Elasticities of Demand and Supply

Introduction:

Elasticity, in economics, measures the responsiveness of one variable to a change in another. Specifically, elasticities of demand and supply measure how much the quantity demanded or supplied changes in response to changes in factors influencing them, like price, income, or the price of related goods. Understanding elasticity is crucial for businesses (pricing decisions, revenue projections), policymakers (tax incidence, market interventions), and consumers (understanding how price changes impact spending).

Key Points:

• Elasticity measures responsiveness.
• Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price.
• Price elasticity of supply (PES) measures the responsiveness of quantity supplied to a change in price.
• Income elasticity of demand (IED) measures responsiveness of quantity demanded to changes in income.
• Cross-price elasticity of demand (XED) measures responsiveness of quantity demanded of one good to changes in the price of another good.
• Elasticity values can be elastic (>1), inelastic (<1), unit elastic (=1), perfectly elastic (∞), or perfectly inelastic (0).

Main Content:

I. Price Elasticity of Demand (PED)

A. Definition

PED measures the percentage change in quantity demanded of a good in response to a percentage change in its price. It's calculated as:

PED = (% Change in Quantity Demanded) / (% Change in Price)

Often, you'll see this written using the Greek letter epsilon (ε) or 'e' for elasticity. A common formula used is:

e_p = (ΔQ/Q) / (ΔP/P) = (ΔQ/ΔP) * (P/Q)

Where:

• ΔQ = Change in Quantity
• Q = Original Quantity
• ΔP = Change in Price
• P = Original Price

Important Note: PED is usually negative because of the law of demand (price and quantity demanded move in opposite directions). However, economists often take the absolute value of PED and focus on the magnitude.

B. Classifications of PED

• Elastic Demand (|PED| > 1): A 1% change in price leads to a greater than 1% change in quantity demanded. Demand is highly responsive to price changes. Example: If the price of a specific brand of coffee increases by 10%, and quantity demanded falls by 20%, demand is elastic.
• Inelastic Demand (|PED| < 1): A 1% change in price leads to a less than 1% change in quantity demanded. Demand is not very responsive to price changes. Example: If the price of gasoline increases by 10%, and quantity demanded falls by only 2%, demand is inelastic.
• Unit Elastic Demand (|PED| = 1): A 1% change in price leads to exactly a 1% change in quantity demanded.
• Perfectly Elastic Demand (|PED| = ∞): Consumers will buy any quantity at a specific price, but nothing at a slightly higher price. This is represented by a horizontal demand curve.
• Perfectly Inelastic Demand (|PED| = 0): Quantity demanded does not change regardless of the price. This is represented by a vertical demand curve.

C. Determinants of PED

Several factors influence PED:

• Availability of Substitutes: Goods with many close substitutes tend to have more elastic demand (consumers can easily switch). Goods with few or no substitutes have inelastic demand.
• Necessity vs. Luxury: Necessities tend to have inelastic demand (people need them regardless of price). Luxuries tend to have elastic demand.
• Proportion of Income: Goods that take up a large proportion of a consumer's income tend to have more elastic demand.
• Time Horizon: Demand tends to be more elastic in the long run than in the short run (consumers have more time to adjust).
• Definition of the Market: The more narrowly defined the market, the more elastic the demand is, because it is easier to find substitutes for narrowly defined goods.

D. Total Revenue and PED

The relationship between PED and total revenue (TR = Price x Quantity) is critical:

• Elastic Demand: If demand is elastic, a price decrease will increase total revenue, and a price increase will decrease total revenue.
• Inelastic Demand: If demand is inelastic, a price decrease will decrease total revenue, and a price increase will increase total revenue.
• Unit Elastic Demand: Total revenue is maximized where demand is unit elastic.

E. Arc Elasticity vs. Point Elasticity

• Point Elasticity: Measures elasticity at a specific point on the demand curve. It uses the derivative of the demand function (if known) or a very small change in price and quantity.

• Arc Elasticity: Measures elasticity over a range of the demand curve. It uses the average price and average quantity over that range. The formula is:

  E_d = [(Q2 - Q1) / ((Q1 + Q2)/2)] / [(P2 - P1) / ((P1 + P2)/2)]

II. Income Elasticity of Demand (IED)

A. Definition

IED measures how much the quantity demanded of a good changes in response to a change in consumers' income.

