02.03 Price Elasticity of Demand

Elasticity: A Comprehensive Guide

What is Elasticity?

• Definition: Elasticity measures how much consumers change their buying behavior in response to changes in price or other demand determinants. In simpler terms, it's about how sensitive demand is to change.

• General Concept: Like how a rubber band stretches, elasticity in economics refers to how much the quantity demanded of a good or service changes when factors like price change.

• Price Elasticity of Demand: This specifically measures how much the quantity demanded changes in response to a change in price.

• Examples:

  • Inelastic Demand: Gasoline in the United States. Even if the price increases, people still buy roughly the same amount.

  • Elastic Demand: A specific brand of chips. If the price increases even a little, consumers will switch to a different brand.

Why Does Elasticity Matter?

Elasticity is crucial for:

• Producers (Sellers): Helps them understand how price changes affect revenue.

• Public Policy Makers: Informs decisions about taxation and its impact on businesses.

Key Questions Answered by Understanding Elasticity:

• "If we raise the price, will we make more money, or will we lose customers and actually make less money?"

• "If the government adds or raises a tax, will it raise much tax revenue, or will it just hurt businesses who sell the product?"

• "If we do a promotional sale, are we likely to increase sales revenue, or are we likely to sell the same quantity but gain less revenue?"

• "Do people seem to think of this product as a luxury or as a need?"

The Determinants of Elasticity

Slope and Price Elasticity - Explained with Graphs

1. Perfectly Elastic Demand:

   • Graph: Flat, horizontal line.

   • Concept: At the market price, there is effectively infinite demand. Above the demand line, quantity demanded is zero.

   • Example: Vending machine with identical candy bars on two racks. If one rack charges even a nickel more, no one will buy from it.

   • Limiting Factor: Supply available.

2. Elastic Demand:

   • Graph: Downward-sloping line.

   • Concept: A relatively small change in price leads to a large change in quantity demanded.

   • Example: Lowering the price from $2 to $1 increases quantity demanded from 1 to 5 units. A 50% price decrease leads to a 400% quantity increase.

3. Inelastic Demand:

   • Graph: Steep downward-sloping line.

   • Concept: A large change in price leads to a small change in quantity demanded.

   • Example: Demand for a kidney. People who need a kidney transplant are unlikely to be very sensitive to price.

4. Perfectly Inelastic Demand:

   • Graph: Vertical line.

   • Concept: Quantity demanded remains the same regardless of price.

5. Unit Elastic Demand:

   • Graph: Downward-sloping line.

   • Concept: Percentage change in price equals the percentage change in quantity demanded.

   • Example: Decreasing the price by two results in an increase of quantity demanded by two - a one-to-one proportion.

Calculating Elasticity

• Elasticity Coefficient: A unitless number that measures elasticity.

• Formula:

  Elasticity=Percentage Change in Price/Percentage Change in Quantity

  

Interpreting the Coefficient

• Elasticity > 1: Elastic range. A 1% change in price leads to a greater than 1% change in quantity demanded.

• Elasticity < 1: Inelastic range. A 1% change in price leads to a less than 1% change in quantity demanded.

• Elasticity = 1: Unit elastic. A 1% change in price leads to a 1% change in quantity demanded. This is often the revenue-maximizing point.

Quirky Math Problem and the Midpoint Formula Solution

• The Problem: Percentages change depending on whether values are increasing or decreasing (e.g., going from 1 to 2 is a 100% increase, but going from 2 to 1 is a 50% decrease).

• Midpoint Formula: Used to avoid errors due to the directional problem of percentages. It calculates percentage changes based on the average of the initial and final values.

• Formula:

  

• Example:

  • Quantity demanded increases from 10 to 14 units; price decreases from $6 to $4.

    1. Change in quantity = 14 - 10 = 4

    2. Average quantity = 14+102=12214+10​=12

    3. % change in quantity = 412=0.33124​=0.33 or 33%

    4. Change in price = $6 - $4 = $2

    5. Average price = 6+42=526+4​=5

    6. % change in price = 25=0.4052​=0.40 or 40%

    7. Elasticity = 0.330.40=0.830.400.33​=0.83

    8. 0.83 < 1, so the range is relatively inelastic.

• Difference Between Point and Midpoint Formulas:

  • Point Formula: Uses the initial value as the base for calculating percentage change.

  • Midpoint Formula: Uses the average of the initial and final values as the base.

  • The midpoint formula is generally preferred because it avoids directional distortions.

Key Considerations

• For price elasticity of demand, ignore the sign (positive or negative).

• Always use percentage changes, not just the raw changes in quantity and price.

• Be comfortable converting between fractions and percentages.

Total Revenue Test

• Ranges of Elasticity: A relatively elastic good can have an inelastic range, and vice versa. This is because elasticity changes along the demand curve.

  • Elasticity is based on percentage changes, not just the slope. *Marginal unit values will yield different values than overall curve values.

• Total Revenue: The amount of money a firm receives from selling its product (Price × Quantity).

• Total Revenue Test: A method to determine elasticity by examining how total revenue changes with price changes.

• Example:

  Price	Quantity	Total Revenue
  $6	0	$0
  $5	1	$5
  $4	2	$8
  $3	3	$9
  $2	4	$8
  $1	5	$5
  $0	6	$0

• Revenue Maximization: Total revenue is maximized at the unit elastic point.

• Elastic Range: Increasing price decreases revenue; decreasing price increases revenue.

• Inelastic Range: Increasing price increases revenue; decreasing price decreases revenue.

Every business wants to find the sweet spot on their demand curve!