Elasticity

Elasticity

  • Definition: Measures the responsiveness of one economic variable to changes in another.

Price Elasticities

  • Concept of Price Elasticity:

    • Price elasticity is the ratio between the percentage change in quantity and the corresponding percentage change in price.

    • Formulated as:

      • Price Elasticity of Demand: ext{Price Elasticity of Demand} = rac{ ext{%} ext{∆ Quantity Demanded}}{ ext{%} ext{∆ Price}}

      • Price Elasticity of Supply: ext{Price Elasticity of Supply} = rac{ ext{%} ext{∆ Quantity Supplied}}{ ext{%} ext{∆ Price}}

    • Core Questions:

      • How price sensitive are consumers?

      • What is the extent of producers' ability to respond to price changes?

      • Can producers ramp up production quickly in response to price changes?

Calculation of “ARC Elasticities” (Using the Midpoint Formula)

  • Definition: Economists use the average percent change in both quantity and price to calculate the elasticity between two points on a linear demand or supply curve.

  • Midpoint Method for Elasticity:

    • Percentage change in quantity:
      ext{% change in quantity} = rac{Q2 - Q1}{(Q2 + Q1)/2}

    • Percentage change in price:
      ext{% change in price} = rac{P2 - P1}{(P2 + P1)/2}

Example – Price Elasticity of Demand

  • Calculation Result:

    • The elasticity of demand between two points A and B is 0.45, indicating it is inelastic (smaller than 1).

    • Important Note: Calculated elasticity is actually −0.45-0.45, as elasticities of demand are always negative, thus absolute value taken.

Example – Price Elasticity of Supply

  • Calculation Result:

    • The elasticity of supply between points A and B is 3.53, indicating it is elastic (greater than 1).

Three Cases of Elasticity

  1. Elastic Demand or Supply:

    • Indicates high responsiveness to changes in price.

  2. Inelastic Demand or Supply:

    • Indicates low responsiveness to price changes.

  3. Unitary Elasticity:

    • Indicates that percentage change in quantity equals percentage change in price (i.e., ext{% quantity} = ext{% price} ).

Real-Life Example and Interpretation

  • Uber Price Cut Case:

    • After Uber cuts fares by 15%, the quantity of rides demanded increases by 30%.

    • The absolute value of price elasticity of demand is:
      | ext{Price Elasticity of Demand}| = rac{30 ext{ ext{%}}}{15 ext{ ext{%}}} = 2

  • Implications of this Elasticity:

    • Customers exhibit price sensitivity.

    • The percentage increase in quantity demanded exceeds the percentage decrease in price.

    • Total Revenue increases when price decreases.

Total Revenue Concepts

  • Definition of Total Revenue (TR): Total revenue is defined as the quantity sold multiplied by the price per unit:
    extTR=PimesQext{TR} = P imes Q

  • Example calculations:

    • If the price per birdhouse is 1010:

      • For 1 unit: 10imes1=1010 imes 1 = 10

      • For 2 units: 10imes2=2010 imes 2 = 20

      • For 3 units: 10imes3=3010 imes 3 = 30

      • For 4 units: 10imes4=4010 imes 4 = 40

The Relationship Between Total Revenue and Price Based on Elasticity

  • If Demand is Elastic:

    • Total Revenue and Price move in opposite directions.

      • When Price decreases, Total Revenue increases due to a large increase in quantity demanded.

  • If Demand is Inelastic:

    • Total Revenue and Price move in the same direction.

      • When Price decreases, Total Revenue decreases due to a small increase in quantity demanded.

Theoretical Extremes of Elasticity

  1. Perfectly Elastic:

    • Any change in price causes an infinitely large change in quantity.

    • Graphically represented as a horizontal curve.

  2. Perfectly Inelastic:

    • Any change in price does not change the quantity.

    • Graphically represented as a vertical curve.

Factors Determining Price Elasticity

  • Time Factor:

    • Elasticities tend to be lower (more inelastic) in the short run compared to the long run.

  • Consumer Behavior:

    • Consumers exhibit more elastic demand when more substitutes exist.

      • Examples include:

        • More competing products.

        • Specific brands that consumers can choose from.

        • Non-essential goods with alternatives.

  • Production Flexibility:

    • Supply is more elastic when production is flexible:

      • Availability of easily obtained inputs.

      • Capacity to store products.

      • Resources for increased production when needed.

      • Ease of market entry and exit.

  • Market Dynamics:

    • In most markets, in the short run, prices fluctuate more than quantities; however, in the long run, quantities typically adjust more than prices.

Comparing Price Elasticity of Demand and Supply Curves

  • Elasticity Comparison:

    • When comparing demand or supply curves that intersect, the flatter curve is more elastic.

    • Visual representation helps identify relative elasticities.

Practice Questions and Scenarios

  • For relative price elasticity of supply where supply 2 is inelastic compared to supply 1:

    • Question: Which good will have a bigger price increase if demand increases?

      • A. Good 2 will see a bigger price increase

      • B. Good 1 will see a bigger price increase

      • C. Price increase will be equal between the two goods

      • D. Indeterminate without further information.

Elasticity in Other Areas

  • Income Elasticity of Demand (IE):

    • Calculated as:
      ext{IE} = rac{ ext{%} ext{∆ Quantity Demanded}}{ ext{%} ext{∆ Income}}

    • Implications of income elasticity:

      • Positive IE indicates normal goods (demand increases as income increases).

      • Negative IE indicates inferior goods (demand decreases as income increases).

  • Cross Price Elasticity of Demand (CPE):

    • Calculated as:
      ext{CPE} = rac{ ext{%} ext{∆ Quantity Demanded for good B}}{ ext{%} ext{∆ Price of good A}}

    • Relationship implications:

      • Positive CPE indicates substitutes.

      • Negative CPE indicates complements.

      • The stronger the relationship, the further from zero the CPE is.

Studying Elasticities

  • Study Steps:

    1. Identify the name of the elasticity to set up the ratio.

    2. Calculate elasticity using:

      • Midpoint formula for price and quantity.

      • Percent changes.

    3. Understand the purpose of elasticity in context.

    4. Interpret the ratio:

      • Consider both sign and magnitude of the elasticity.