In economics, it’s generally helpful to have some measure of how responsive consumers and producers are to changes in price (or income, or whatever, but mainly price). In some cases, consumers will just grin and bear a price increase, while in other situations they will avoid the more expensive product like the plague. Similarly, sometimes suppliers will greatly increase production when they see higher prices to be had, and sometimes they are stuck with a certain level of capacity and thus an upper limit on output (at least in the short term). Also, economists find that people often think about these decisions in terms of relative price changes rather than absolute ones. For example, people report that they are much more willing to drive out of their way to save $10 on a $30 calculator than to save $10 on a $2000 computer, even though they are saving the same $10 in either case. (Yes, this is an actual study. The numbers may not be exactly accurate, since I couldn’t find a good reference online, but the right idea is there.)
As such, economists use the concept of elasticity, which is defined as a ratio of relative changes. For example, price elasticity of demand is the percent change in the quantity demanded of an item in response to a one percent change in price. The price elasticity of supply is the percent change in the quantity supplied by firms in response to a one percent change in price. The income elasticity of demand is the percent change in quantity demanded of an item in response to a one percent change in income. And so on. To summarize mathematically:
- price elasticity of demand = % change in quantity demanded / % change in price (Note that this would mathematically always be a negative number because people want less of things when they get more expensive. Despite this fact, price elasticity of demand is usually reported as a positive number, i.e. the absolute value of this quantity.)
- price elasticity of supply = % change in quantity supplied / % change in price
- income elasticity of demand = % change in quantity demanded / % change in income
If you want, you can think of a rubber band analogy here: the change in price or income is the force on the rubber band, and elasticity measures how much the rubber band stretches in response to that force. If the rubber band stretches a lot, it is said to be very elastic, and if it stretches only a tiny bit, it is said to be very inelastic. In this way, bigger numbers for the quantities above are said to give higher elasticity. Specifically, elasticity estimates greater than 1 are said to be elastic and elasticity estimates less than 1 are said to be inelastic.
This is all cute mathematically, but why am I telling you this? As it turns out, elasticity has a fun application when it comes to changes in revenue. Let’s say, hypothetically of course, that you are selling concert tickets. Consider the following question: If you lower the price of your tickets, is your revenue going to go up or down? The answer isn’t entirely obvious, since there are two competing effects in play. On the up side, you’re going to be selling more tickets. On the down side, you’re going to be selling ALL of the tickets at a lower price, not just the new ones. So which effect dominates? Turns out that the answer has to do with elasticity:
- If your demand is elastic (i.e. greater than 1) when you calculate it moving from the old price to the new price, then the percentage increase in sales is greater than the percentage decrease in price. For example, this would be the case if you decreased your price by 10 percent and doubled (i.e. increased by 100 percent) your quantity sold. This, not surprisingly given the numbers in the example, is going to lead to increased revenue.
- If your demand is inelastic (i.e. less than 1) when you calculate it moving from the old price to the new price, then the percentage increase in sales is LESS than the percentage decrease in price. This would be the case if, for example, you cut your price in half (i.e. reduced by 50 percent) and only got, say, a 10 percent bump in quantity sold. This is going to lead to a decrease in revenue.
Let’s look at what happened with Live Nation when it offered 2 for the price of 1 concert tickets:
After seeing a sales increase of 300% over the previous weeks’ promotions, with fans saving more than $350,000, Live Nation announced today that they will continue there[sic] 2-for-1 concert ticket offer for a second week. The offering will expand to more than 450 shows and 250,000 tickets at its company owned nightclubs including the Filmore and House of Blues chains.
(Sidenote: I object to the use of the word “saving” above, since fans as a group are spending more than they were before. This “savings” assumes that all of the people would have bought the tickets at the higher price, which is clearly not the case. If I buy something at $10 that I wouldn’t have purchased at $20, I have in fact spent $10, not saved $10. Just saying.)
Let’s see. 2-for-1 is essentially a 50 percent price reduction. It’s unclear from the article whether by “sales increase” they mean unit sales or dollar sales. If they mean dollar sales, then clearly the price drop increased revenue. If they meant unit sales, then the elasticity of demand was 300 percent divided by 50 percent, or 6. This number would also imply that Live Nation’s revenue increased. (Not surprising, since it’s selling 4 times as many tickets at half the price.)
Given this analysis, why wouldn’t a company lower its prices whenever it faces elastic demand? The simple answer is that it’s because firms generally care about profits and not just top line revenue, and the analysis above doesn’t take production costs into account. (In other words, what is revenue-maximizing and what is profit-maximizing need not be the same. The profit-maximizing quantity is almost always lower.) But let’s think about the logistics of the concert tickets. What is the marginal cost of a concert ticket? In other words, what is the variable cost associated with one more concert ticket? That would be virtually zero, since the venue, the band, the ticket systems, etc. are all more or less fixed costs. In this way, Live Nation (along with the related concert businesses) actually has a pretty close coincidence between what is revenue-maximizing and what is profit-maximizing.
There is, however, one small catch here. Live Nation can’t just increase its ticket sales without bound, since it is limited by the capacity of its venues. Therefore, in order to have this 2-for-1 deal be worth it, it would have had to in the best case scenario been only selling half of its capacity at full price. In fact, if sales increased 300 percent, this would imply that they had been selling at most one-quarter of its capacity. Yikes. Maybe I should do my part and remember to purchase those Train* tickets.
* Yes, I realize that it’s not 2001 and I am no longer a college co-ed, but I like what I like, okay? Besides, Pat Monahan does a sick cover of Ramble On. Not surprising, given that he started out in a Led Zeppelin cover band.