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Elasticity Lecture Review

Introduction to Elasticity

  • The name of any elasticity provides its definition and indicates the type of formula to be used.
  • Elasticity measures the responsiveness of quantity demanded or supplied to a change in one of its determinants (e.g., price, income).

Price Elasticity of Demand ( E_D )

Definition and Formula

  • Price Elasticity of Demand ( ED ) quantifies how much the quantity demanded ( QD ) of a good responds to a change in its price ( P ).

  • Formula (Midpoint Method): To calculate the price elasticity of demand between two points ( (P1, Q1) and (P2, Q2) ), the midpoint method is preferred as it yields the same elasticity regardless of the direction of the price change.

    ED = rac{ ext{Percentage Change in Quantity Demanded}}{ ext{Percentage Change in Price}} = rac{ rac{Q2 - Q1}{(Q1 + Q2)/2}}{ rac{P2 - P1}{(P1 + P_2)/2}}

  • By convention, the absolute value of the price elasticity of demand is often used because price and quantity demanded always move in opposite directions (Law of Demand), resulting in a negative value for E_D . The negative sign simply indicates this inverse relationship.

Types of Price Elasticity of Demand

There are five types of price elasticity of demand, categorized by the magnitude of E_D :

  1. Perfectly Inelastic Demand ( E_D = 0 )

    • Response: Quantity demanded does not change at all, regardless of the price change.
    • Graph: A vertical demand curve.
    • Example: Life-saving medicine with no substitutes for a person who absolutely needs it.

  2. Inelastic Demand ( 0 < E_D < 1 )

    • Response: Quantity demanded changes only slightly in response to a larger percentage change in price (small response).
    • Graph: A relatively steep demand curve.
    • Example: Basic necessities like bread. If price changes by 10 ext{ percent} , quantity demanded might change by less than 10 ext{ percent} .

  3. Unit Elastic Demand ( E_D = 1 )

    • Response: Quantity demanded changes by the same percentage as the price change (some response).
    • Graph: A demand curve that is neither steep nor flat, where total revenue remains constant as price changes.

  4. Elastic Demand ( E_D > 1 )

    • Response: Quantity demanded changes significantly in response to a smaller percentage change in price (big response).
    • Graph: A relatively flat demand curve.
    • Example: Luxury items or goods with many close substitutes. If price changes by 10 ext{ percent} , quantity demanded might change by more than 10 ext{ percent} .

  5. Perfectly Elastic Demand ( E_D = ext{infinity} )

    • Response: Any price change, even tiny, leads to an infinite change in quantity demanded; consumers will buy nothing if the price rises above a certain level.
    • Graph: A horizontal demand curve.
    • Example: A single seller in a perfectly competitive market where many identical products are available from other sellers at the market price.

Price Elasticity and Total Revenue

  • Total Revenue (TR) is the total amount paid by buyers and received by sellers, calculated as TR = P imes Q .
  • Understanding how E_D affects total revenue is crucial for businesses.
  • Inelastic Demand ( E_D < 1 ): If demand is inelastic, an increase in price leads to a proportionately smaller decrease in quantity demanded. Therefore, total revenue increases (price change is dominant).
    • Example: When the price of bread increases, and the demand is inelastic, people still buy a relatively similar amount, leading to higher revenue for sellers.
  • Elastic Demand ( E_D > 1 ): If demand is elastic, an increase in price leads to a proportionately larger decrease in quantity demanded. Therefore, total revenue decreases (quantity change is dominant).
    • Example: If the price of a luxury watch increases, many consumers might opt not to buy it, leading to a significant drop in quantity sold and thus lower revenue.
  • Unit Elastic Demand ( E_D = 1 ): If demand is unit elastic, an increase in price leads to a proportionately equal decrease in quantity demanded. Total revenue remains unchanged.

Calculating Price Elasticity of Demand: Midpoint Method Example

To calculate E_D , follow these steps:

  1. Identify initial and final values: Label P1, Q1, P2, Q2 .
    • Example: When the price of bread ( P1 ) is $2 , consumers purchase 100 loaves ( Q1 ). When the price increases to $3 ( P2 ), consumers purchase 80 loaves ( Q2 ).
  2. Apply the Midpoint Formula:
    • Percentage Change in Quantity Demanded = rac{80 - 100}{(100 + 80)/2} = rac{-20}{90} hickapprox -0.222
    • Percentage Change in Price = rac{3 - 2}{(2 + 3)/2} = rac{1}{2.5} = 0.4
    • E_D = rac{-0.222}{0.4} hickapprox -0.555
  3. Interpret the result: The absolute value is 0.555 . Since 0 < 0.555 < 1 , this demand is inelastic.

