ELASTICITY AND TOTAL REVENUE ALONG A LINEAR DEMAND CURVE
Although some demand curves have an elasticity that is the same along the entire curve, this is not always the case, An example of a demand curve along which elasticity changes is a straight line. A linear demand curve has a constant slope. Recall that slope is defmed as “rise over run,” which here is the ratio of the change in price (“‘rise”) to the change in quantity (“run”). This particular demand curve’s, slope is constant because each $1 increase in price causes the same two unit decrease in the quantity demanded.
Even though the slope of a luiear demand curve is constant, the elasticity is not. The reason is that the slope is the ratio of changes 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, 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 $1. 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 $4, demand is exactly unit elastic, and total revenue is the same at these two prices.
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