In Depth Notes on Elasticity in Economics

Transition to Elasticity

• Unit Four introduces the concept of elasticity, shifting from the theory of the firm.
• Focus on how demand responses to changes in price and income.

Theory of the Firm vs. Theory of Households

• Firms: Simple objective (maximize profits) and straightforward decision-making.
• Households: Complex objective (maximize happiness) and complicated decision-making, harder to model mathematically.
  • Lack of direct measurement for happiness (e.g., can't quantify happiness from chocolate cookies vs. fruits).
  • Firms have clear profit metrics; household happiness is abstract and non-linear.

Revealed Preference Theory

• Observation of choices provides insights into households' preferences and values.
• Choices are assumed to be rational and consistent with underlying preferences:
  • Variations are influenced by income differences and changing prices.

Three Types of Elasticity

1. Price Elasticity of Demand

   • Measures how quantity demanded responds to changes in product price.
   • E.g., if price of salami increases, how does that affect the quantity purchased?
   • Elastic vs. Inelastic Demand:
     • Elastic Demand: Quantity changes significantly with price changes.
     • Inelastic Demand: Quantity remains fairly stable with price changes.

2. Income Elasticity of Demand

   • Examines how changes in income affect quantity demanded.
   • Luxury goods (elastic > 1) vs. staple goods (0 < income elasticity < 1).
   • Example of luxury goods: Travel or vacation spending (increases significantly with income).
   • Example of staple goods: Basic food items—slight decrease in quantity demand despite income decrease.

3. Cross Price Elasticity of Demand

   • Looks at how a change in the price of one good affects the quantity demanded of another good.
   • Positive for substitutes (e.g., if corn chips’ price rises, demand for potato chips increases).
   • Negative for complements (e.g., if bagels become expensive, demand for cream cheese decreases).

Importance of Understanding Demand Elasticities

• Helps predict behavior of consumers under varying economic conditions:
  • Elastic Demand: Raising price decreases total revenue; lowering price increases total revenue.
  • Inelastic Demand: Raising price increases total revenue; lowering price decreases total revenue.

Price Elasticity of Demand Calculation

• Formula:
  $E_d = \frac{\text{Percentage change in quantity}}{\text{Percentage change in price}}$
• Example calculation when price changes from $74.88 to $91.52 and quantity from 506,000 to 414,000.
• Importance of notation with 3 decimal places for answers.

Characteristics of Elastic vs. Inelastic Demand

• Elastic Demand: Absolute value > 1.
• Inelastic Demand: Absolute value < 1.
• Unit Elastic Demand: Demand elasticity = 1, does not change total revenue despite price changes.
• Examples:
  • Everyday Items: Soft drinks (elastic), medications (inelastic), staple foods (inelastic).

Applications of Income Elasticity of Demand

• Higher income may lead to lower sales of inferior goods.
• Luxury Goods: Significant increase in demand with income.
• Staple Goods: Demand may remain stable with income fluctuations, less sensitive.
• Inferior Goods: Demand increases when income decreases.

Cross Price Elasticity of Demand Calculations

• Formula:
  $E_{xy} = \frac{\text{Percentage change in quantity of good X}}{\text{Percentage change in price of good Y}}$
• Practical significance in market strategies for firms by anticipating substitute and complement behaviors.