## A Linear Demand Curve

Let's examine how elasticity varies along a linear demand curve, as shown in Figure 4. We know that a straight line has a constant slope. Slope is defined as "rise over run," which here is the ralio of the change in price ("rise") to the change in quantity ("run")- This particular demand curve's slope is constant because each increase in price causes the same two-unit decrease in the quantity demanded-

Even though the slope of a linear demand curve is constant, the elasticity is not. This is true because the slope is the ratio of dtartge* in the two variables, whereas the elasticity is the ratio of percentage changes in the two variables- You can see this by looking at the table in Figure 4, which shows the demand schedule for the linear demand curve in the graph. The table uses the midpoint method to calculate the price elasticity of demand. At points with a low price and high quantity, the demand curve is inelastic. At points with a high price and low quantity, the demand curve is elastic.

The table also presents total revenue at each point on the demand curve. These numbers illustrate the relationship between total revenue and elasticity. When the price is 51, for instance, demand is inelastic, and a price increase to \$2 raises total revenue. When the price is \$5, demand is elastic, and a price increase to \$6 reduces total revenue. Between \$3 and M- demand is exactly unit elastic, and total revenue is the sime at these two prices-

The linear demand curve illustrates that the price elasticity of demand need not be the same a I all points on a demand curve. A constant elasticity is possible, but it is not always the case. 