elasticity

Elasticities

• Key Phrases/Concepts
  • Price elasticity of demand
  • Price elasticity of supply
  • Income elasticity of demand
  • Cross-price elasticity of demand
  • Tax incidence

Price Elasticity of Demand

$${ϵ}_X=\frac{\%\Delta Q_X}{\%\Delta P_X}$$

• Probably a negative value.
• Categories
  • Elastic = $|{ϵ}_X|>1$
  • Inelastic = $|{ϵ}_X|<1$, increasing the price results in larger total revenue
  • Unitary = $|{ϵ}_X|=1$
• Factors affecting elasticity
  • Goods with more substitutes are more elastic.
  • In general, the higher the price, the more elastic.
  • In general, the longer the time frame, the more elastic, as we have time to adjust and to find substitutes.
• Demand curve
  • Perfectly inelastic = vertical line; Perfectly elastic = horizontal line
  • As we move along the demand curve, the elasticity changes as well.

Other Elasticities

$$\frac{\%\Delta y}{\%\Delta x}$$

in which $x$ and $y$ can be anything to measure other elasticities.

$$\frac{\%\Delta Q}{\%\Delta I}$$

• The Income Elasticities
  • Normal goods = Positive income elasticity
  • Inferior goods = Negative income elasticity

$$\frac{\%\Delta Q_x}{\%\Delta P_y}$$

• The cross-price elasticities
  • Complement goods = Negative cross-price elasticity
  • Substitute goods = Positive cross-price elasticity

Price Elasticity of Supply

$$\frac{\%\Delta Q_X}{\%\Delta P_X}$$

in which $Q_X$ is the quantity supplied.

• Supply curve
  • Perfectly elastic = vertical line
  • Perfectly inelastic = horizontal line
• More elasticity = More rapidly change in production

An Application: The Incidence of Taxation

• Per-Unit Taxes

• Tax is a pain imposed on the participants of a relationship

  • The person who is the most in love, who is the most in love, i.e. who has the most inelastic demand, will do most of the travelling.
  • Such one will share most of the burden

• Calculate the burden

  • Supposed imposed on the buyers
  • Demand curve shifts down (shifts left)
  • Price goes down, hence some of the burden is imposed on sellers
  • Or, go another way around, supposed imposed on the sellers

Which side of the market is more inelastic? That side will bear most of

the burden. But again, elasticity changes in different time frame.

Conclusion

• Legalization of drugs?
  • If the demand is really inelastic, cutting the supply will not decrease the drugs traded a lot, but will increase the price by a lot.
  • If that’s the case, the revenue of the drug dealers actually increases a lot!
  • Solution: cut the supply SIGNIFICANTLY