Other Demand Elasticities

Income Elasticity of Demand ( E_I )

  • Definition: Measures how the quantity demanded responds to a change in consumers' income.
  • Formula:
    E_I = rac{ ext{Percentage Change in Quantity Demanded}}{ ext{Percentage Change in Income}}
  • Interpretation:
    • Normal Goods ( E_I > 0 ): As income rises, the quantity demanded increases. (Requires two positive numbers or two negative numbers in the fraction, thus a positive result.)
    • Inferior Goods ( E_I < 0 ): As income rises, the quantity demanded decreases. (Requires one positive and one negative number in the fraction, thus a negative result.)

Cross-Price Elasticity of Demand ( E_C )

  • Definition: Measures how the quantity demanded of one good responds to a change in the price of another good.
  • Connection: This concept relates to demand shifters concerning changes in the prices of related goods (substitutes or complements).
  • Formula:
    E_C = rac{ ext{Percentage Change in Quantity Demanded of Good A}}{ ext{Percentage Change in Price of Good B}}
  • Interpretation:
    • Substitutes ( E_C > 0 ): If the price of Good B increases, the quantity demanded of Good A increases. (Example: Price of coffee rises, demand for tea increases).
    • Complements ( E_C < 0 ): If the price of Good B increases, the quantity demanded of Good A decreases. (Example: Price of hot dogs rises, demand for hot dog buns decreases).

Price Elasticity of Supply ( E_S )

Definition and Formula

  • Price Elasticity of Supply ( ES ) quantifies how much the quantity supplied ( QS ) of a good responds to a change in its price ( P ).

  • Formula (Midpoint Method): Similar to demand elasticity, using quantity supplied.

    ES = rac{ ext{Percentage Change in Quantity Supplied}}{ ext{Percentage Change in Price}} = rac{ rac{Q2 - Q1}{(Q1 + Q2)/2}}{ rac{P2 - P1}{(P1 + P_2)/2}}

  • The price elasticity of supply is typically positive because price and quantity supplied move in the same direction (Law of Supply).

Types of Price Elasticity of Supply

Similar to demand, there are five types of price elasticity of supply:

  1. Perfectly Inelastic Supply ( E_S = 0 )

    • Response: Quantity supplied does not change at all, regardless of the price change.
    • Graph: A vertical supply curve.
    • Example: The amount of specific vintage wine produced in a past year (e.g., wine from 1984 ); its supply cannot be increased.

  2. Inelastic Supply ( 0 < E_S < 1 )

    • Response: Quantity supplied changes only slightly in response to a larger percentage change in price (small response from producers).
    • Graph: A relatively steep supply curve.

  3. Unit Elastic Supply ( E_S = 1 )

    • Response: Quantity supplied changes by the same percentage as the price change (some response).
    • Graph: A supply curve that is a straight line passing through the origin.

  4. Elastic Supply ( E_S > 1 )

    • Response: Quantity supplied changes significantly in response to a smaller percentage change in price (big response from producers).
    • Graph: A relatively flat supply curve.

  5. Perfectly Elastic Supply ( E_S = ext{infinity} )

    • Response: Any price change, even tiny, leads to an infinite change in quantity supplied; producers will supply nothing below a certain price but an infinite amount at that price.
    • Graph: A horizontal supply curve.

Determinants of Price Elasticity of Supply

  • The primary determinant of the price elasticity of supply is time.
    • Longer Time Horizon: The more time suppliers have to adjust production in response to a change in price, the more elastic the supply will be.
      • Example: Wheat supply is elastic over the long run because farmers can decide to plant more wheat (or switch from other crops like soy to wheat) if they see sustained price increases.
    • Shorter Time Horizon: In the short run, it may be difficult or impossible to increase production significantly, leading to a more inelastic supply.
      • Example: The supply of parking spots in a city is often inelastic in the short term, as building new parking structures takes time. Thus, an increase in demand (e.g., population doubling) would lead to a small increase in quantity available but a relatively large increase in price.

General Approach to Elasticity Problems

  • Identify Variables: Clearly label P1, Q1, P2, Q2 from the problem statement.
  • Choose the Correct Formula: The name of the elasticity (e.g., price elasticity of demand, income elasticity, price elasticity of supply) dictates which formula to use.
  • Calculate: Plug the values into the midpoint formula and perform the calculation.
  • Interpret: Compare the calculated elasticity value to 0 , 1 , or infinity to determine the type of elasticity (inelastic, elastic, unit elastic, perfectly elastic/inelastic) and its implications. For demand elasticities, remember to consider the absolute value, but also understand the meaning of the negative sign for income and cross-price elasticities.
  • Relate to Total Revenue: For price elasticity of demand, consider how the elasticity type affects total revenue, as it helps identify the dominant effect (price change vs. quantity change).