elasticity of supply

Overview of Elasticity and Tax Incidence

Introduction

• The discussion centers on the concept of price elasticity in both demand and supply.
• Aims to understand the true incidence of taxes, determining who bears the burden - buyers or sellers.

Price Elasticity of Demand

• Definition: Price elasticity of demand measures how responsive the quantity demanded is to a change in price.
  • Mathematically defined as:
    (E_d = rac{ ext{Percentage change in quantity demanded}}{ ext{Percentage change in price}})
• Calculation on a Linear Demand Curve:
  • For a linear demand curve, the elasticity formula is:
    (E_d = rac{P}{Q} imes rac{1}{|slope|})
  • The slope remains constant across the linear curve, but the elasticity varies with the price and quantity levels along the curve.
• Elasticity Points:
  • At the top (high price, low quantity): Elasticity is infinite.
  • At the bottom (low price, high quantity): Elasticity is zero.
  • At the midpoint: Elasticity equals 1, indicating unit elasticity.

Understanding Elasticity of Demand Changes

• As you move down the demand curve:
  • Elasticity varies from greater than 1 (elastic) to less than 1 (inelastic) approaching the bottom.
• Importance of Elasticity:
  • Elasticity affects total revenue which is defined as:
    (Total Revenue = Price imes Quantity)
  • When demand is elastic ($E_d > 1$), a price increase leads to a decrease in total revenue.
  • When demand is inelastic ($E_d < 1$), a price increase leads to an increase in total revenue.

Application of Elasticity to Tax Incidence

• Tax Incidence: Refers to how the burden of a tax is distributed between buyers and sellers.
  • Tax incidence depends on the price elasticity of demand and supply.
• If demand is inelastic, buyers bear more of the tax; if elastic, sellers bear more of the tax.

Price Elasticity of Supply

• Definition: Price elasticity of supply measures how responsive the quantity supplied is to a change in price.
  • Mathematically:
    (E_s = rac{ ext{Percentage change in quantity supplied}}{ ext{Percentage change in price}})
• Supply Curve Characteristics:
  • Typically upward sloping, indicating that price increases lead to greater quantities supplied.
  • Elasticity can be calculated similarly to demand:
    (E_s = rac{P}{Q} imes rac{1}{|slope|})
• Extreme Cases:
  • Perfectly inelastic supply (vertical line): $E_s = 0$, quantity supplied does not change regardless of price changes.
  • Perfectly elastic supply (horizontal line): Involves extreme responsiveness to price changes.

Factors Determining Elasticity of Supply

• Ease of Production: Response time to change in price varies depending on input availability and production capacity.
• Example scenarios:
  • Short-term supply may be highly inelastic (as in perishable goods like fish).
  • Long-term supply tends to be more elastic as producers can adjust and enter the market.

Tax Implications and Market Response

• Tax Wedge Analysis:
  • Establishes the difference between what buyers pay and what sellers receive after a tax is imposed.
  • Graphically depicted as the distance between the demand and supply curves reflecting the tax amount.
• Example with Tax:
  • A tax increases buyers' price and decreases sellers' price.
  • Example: If tax = $4, buyers may face a price increase of $3, while sellers experience a decrease of $1.

Applying Elasticities to Tax Incidence Calculation

• Formula for Tax Incidence Share:
  • Share of tax burden on buyers:
    ( ext{Change in buyer's price} = rac{Es}{Es + E_d} imes ext{Tax} )
  • Share of tax burden on sellers:
    ( ext{Change in seller's price} = 1 - rac{Es}{Es + E_d} )
• Illustrative Example:
  • Consider: Demand equation: ( P_d = 10 - 0.1Q )
  • Supply equation: ( P_s = 4 + 2Q )
  • Equilibrium found at a specific quantity can be adjusted for tax to evaluate impacts on buyers and sellers.

Conclusion

• Understanding the dynamics of elasticity is crucial for analyzing market behavior in response to price changes and taxes.
• Elasticity determines how burdens from taxes are shared and aids in predicting shifts in revenue and quantity sold.

These notes encapsulate the definition, calculation, and application of elasticity and tax incidence, providing a comprehensive guide to the topic for academic purposes.