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101 Concepts for the Level I Exam

Concept 17: Price, Income and Cross-Price Elasticities of Demand


Elasticity of demand is measured as a ratio of percentage change in quantity demanded to a percentage change in other variables.

Own-price elasticity

  $Own\ price\ elasticity={{\%\ change\ in\ quanitity\ demanded}\over {\%\ change\ in\ own\ price}}$

  • Own-price elasticity of demand is usually always negative.
  • If |own price elasticity| > 1, then demand is elastic.
  • If |own price elasticity| < 1, then demand is inelastic.
  • If own price elasticity = -1, then demand is unit, or unitary, elastic.

Income elasticity

  $Income\ elasticity={{\%\ change\ in\ quanitity\ demanded}\over {\%\ change\ in\ income}}$

  • If income elasticity > 0, then the good is a normal good.
  • If income elasticity < 0, then the good is an inferior good.

Cross price elasticity

  $Cross\ price\ elasticity={{\%\ change\ in\ quanitity\ demanded}\over {\%\ change\ in\ \ price\ of\ related\ good}}$

  • If cross price elasticity > 0, then the related good is a substitute.
  • If cross price elasticity < 0, then the related good is a complement.

A demand function for chairs is as follows:

     $$Q_{chairs}=200-2P_{chairs}+0.05Income-0.8P_{tables}+{1.2P}_{stools}$$

At current average prices, a chair costs $50, a table costs $100 and a stool costs $30. Average income is $5,000. Calculate the income elasticity of demand for chairs.

Solution:

Substitute current values for the independent variables (except income)

     $$Q_{chairs}=200-2(50)+0.05Income-0.8(100)+1.2(30)$$

     $$Q_{chairs}=56+0.05Income$$

The slope of income is 0.05

For an income of $5,000; Qchairs = 306

     $$Income\ elasticity={{I_0}\over {Q_0}}\times {{\italic{\Delta}Q}\over {\italic{\Delta}I}}={{5,000}\over {306}}\times 0.05=0.82$$

Factors impacting the own price elasticity of demand for a product include:

  • Substitutes: If the number of substitutes for this product is high, then elasticity will be high.
  • Portion of total budget: If the portion of total budget spent on this product is high, then elasticity will be high.
  • Time horizon: If the time horizon we consider is long, then elasticity will be high. This is because consumers will have enough time to respond to changes in the price of this product.
  • Discretionary (optional) versus non-discretionary (necessary): If the product is discretionary rather than non-discretionary, then the elasticity will be high.