Chapter 7.1 Elasticity & Revenue
The link between elasticity and revenue:
Revenue is defined as price times quantity. A natural question we might ask is how changes in a firm’s revenues are affected by price elasticity of demand. The key intuition to develop is that the impact of a price change on revenue depends on whether the quantity or price effect are stronger.
Falling prices will exert downward pressure on revenue but at the same time by the law of demand we expect quantity to be rising which exerts upward pressure on revenue. If prices fall more than quantity rise, revenue falls. This occurs precisely when demand is inelastic. If prices fall less than quantity rises, revenue rises. This occurs precisely when demand is elastic. Simply put:
In order to increase revenue you need to:
Increase prices if demand is inelastic (less sensitive to that price increase)
Decrease prices if demand is elastic (more sensitive to that price increase)
This can be more easily seen through a simple numerical example: Demand, revenue, and elasticity for the demand curve: P=10 - Q. I’ve built four columns. The first two columns are just listing price and quantity points from this equation. The third column is revenue, computed by multiplying the price by the quantity. The fourth column gives the elasticity computed at the particular point specified by the associated price and quantity using the point elasticity formula introduced above.
Sometimes it can be helpful to see this depicted on a graph as well. My picture shows the demand curve P=10-Q plotted in the upper panel and its corresponding revenue curve plotted in the lower panel. Total revenue is given by the formula Revenue = P*Q and in this case we have Revenue = (10 - Q)*Q . For a linear demand curve, the total revenue curve will always be a downward opening quadratic. We see the revenue maximizing quantity is Q=5 which corresponds to the midpoint of the demand curve. Over smaller quantities demand is elastic, over larger quantities demand is inelastic. Over smaller quantities revenue increases as quantity rises (which requires that price falls). Over larger quantity revenue decreases as quantity rises (which requires that price falls).
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