Elasticity and its Application

Elasticity: Overview

• Elasticity measures how one variable responds to changes in another
• Types of elasticity:
  • Price elasticity of demand
  • Price elasticity of supply
  • Income elasticity of demand
  • Cross-price elasticity of demand

Price Elasticity of Demand

• Definition: Measures responsiveness of quantity demanded (Qd) to a change in price (P).
• Formula:$Price\,Elasticity\ of\ Demand = \frac{\%\ change\ in\ Qd}{\%\ change\ in\ P}$
  • Example: If price rises by 10% and quantity falls by 15%,
    $Price\ Elasticity\ of\ Demand = \frac{15\%}{10\%} = 1.5$
• Along a demand curve, as price (P) increases, quantity demanded (Qd) decreases, thus yielding a negative elasticity value which is reported as positive.

Calculating Percentage Changes

• Use standard method:
  $Percentage\ change\ = \frac{end\ value - start\ value}{start\ value} \times 100\%$
• Important: The computation can yield different results based on start and end points hence we use the midpoint method to avoid this.
• Midpoint Method:
  $Percentage\ change = \frac{end\ value - start\ value}{midpoint} \times 100\%$
• Midpoint = average of start and end values.

Determinants of Price Elasticity of Demand

• Price elasticity varies based on several factors:
  • Availability of substitutes
  • Necessity vs luxury goods
  • Definition of the good (broad vs narrow)
  • Time frame (long run vs short run)

Demand Curves and Elasticity

• The slope of the demand curve relates to elasticity:
  • Flatter curves correspond to greater elasticity
  • Steeper curves indicate lower elasticity

Classifications of Demand Curves

1. Perfectly Inelastic:
   • Qd does not change with P.
   • Elasticity = 0
   • Graph: Vertical line
2. Inelastic Demand:
   • Qd changes less than proportionately with P.
   • Elasticity < 1
   • Graph: Relatively steep curve
3. Unit Elastic Demand:
   • Qd changes proportionately with P.
   • Elasticity = 1
   • Graph: Intermediate slope
4. Elastic Demand:
   • Qd changes more than proportionately with P.
   • Elasticity > 1
   • Graph: Relatively flat curve
5. Perfectly Elastic Demand:
   • Qd changes by any amount with no change in P.
   • Elasticity = Infinity
   • Graph: Horizontal line

Price Elasticity and Total Revenue

• Impact of price changes on revenue:
  • Elastic Demand (Elasticity > 1):
  • Price increase leads to revenue decrease
  • Inelastic Demand (Elasticity < 1):
  • Price increase leads to revenue increase
  • Unit Elastic (Elasticity = 1): No effect on revenue

Applications of Elasticity

1. Drug Policy Impact:
   • Inelastic demand for drugs implies policies that reduce supply raise price and increase drug-related crime.
2. Supply Elasticity:
   • Price Elasticity of Supply:
     $Price\ Elasticity\ of\ Supply = \frac{\%\ change\ in\ Qs}{\%\ change\ in\ P}$
   • The elasticity of supply depends on how easily sellers can change their production quantities.

Other Elasticities

• Income Elasticity of Demand:
  • $Income\ Elasticity\ of\ Demand = \frac{\%\ change\ in\ Qd}{\%\ change\ in\ income}$
  • Normal goods: Elasticity > 0
  • Inferior goods: Elasticity < 0
• Cross-Price Elasticity of Demand:
  • $Cross-price\ Elasticity = \frac{\%\ change\ in\ Qd\ for\ good\ 1}{\%\ change\ in\ price\ of\ good\ 2}$
  • Substitutes: Elasticity > 0
  • Complements: Elasticity < 0