Business revenue and elasticities

SUMMARY: If price elasticity of a good is inelastic (<1), then a firm can increase revenue by raising price.  If the price elasticity of a good is elastic (>1), then a firm can increase revenue by lowering price.

Understanding what the price elasticity of demand is can be confusing.  You may also be asking yourself why you need to know it in the first place.  But understanding what the price elasticity of demand measure is for a specific good can be important to business and marketing people when they are trying to maximize their revenue.  Take for example the common problem of choosing the price at which you want to sell a good.

Begin with a firm that already has its price set.  It knows what the price elasticity of demand is, and has to make a judgement call on whether to a price increase or decrease will increase their revenue.

First we have to remember the equation for the price elasticity of demand:
Percent change in quantity/percent change in price = price elasticity of demand.

So we know that if the percent change in quantity is greater than the percent change in price, then we
will get a number that is greater than one (in absolute value terms, because it should be negative).  This would mean that the good in question is elastic, because as we change the price by a certain percentage, we see an even larger percentage change in quantity being demanded (it is elastic because it is responsive).  Likewise, the good is inelastic if we can change the price a lot and we see little percent change in the quantity being demanded (this would give us a value much closer to zero for the price elasticity of demand).

So let's go through an example.  If the price elasticity of demand for a good is -2.5 then a price increase of 30% means that we will see a quantity decrease of 75% (which is 30%*-2.5).  Does this sound like a good idea?  What happens is that you are getting a 30% higher price on the goods you do sell, but you are losing 75% of your sales!  This is a bad idea, because your total revenue will go down, lets plug in some numbers to demonstrate.

If your original price is $10, and your original sales were 100, then your revenue would be $1,000 (10*100).  Now lets raise prices by 30%, and lower quantity sold by 75%.  Our new price is $13, and our new quantity sold is 25.  So our new revenue is $325 (13*25) which is significantly lower than our original revenue.

What is we instead lower prices by 30%?  Our new price would be $7, and our new sales would be 175.  Thus, our new revenue would be $1,225 (7*175) which is higher than our original.

This means that when the price elasticity of demand is elastic then we need to lower prices in order to increase total revenue.  However, when price elasticity of demand is inelastic we can raise prices in order to increase total revenue.  And when the price elasticity of demand is unit elastic, any change in price will reduce revenue because we have already hit the sweet spot.