Microeconomic Concepts on Demand Elasticity and Practical Applications

Price Elasticity of Demand (PED)

Definition and Advanced Measurement

• Price Elasticity of Demand (PED) is a unitless measure that quantifies the responsiveness of the quantity demanded for a specific good to a change in its price. Because it is unitless, it allows economists to compare various products and markets regardless of currency or measurement units.

• Point Elasticity: Used to calculate the elasticity at a specific coordinate on the demand curve. It is particularly useful for infinitesimal changes in price.
  $\text{Elasticity} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$

• Arc (Midpoint) Elasticity: Recommended when there is a significant price gap between two points to avoid the "index number problem" (where the result differs depending on the direction of change).
  $\text{Arc Elasticity} = \frac{(Q<em>2 - Q</em>1) / [(Q<em>2 + Q</em>1) / 2]}{(P<em>2 - P</em>1) / [(P<em>2 + P</em>1) / 2]}$

Numerical Example: Gasoline Market

• Consider a market demand function for gasoline: $Q = 57 - 6.39P_x$

  • At a price of ‑1.48 per liter: The quantity demanded is high, and the calculated elasticity is $\approx -0.2$. This represents inelastic demand, where consumers do not significantly reduce consumption despite price hikes (likely due to commuting necessity).

  • At a higher price of ‑5 per liter: The elasticity shifts to $\approx -1.28$. At this threshold, the demand becomes elastic, meaning consumers are more likely to find alternatives (public transit, carpooling) as the price becomes a larger burden.

Detailed Classification of Elasticity

1. Elastic Demand (|E| > 1): A change in price triggers a more than proportional change in quantity demanded. Total revenue decreases if prices rise.

2. Inelastic Demand (|E| < 1): A change in price triggers a less than proportional change in quantity demanded. Total revenue increases if prices rise.

3. Unit Elastic Demand ($|E| = 1$): A change in price triggers an exactly proportional change in quantity. This is the point where Total Revenue is maximized.

4. Perfectly Inelastic ($|E| = 0$): A vertical demand curve. Consumers buy the same amount regardless of price (e.g., life-saving insulin).

5. Perfectly Elastic ($|E| = \infty$): A horizontal demand curve. Any price increase leads to quantity demanded dropping to zero (common in perfectly competitive markets).

Characteristics of Linear Demand Curves

• While the slope of a linear demand curve is constant ($\frac{\Delta P}{\Delta Q}$), the elasticity changes at every point along the line:

  • In the Upper Half: Prices are high and quantities are low, leading to a high $P/Q$ ratio, which results in elastic demand.

  • At the Midpoint: The elasticity is exactly $-1$. This coincides with the peak of the Total Revenue curve.

  • In the Lower Half: Prices are low and quantities are high, leading to a low $P/Q$ ratio, resulting in inelastic demand.

Extended Factors Affecting Elasticity

1. Availability of Substitutes: The primary determinant. The more close substitutes available, the easier it is for consumers to switch, making demand more elastic.

2. Budget Share: If a good represents a significant portion of a consumer's total budget (e.g., housing or cars), a price change has a massive impact on purchasing power, making it more elastic.

3. Time Horizon: In the short run, demand is often inelastic because consumers need time to adjust habits or find alternatives. Demand becomes more elastic in the long run.

4. Degree of Necessity: Necessities (bread, heat) stay inelastic even at high prices, whereas luxuries (designer watches) are highly elastic.

Income Elasticity of Demand (YED)

• YED measures how the quantity demanded of a good responds to a change in the consumers' income ($I$).
  $\text{Income Elasticity} = \frac{\% \Delta Q}{\% \Delta I}$

• Classification of Goods:

  • Normal Goods (\text{YED} > 0): Demand increases as income increases. Subdivided into Necessities (0 < YED < 1) and Luxuries (YED > 1).

  • Inferior Goods (\text{YED} < 0): Demand decreases as income increases (e.g., generic brands or public transit).

Cross-Price Elasticity of Demand (XED)

• XED measures the responsiveness of demand for Good X to a price change in Good Y. It determines the relationship between goods.

  • Substitutes (\text{XED} > 0): An increase in the price of Good Y leads to more people buying Good X (e.g., butter price rises, margarine demand rises).

  • Complements (\text{XED} < 0): An increase in the price of Good Y decreases the demand for Good X (e.g., car prices rise, gasoline demand falls).

Income and Substitution Effects

• Substitution Effect: When the price of a good falls, it becomes relatively cheaper compared to other goods, so consumers substitute away from more expensive goods toward the cheaper one. This always has an inverse relationship with price.

• Income Effect: A price decrease acts like an increase in "real income," giving the consumer more purchasing power.

  • For Normal Goods: Both effects work together to increase demand when price falls.

  • For Inferior Goods: The income effect works against the substitution effect. If the income effect is so strong it outweighs substitution, the good is known as a Giffen Good (a theoretical upward-sloping demand curve).

Market Demand Function Case Study

• Comprehensive demand function analysis: $Q = 84,500 - 6,390 P<em>x + 250 I - 2,000 P</em>y$

  • The coefficient for $P_x$ ($-6,390$) confirms the Law of Demand.

  • The positive coefficient for $I$ ($+250$) identifies the product as a normal good.

  • The negative coefficient for $P_y$ ($-2,000$) identifies Goods X and Y as complements.