Elasticities

Perloff 3.1-4. WB 3.
You do not need to remember which Greek letter is associated with which elasticity. In questions, elasticities will always be referred to by name, not symbol.

# The general formula

Suppose X increases by 1%; the “X elasticity of Y” is the percent change in Y that results (divided by 100).

# Price elasticity of Demand

The (own-) price elasticity of Demand is given by any of the following formulas:

(1)
\begin{align} \varepsilon=\frac{\text{% change in }Q}{\text{% change in P}}=\frac{\Delta Q/Q}{\Delta P/P}=\frac{\Delta Q}{\Delta P}\times\frac{P}{Q}=\frac{1}{slope}\times\frac{P}{Q} \end{align}
(2)
\begin{align} \varepsilon=\frac{1}{slope}\times\frac{P}{Q} \end{align}

where $\Delta P$ and $\Delta Q$ are small changes in the price and quantity that keep you on the Demand curve. The term ${\Delta Q}/{\Delta P}$ is one over the slope of the Demand curve (recall that P is on the y-axis). This slope is negative (by the Law of Demand), so the price elasticity of Demand is always negative.

# Other elasticities

The calculation of other elasticities is similar.

# Applying elasticities

• The (own-price) elasticities of demand $\varepsilon$ and of supply $\eta$ are used in evaluating how much producers and consumers are hurt by a per-unit tax.
• The elasticity of demand $\varepsilon$ is also used in finding the monopoly price markup.
• The income elasticity of Demand $\xi$ tells us whether a good is normal or inferior and what share of a consumer's spending goes towards it.
• The XY cross-price elasticity of Demand $\varepsilon_{XY}$ tells us whether two goods are complements or substitutes, and to what degree.

# More resources

• Krugman and Wells, Chapter 5 “Elasticity”