Price Elasticity  The Significance of Revenue
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Price Elasticity  The Significance of Revenue
So far, we have looked at how to calculate the price elasticity of demand and illustrated the difference between elastic and inelastic demand. This is all important 'bread and butter' stuff, but examiners want you to show that you can discuss the significance of these values with reference, in particular, to a firm's revenue. What is the point, after all, of a firm knowing the elasticity of demand for the product he sells? The answer is that if he can assess what the change in his sales will be for a given change in the price of his product, and then he can work out the change in his revenue.
Below is the question about the greengrocer and his bananas from earlier. The question has now been extended to consider the effect on revenue:
A greengrocer decides to cut the price of his bananas from 40p per lb to 32p per lb. The price elasticity of demand for this product is 2. He currently sells 80lbs of bananas a day. How many will he sell after the price cut? What is the effect of this decision on the greengrocer's revenue?
We already know the answer to the first question. The greengrocer's sales increase to 112lbs of bananas. But what will happen to his revenue?
Revenue before the price cut:  Revenue = price × quantity sold = 40p × 80lbs = £32.00 
Revenue after the price cut:  Revenue = price × quantity sold = 32p × 112lbs = £35.84 
So the price cut causes revenue to increase. This may seem odd at first glance, but remember that the demand for bananas was 2, which is relatively elastic. This means that the rise in demand as a result of the price cut was proportionately higher than the fall in price. In other words, although the greengrocers receives 8p less for each of the 80lbs that he used to sell, he sells so many more bananas at the new lower price that his total revenue rises. I think that this is best illustrated with a diagram:
Notice that the demand curve drawn is relatively flat, signifying that the demand for bananas is relatively elastic. The red box marked 'loss' represents the loss in revenue due to the fact that the first 80lbs of bananas are sold at a lower price. The green box marked 'gain' represents the extra revenue received as a result of selling 32 extra lbs of bananas at the lower price. It is fairly easy to see that the 'gain' box is larger than the 'loss' box, so the greengrocer's total revenue has increased.
What would have happened if the greengrocer (not understanding elasticities!) had tried to increase his revenue by raising the price to, say, 44p per lb (ceteris paribus)?
Revenue before the price increase:  Revenue = price × quantity sold = 40p × 80lbs = £32.00 
Revenue after the price increase:  Revenue = price × quantity sold = 44p × 64lbs = £28.16 
He sells 20% fewer lbs of bananas.
What are the implications of price changes if a firm faces a relatively inelastic demand curve? The diagrams below show us what they are:
Petrol is a good with relatively inelastic demand. Let us assume that the value of the elasticity is 0.5, the initial price is 80p per litre and this gives sales of 4000 litres per day.
The diagram on the left shows us what happens to the forecourt's revenue when the price is cut to 72p per litre. This 10% cut in the price will lead to an increase in demand of only 5% (as the elasticity is only 0.5). The new demand will be 4200 litres. So the change in revenue can be calculated:
Revenue before the price cut:  Revenue = price × quantity sold = 80p × 4000 litres = £3200 
Revenue after the price cut:  Revenue = price × quantity sold = 72p × 4200 litres = £3024 
This fall in total revenue is illustrated in the diagram, where the 'loss' box is much bigger than the 'gain' box.
The diagram on the right shows us what happens if the forecourt manager decides to raise the price to 88p per litre. This 10% rise in the price will lead to a fall in demand, but by only 5%. The new demand will be 3800 litres. Again, we can calculate the change in revenue:
Revenue before the price cut:  Revenue = price × quantity sold = 80p × 4000 litres = £3200 
Revenue after the price cut:  Revenue = price × quantity sold = 88p × 3800 litres = £3344 
This rise in total revenue is illustrated in the diagram on the right, where the 'gain' box is much bigger than the 'loss' box.
So, to summarise:
Value of the elasticity  Price rise or cut?  What will happen to the quantity demanded?  Will total revenue rise or fall?  

E_{d} = 0  Price rise  The demand curve is vertical, so demand remains the same but with a higher price.  Rise  
(Perfectly inelastic)  Price cut  The demand curve is vertical, so demand remains the same but with a lower price.  Fall  
0 < E_{d} 1  Price rise  The demand curve is relatively steep, so the fall in demand will be proportionately smaller than the rise in price.  Rise  
(Relatively inelastic)  Price cut  The demand curve is relatively steep, so the rise in demand will be proportionately smaller than the cut in price.  Fall  

Price rise or a price cut  The demand curve is a parabola, so the change in price (up or down) will be proportionately the same as the change in demand.  Unchanged Revenue  
1 < E_{d} < ∞  Price rise  The demand curve is relatively flat, so the fall in demand will be proportionately larger than the rise in price.  Fall  
(Relatively elastic)  Price cut  The demand curve is relatively flat, so the rise in demand will be proportionately larger than the cut in price.  Rise 
Note that infinite elasticity has not been included in the table. In is assumed that the price must remain constant when the demand curve is horizontal.