## Calculating the Price Elasticity of Supply

Assume that an apartment rents for $650 per month and at that price 10,000 units are rented as shown in this figure. When the price increases to $700 per month, 13,000 units are supplied into the market. By what percentage does apartment supply increase? What is the price sensitivity?

**Price Elasticity of Supply**

Using the **Midpoint Method**,

\(\begin{array}{rcl}\text{% change in quantity}& =& \cfrac{13,000–10,000}{(13,000+10,000)/2}× 100\\ & =& \cfrac{3,000}{11,500}× 100\\ & =& 26.1\\ \text{% change in price}& =& \cfrac{$700–$650}{($700+$650)/2}× 100\\ & =& \cfrac{50}{675}× 100\\ & =& 7.4\\ \text{Price Elasticity of Supply}& =& \cfrac{26.1\%}{7.4\%}\\ & =& 3.53\end{array}\)

Again, as with the elasticity of demand, the elasticity of supply is not followed by any units. Elasticity is a ratio of one percentage change to another percentage change—nothing more—and is read as an absolute value. In this case, a 1% rise in price causes an increase in quantity supplied of 3.5%. The greater than one elasticity of supply means that the percentage change in quantity supplied will be greater than a one percent price change. If you’re starting to wonder if the concept of slope fits into this calculation, read the following Clear It Up box.

### Is the elasticity the slope?

It is a common mistake to confuse the slope of either the supply or demand curve with its elasticity. The slope is the rate of change in units along the curve, or the rise/run (change in y over the change in x). For example, in this figure, each point shown on the demand curve, price drops by $10 and the number of units demanded increases by 200. So the slope is –10/200 along the entire demand curve and does not change. The price elasticity, however, changes along the curve. Elasticity between points A and B was 0.45 and increased to 1.47 between points G and H. Elasticity is the *percentage* change, which is a different calculation from the slope and has a different meaning.

When we are at the upper end of a demand curve, where price is high and the quantity demanded is low, a small change in the quantity demanded, even in, say, one unit, is pretty big in percentage terms. A change in price of, say, a dollar, is going to be much less important in percentage terms than it would have been at the bottom of the demand curve. Likewise, at the bottom of the demand curve, that one unit change when the quantity demanded is high will be small as a percentage.

So, at one end of the demand curve, where we have a large percentage change in quantity demanded over a small percentage change in price, the elasticity value would be high, or demand would be relatively elastic. Even with the same change in the price and the same change in the quantity demanded, at the other end of the demand curve the quantity is much higher, and the price is much lower, so the percentage change in quantity demanded is smaller and the percentage change in price is much higher. That means at the bottom of the curve we’d have a small numerator over a large denominator, so the elasticity measure would be much lower, or inelastic.

As we move along the demand curve, the values for quantity and price go up or down, depending on which way we are moving, so the percentages for, say, a $1 difference in price or a one unit difference in quantity, will change as well, which means the ratios of those percentages will change.