usage of child labour.

Questions & Discussion

  • Quiz Links (Flux.qa):

    • Mon 10am: https://flux.qa/GLFHHZ

    • Mon 1pm: https://flux.qa/D5JWNH

    • Mon 3pm: https://flux.qa/LU5BGM

    • Tue 11am: https://flux.qa/NV3XN4

    • Tue 2pm: https://flux.qa/HATHX2