Elasticity

Outcome 2

• Remember the assumptions of the model.

• Remember the definitions of demand and supply and their laws.

• Solve the equilibrium given the demand and supply.

• Analyze how equilibrium changes with shifts in demand and supply.

• Remember examples of violations of the law of demand and supply.

• Recall the double auction experiment.

• Understand index inclusion/exclusion.

Elasticity

Chapter 4

• Prepare for welfare analysis.

Outline

• Why we need to define elasticity.

• Calculate elasticity.

• Pitfalls of elasticity.

• The size of elasticity.

• Factors that affect elasticity.

• Redefine goods with elasticity.

• Review violation of laws with elasticity.

• Outcomes required.

Why the Size of the Slope of Supply Is Important

• COVID-19 pandemic examples illustrating slope differences in supply indicating price changes:

  • Demand for specialized goods:

    • Ventilators and N95 masks saw skyrocketing demand, resulting in a sharp price increase due to limited production capabilities.

  • Demand for general goods:

    • Items like reusable cloth masks, hand sanitizers, and toilet paper had increased demand but were easier to produce, demonstrating higher supply slope.

The Problem of Using the Slope

• Slope of a demand/supply curve is influenced by units (e.g., dollars vs. cents, gallons vs. liters).

We Need A Unit-free Solution

• Elasticity is unit-free, measuring responsiveness in percentages to allow comparisons across diverse goods and contexts.

• It provides a way to compare the price sensitivity of demand for different goods.

Elasticity of Demand

• Definition: Price elasticity of demand is the percentage change in the quantity demanded divided by the percentage change in the price of a good.

  • Formula:
    ext{Price Elasticity of Demand} = rac{ ext{percentage change in quantity demanded}}{ ext{percentage change in price}} = rac{ ext{∆Q/Q}}{ ext{∆P/P}}

Example: Figure 1 - Comparing Different Sizes of the Price Elasticity of Demand

• Price of Oil (in dollars per barrel): 10, 22, 30.

• Quantity demanded shows high sensitivity to price changes:

  • A 10 percent price increase decreases quantity demanded by 20 percent.

Calculating the Price Elasticity of Demand from A to B

• Price increases from $20 to $22 while quantity decreases from 60 million barrels to 48 million barrels:

  • Percentage change in quantity:
    rac{48 - 60}{60} imes 100 = -20 ext{ percent}

  • Percentage change in price:
    rac{22 - 20}{20} imes 100 = 10 ext{ percent}

  • Price Elasticity of Demand: ext{PED} = igg| rac{-20 ext{ ext{ percent}}}{10 ext{ ext{ percent}}} igg| = 2

    • Implication: A 1% increase in price results in a 2% decrease in quantity demanded.

Calculating the Price Elasticity of Demand from B to A

• Price decreases from $22 to $20, quantity increases from 48 million barrels to 60 million barrels:

  • Percentage change in quantity:
    rac{60 - 48}{48} imes 100 = 25 ext{ percent}

  • Percentage change in price:
    rac{20 - 22}{22} imes 100 = -9 ext{ percent}

  • Price Elasticity of Demand: ext{PED} = igg| rac{-25 ext{ ext{ percent}}}{-9 ext{ ext{ percent}}} igg| = 2.8

    • Noteworthy: The direction of price changes can affect measured elasticity due to base value dependency.

Two Ways to Mute the Effect of Direction

1. Use the midpoint as the base for percentage change calculations (preferred).

2. Use derivatives to calculate percentage change (not preferred).

Calculating the Elasticity with a Midpoint Formula

• General formula:
  ext{Price elasticity of demand} = rac{ ext{Change in quantity}}{ ext{average of old and new quantities}} igg/ rac{ ext{Change in price}}{ ext{average of old and new prices}}

Example Calculation Using Midpoint Formula

• From A to B:
  ext{PED} = rac{48-60}{(60+48)/2} igg/ rac{22-20}{(20+22)/2} = -2.33

• From B to A:
  ext{PED} = rac{60-48}{(60+48)/2} igg/ rac{20-22}{(20+22)/2} = -2.33

Figure 2 - Comparing Different Sizes of the Price Elasticity of Demand

• Illustrates less sensitivity compared to Figure 1:

  • A 10% price increase from $20 leads to only a 5% drop in quantity demanded (to 57 million barrels).

The Size of the Elasticity: High vs. Low

• Figure 1 shows higher elasticity (2) compared to Figure 2 (1/2).

• Both have the same base point and price change from $20 to $22, elucidating sensitivity differences to price shifts.

The Impact of Changes in Supply on Price of Oil

• Shift analysis for supply decreases can indicate higher equilibrium prices in less elastic demand scenarios.

• Figure 3 illustrates the impact of leftward supply shifts on equilibrium price variances.

Comparing the Effects of Elasticity on Equilibrium Change

• Must consider:

  • Same original point.

