Comprehensive Elasticity Review: Demand, Supply, Income, and Cross-Price

Elasticity Review

This review covers four important applications of elasticity, crucial for understanding how changes in price, income, or related goods affect quantity demanded or supplied. Deep comprehension of the 'why' behind each concept, combined with practice using the formulas, is essential.

I. Price Elasticity of Demand (EdE_d)

  • Definition: Measures how responsive the quantity demanded of a good is to a change in its price.

  • Formula: Ed=%Δ quantity demanded%Δ priceE_d = \frac{\%\Delta \text{ quantity demanded}}{\%\Delta \text{ price}}

    • Note: For price elasticity of demand, any and all negative signs are ignored, as the law of demand dictates an inverse relationship, making the coefficient inherently negative. We typically consider its absolute value.

Categories of Price Elasticity of Demand:

  • Perfectly Inelastic Demand

    • Coefficient Range: Ed=0E_d = 0

    • Impact of Price Change: Changes in price have absolutely no effect on the quantity demanded.

    • Demand Curve Shape: The demand curve is vertical.

  • Inelastic Demand

    • Coefficient Range: 0 < E_d < 1

    • Impact of Price Change: A rise in price increases total revenue.

  • Unit-Elastic Demand

    • Coefficient Range: Ed=1E_d = 1

    • Impact of Price Change: Changes in price have no effect on total revenue. The percent change in price equals the percent change in quantity demanded.

  • Elastic Demand

    • Coefficient Range: 1 < E_d < \text{Infinity}

    • Impact of Price Change: A rise in price reduces total revenue.

  • Perfectly Elastic Demand

    • Coefficient Range: Ed=InfinityE_d = \text{Infinity}

    • Impact of Price Change: A rise in price causes quantity demanded to fall to 00. Conversely, a fall in price causes quantity demanded to approach infinity.

    • Demand Curve Shape: The demand curve is horizontal.

II. Price Elasticity of Supply (EsE_s)

  • Definition: Measures how responsive the quantity supplied of a good is to a change in its price.

  • Formula: Es=%Δ quantity supplied%Δ priceE_s = \frac{\%\Delta \text{ quantity supplied}}{\%\Delta \text{ price}}

Categories of Price Elasticity of Supply:

  • Perfectly Inelastic Supply

    • Coefficient Range: Es=0E_s = 0

    • Impact of Price Change: Price has no effect on the quantity supplied.

    • Supply Curve Shape: The supply curve is vertical.

  • Inelastic Supply

    • Coefficient Range: 0 < E_s < 1

    • Impact of Price Change: Quantity supplied rises by a smaller percentage than the price increase.

  • Unit-Elastic Supply

    • Coefficient Range: Es=1E_s = 1

    • Impact of Price Change: Quantity supplied rises by the same percentage as the price increase.

  • Elastic Supply

    • Coefficient Range: 1 < E_s < \text{Infinity}

    • Impact of Price Change: Quantity supplied rises by a greater percentage than the price increase.

  • Perfectly Elastic Supply

    • Coefficient Range: Es=InfinityE_s = \text{Infinity}

    • Impact of Price Change: Any fall in price causes quantity supplied to fall to 00. Any rise in price elicits a quantity supplied that approaches infinity.

    • Supply Curve Shape: The supply curve is horizontal.

III. Income Elasticity of Demand (EiE_i)

  • Definition: Measures how responsive the quantity demanded of a good is to a change in consumer income.

  • Formula: Ei=%Δ quantity demanded%Δ consumer incomeE_i = \frac{\%\Delta \text{ quantity demanded}}{\%\Delta \text{ consumer income}}

Categories of Income Elasticity of Demand:

  • Inferior Good

    • Coefficient Range: Negative number ( E_i < 0 )

    • Impact of Income Change: Quantity demanded falls when consumer income rises.

  • Normal Good, Income Inelastic

    • Coefficient Range: Positive number less than 11 ( 0 < E_i < 1 )

    • Impact of Income Change: Quantity demanded rises when income rises, but not as rapidly as the income itself.

  • Normal Good, Income-Elastic

    • Coefficient Range: Positive number greater than 11 ( E_i > 1 )

    • Impact of Income Change: Quantity demanded rises when income rises, and more rapidly than the income itself.

IV. Cross-Price Elasticity of Demand (EcE_c)

  • Definition: Measures how responsive the quantity demanded of one good is to a change in the price of another good.

  • Formula: Ec=%Δ quantity demanded of Good A%Δ price of Good BE_c = \frac{\%\Delta \text{ quantity demanded of Good A}}{\%\Delta \text{ price of Good B}}

Categories of Cross-Price Elasticity of Demand:

  • Complements

    • Coefficient Range: Negative number ( E_c < 0 )

    • Impact of Price Change: The quantity demanded of one good falls when the price of the other good rises (e.g., if the price of coffee rises, the demand for cream falls).

  • Substitutes

    • Coefficient Range: Positive number ( E_c > 0 )

    • Impact of Price Change: The quantity demanded of one good rises when the price of the other good rises (e.g., if the price of Pepsi rises, the demand for Coke rises).