# How to calculate expenditure elasticity

The expenditure elasticity is a measurement of how expenditure on a good changes in response to a price change. The formula for the expenditure elasticity $\epsilon$ is defined:

$\quad \epsilon = \frac{\frac{P_1 X_1 - P_0 X_0}{P_0 X_0}}{\frac{P_1 - P_0}{P_0}}$

where $P_1$ and $X_1$ is the price and quantity of good $X$ in period 1 and $P_0$ and $X_0$ is the price and quantity in period 0.

The expenditure elasticity is different to the usual measures of elasticity in that it measures how expenditure changes in response to a price change instead of how the quantity of a good changes in response to a price change. In essence, the expenditure elasticity measures how much consumers increase or decrease their spending after a price increase.

If the expenditure elasticity is positive, the total expenditure on good X increases after a price increase.

If the expenditure elasticity is negative, the total expenditure on good Y decreases after a price increase.

Consider the following hypothetical sales data presented in the table below

 Price Quantity Expenditure $2 8$16 $4 6$24 $6 4$24 $8 2$16

We can calculate the expenditure elasticity when the price increases from $2 to$4 as follows:

$\quad \epsilon = \frac{\frac{24-16}{16}}{\frac{4-2}{2}}$

$\quad \epsilon = 0.5$

The expenditure elasticity is larger than zero, which is confirmed by the fact that expenditure clearly rose when the price increased from $2 to$4.

We can also calculate the expenditure elasticity when the price increases from $4 to$6, as follows:

$\quad \epsilon = \frac{\frac{24-24}{24}}{\frac{6-4}{4}}$

$\quad \epsilon = 0$

Since the expenditure did not change, the expenditure elasticity is 0.

Finally, if the price increases from $6 to$8 we can calculate the expenditure elasticity as

$\quad \epsilon = \frac{\frac{16-24}{24}}{\frac{8-6}{6}}$

$\quad \epsilon = -1$

In this case, the expenditure elasticity is negative since expenditure decreased when the price increased.

* Usually