C.2 Degrees of Elasticity
There are two important aspects of any measure of elasticity: its sign, and its magnitude.
The sign of an elasticity indicates whether the two variables are positively related or negatively related. For example, we generally assume that an increase in the price of a good results in a decrease in the quantity demanded of that good; therefore demand elasticity of the sort we looked at above will generally be negative. However, if we think about how an increase in the price of a good affects the demand for some other good, the sign becomes important: depending on whether the two goods are complements or substitutes, it might be negative or positive.
The magnitude of elasticity — specifically, whether it is greater or less than one — describes whether a change in the exogenous variable results in a proportional, less than proportional, or greater than proportional change in the endogenous variable. That is, we can characterize elasticity as follows:
- Perfectly inelastic ($|\epsilon| = 0$ or $|\% \Delta Y| = 0$): the endogenous variable does not change when the exogenous variable increases
- Inelastic ($|\epsilon| < 1$, or $|\% \Delta Y| < |\% \Delta X|$): the percentage change in the endogenous variable is less than the percentage change in the exogenous variable.
- Unit elastic ($ |\epsilon| = 1$, or $|\% \Delta Y| = |\% \Delta X|$): the percentage change in the endogenous variable is the same as the percentage change in the exogenous variable
- Elastic ($|\epsilon| > 1$, or $|\% \Delta Y| > |\% \Delta X|$): the percentage change in the endogenous variable is greater than the percentage change in the exogenous variable
- Perfectly elastic ($|\epsilon| = \infty$, or $|\% \Delta X| = 0$): any change in the exogenous variable would cause the exogenous variable to change “infinitely” in percentage terms (usually this means going from a positive number to zero or vice versa)