IED = (% Change in Quantity Demanded) / (% Change in Income) e_i= (ΔQ/Q) / (ΔI/I)

B. Classifications of IED

• Normal Goods (IED > 0): As income rises, quantity demanded rises.
  • Necessities (0 < IED < 1): Income rises, quantity demanded rises, but less than proportionately. Example: food.
  • Luxuries (IED > 1): Income rises, quantity demanded rises more than proportionately. Example: expensive cars.
• Inferior Goods (IED < 0): As income rises, quantity demanded falls. Consumers switch to higher-quality substitutes. Example: generic brands, instant noodles.

III. Cross-Price Elasticity of Demand (XED)

A. Definition

XED measures the responsiveness of the quantity demanded of one good (Good A) to a change in the price of another good (Good B).

XED = (% Change in Quantity Demanded of Good A) / (% Change in Price of Good B) e_xy= (ΔQ_x/Q_x) / (ΔP_y/P_y)

B. Classifications of XED

• Substitutes (XED > 0): If the price of Good B increases, the quantity demanded of Good A increases (and vice versa). Example: Coffee and tea.
• Complements (XED < 0): If the price of Good B increases, the quantity demanded of Good A decreases (and vice versa). Example: Cars and gasoline.
• Unrelated Goods (XED = 0): The price of Good B has no effect on the quantity demanded of Good A.

IV. Price Elasticity of Supply (PES)

A. Definition

PES measures the responsiveness of quantity supplied of a good to changes in its price. PES = (% Change in Quantity Supplied) / (% Change in Price) e_s= (ΔQ/Q) / (ΔP/P)

B. Classifications of PES

• Elastic Supply (PES > 1): A 1% change in price leads to a greater than 1% change in quantity supplied.
• Inelastic Supply (PES < 1): A 1% change in price leads to a less than 1% change in quantity supplied.
• Unit Elastic Supply (PES = 1): A 1% change in price leads to a 1% change in quantity supplied.
• **Perfectly Elastic Supply (PES = ∞):**Suppliers will supply any quantity at a specific price. Represented by horizontal line.
• **Perfectly Inelastic Supply (PES = 0):**Quantity supplied does not change with the price.Represented by vertical line.

C. Determinants of PES

• Time Horizon: Supply is generally more elastic in the long run than in the short run. Firms have more time to adjust production levels, build new factories, or enter/exit the market.
• Availability of Inputs: If inputs are readily available, supply is more elastic.
• Mobility of Factors of Production: If factors of production can be easily shifted to producing this good, supply is more elastic.
• Capacity: If there is spare capacity in the industry, it's easier to increase output and so supply is more elastic.
• Stock Levels: High stock levels lead to more elastic supply.

Mermaid Diagram (Illustrating Elasticities):

graph LR
    subgraph Demand
        A[Price] --> B(Quantity Demanded)
        B -- "Elastic (ε>1)" --> C[Large % Change]
        B -- "Inelastic (ε<1)" --> D[Small % Change]
        B -- "Unit Elastic (ε=1)" --> E[Equal % Change]
    end

    subgraph Supply
        F[Price] --> G(Quantity Supplied)
        G -- "Elastic (ε>1)" --> H[Large % Change]
        G -- "Inelastic (ε<1)" --> I[Small % Change]
        G -- "Unit Elastic (ε=1)" --> J[Equal % Change]
    end

    subgraph Income_Demand
      K[Income] -->L(Quantity Demanded)
      L -- "Normal Good(IED>0)" -->M[Increase]
      L -- "Inferior Good(IED<0)" -->N[Decrease]
    end

    subgraph CrossPrice_Demand
      O[Price of Good B] -->P(Quantity Demanded of Good A)
      P -- "Substitutes(XED >0)" -->Q[Increase]
      P -- "Complements(XED<0)" -->R[Decrease]
    end

Conclusion:

Elasticities are fundamental concepts in economics, providing a framework for understanding how markets react to changes in various economic factors. They help analyze the behavior of both consumers (demand) and producers (supply). Key takeaways include understanding the different types of elasticities (price, income, cross-price), their classifications (elastic, inelastic, etc.), the factors that influence them, and their practical implications, such as the impact of price changes on total revenue.