  • Same price change/demand change.

• Challenges arise from unique market equilibria and supply shifts affecting price changes.

Pitfalls in Using Elasticity

• Common mistake: confusing price elasticity with the slope of the demand curve.

• Elasticity differentiates itself by being unit-free while slope varies along the demand curve.

Example Comparison: Different Demand Curves

• A demand curve example comparing rice and steak showing identical elasticities at specific points despite differing slopes:

  • Rice: Price rises by $0.10 resulting in a 5% drop in quantity.

  • Steak: Price rises by $1 resulting in an identical 5% drop in quantity.

Revenue and Price Elasticity of Demand

• Revenue Formula:
  ext{Revenue} = P imes Q (price times quantity sold).

• Example:

  • Oil Scenario:

    • Selling 60 million barrels at $20 results in:
      ext{Revenue} = 60 ext{ million} imes 20 = 1200 ext{ million} = 1.2 ext{ billion}

• Effects of price changes based on elasticity:

  • Price increase in elastic regions decreases revenue.

  • Price increase in inelastic regions increases revenue.

Elasticity Implications on Revenue Based on Demand Curve

• Straight-line demand curve classifications:

  • Inelastic region: increases in price lead to revenue increases.

  • Elastic region: increases in price lead to revenue decreases.

Tables on Revenue and Elasticity

• 
  

• Table 1: Terminology for Price Elasticity of Demand.

  Term	Value of Price Elasticity of Demand (ed)
  Perfectly inelastic	0 (vertical demand curve)
  Inelastic	Less than 1
  Elastic	Greater than 1
  Perfectly elastic	Infinity (horizontal demand curve)

• 
  

• Table 2: Revenue and the Price Elasticity of Demand.
  

  Elasticity Is	Effect of a Price Increase on Revenue	Effect of a Price Decrease on Revenue
  Less than 1 (<1) | Revenue increases | Revenue decreases | | Equal to 1 (=1) | No change in revenue | No change in revenue | | Greater than 1 (>1)	Revenue decreases	Revenue increases
  Estimation of Income Elasticities of Demand

  Type of Good or Service	Income Elasticity
  Food	0.58
  Clothing/footwear	0.58
  Transport	1.18
  Medical care	1.35
  Recreation	1.42

  Income Elasticity of Demand

  • Definition:

    • The percentage change in quantity demanded divided by the percentage change in income.

    • Formula:
      ext{Income Elasticity of Demand} = rac{ ext{percentage change in quantity demanded}}{ ext{percentage change in income}}

  • Determination of Goods:

    • Normal goods show positive income elasticity (demand increases with income).

    • Inferior goods demonstrate negative income elasticity (demand decreases with income).

  Types Based on Income Elasticity

  • 
    

  • Table 5: Necessity vs. Luxury
    

    Elasticity Is	Type
    0~1	Necessity (Normal)
    >1	Luxury (Normal)
    <0	Inferior
    Cross-Price Elasticity of Demand

    • Definition: Cross-price elasticity of demand assesses the response of quantity demanded of one good to the price change of another good.

      • Formula:
        ext{Cross-Price Elasticity of Demand} = rac{ ext{percentage change in quantity demanded}}{ ext{percentage change in price of related good}}

      • Positive value indicates substitutability; negative value indicates complementarity.

    Elasticity of Supply

    • Definition: Price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price.

      • Formula:
        ext{Price Elasticity of Supply (es)} = rac{ ext{percentage change in quantity supplied}}{ ext{percentage change in price}}

    Elastic Versus Inelastic Supply

    • Definitions based on elasticity values:

      • Elastic Supply: Where price elasticity is greater than one.

      • Inelastic Supply: Where price elasticity is less than one.

      • Unit Elastic Supply: Where price elasticity equals one.

    Comparing Sizes of the Elasticity of Supply

    • Demonstrates different responses based on elasticity magnitude:

      • High elasticity results in larger quantity increases per price increase than low elasticity.

    Importance of Price Elasticity of Supply

    • Critical for understanding market reactions to demand changes and price shifts—same shifts yield variable equilibrium changes based on the elasticity of supply.

    Review of the Violations of the Laws with Elasticity

    • Analysis: Perfectly elastic/inelastic markets do not violate laws of supply/demand.

      • Upward sloping demand curves and backward-bending supply curves indicate market divergence from equilibrium, with examples like Veblen Goods, Speculative Demand, and Giffen Goods.

      • Backward-bending labor supply exemplifies these principles.

    Outcomes Expected

    • Calculate elasticity accurately.

    • Understand the relationship between demand elasticity and revenue changes.

    • Recognize common pitfalls associated with elasticity.

    • Analyze factors affecting elasticity.

    • Memorize definitions for goods categories: normal, inferior, necessity, luxury, substitutes, and complements.