Finding the Price Elasticity of Demand

Calculate the price elasticity of demand using the data in Figure 1 for an increase in price from G to H. Has the elasticity increased or decreased?

Step 1. We know that:

[latex]\begin{array}{rcl}\text{Price Elasticity of Demand}& = & \frac{\text{% change in quantity}}{\text{% change in price}}\end{array}[/latex]

Step 2. From the Midpoint Formula we know that:

[latex]\begin{array}{rcl}\text{% change in quantity}& = & \frac{Q_{2} - Q_{1}}{\frac{Q_{2} + Q_{1}}{2}} \times 100\end{array}[/latex]

[latex]\begin{array}{rcl}\text{% change in price}& = & \frac{P_{2} - P_{1}}{\frac{P_{2} + P_{1}}{2}} \times 100\end{array}[/latex]

Step 3. So we can use the values provided in the figure in each equation:

[latex]\begin{array}{rcl}\text{% change in quantity}& = & \frac{1,600 - 1,800}{\frac{1,800 + 1,600}{2}} \times 100 \\ & = & \frac{-200}{1,700} \times 100 \\ & = & -11.76\end{array}[/latex]

[latex]\begin{array}{rcl}\text{% change in price}& = & \frac{130 - 120}{\frac{120 + 130}{2}} \times 100 \\ & = & \frac{10}{125} \times 100 \\ & = & 8.0\end{array}[/latex]

Step 4. Then, those values can be used to determine the price elasticity of demand:

[latex]\begin{array}{rcl}\text{Price Elasticity of Demand}& = & \frac{\text{% change in quantity}}{\text{% change in price}} \\ & = & \frac{-11.76}{8} \\ & = & 1.47\end{array}[/latex]

Therefore, the elasticity of demand from G to H 1.47.  (Note, again, the calculation would normally come out negative, but we've implicitly taken the absolute value.) The magnitude of the elasticity has increased (in absolute value) as we moved up along the demand curve from points A to B. Recall that the elasticity between these two points was 0.45. Demand was inelastic between points A and B and elastic between points G and H. This shows us that price elasticity of demand changes at different points along a straight-line demand curve.

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 Figure 1, 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.