Let’s begin with the basic analysis. It’s Tuesday, and you have something on offer for Saturday night. You might be a hotel owner and you have vacancies for that night, your airline might have a scheduled flight from Tulsa to Kansas City with some seats still available, or you might be putting on a show that has not yet sold out. In each of these cases, you are certainly charging a current price well above marginal cost (the cost to you of putting a family in the otherwise empty hotel room, or getting a extra passenger on the flight, or directing a patron to her seat for your show). And if you end up not making a sale for that Saturday night the potential revenue is lost to you forever – you don’t get to try to sell the ticket for that Saturday night after the fact. Running a theater is like running a clothing store where every night after closing, moths come out and devour your entire inventory, which must then be restocked.
If you are in a situation where you must, in advance, post a price (or menu of prices for quality of seat, student discounts, etc.) that is not changeable, then it is not necessarily the case that the prices you charge will fill the theater. At any potential set of prices, you would ask, “how much additional revenue would we gain if we lowered our prices a smidgen in order to sell one more seat [economists refer to this number as marginal revenue]?” If you would gain an amount greater than marginal cost, then you should go ahead and lower the price: you gain more than it will cost you. But if you would not gain an amount greater than marginal cost, or if you would actually lose revenue (which would occur if you had to lower the posted unchangeable price by a great deal just to sell one more ticket), then you would not lower the price, even if it would leave you with some empty seats.
But what if your price is variable, as it is for the hotel owner, the airline, and, for those who practice dynamic pricing, theaters? Suppose the ticket price you have been offering so far is $20, and this price was chosen as the one that, before tickets went on sale, but with the information you had at the time, would be the price that would in the end maximize net revenue. To keep it simple (and fairly realistic), suppose there is no marginal cost to putting someone in a seat – the ushers are there anyway. As tickets have been selling you are gaining new information about the popularity of the show. For Saturday night, row G seat 7 remains unsold. You reckon that if you keep the price at $20, the probability is x% that the seat will sell, and you also believe that if you were to now lower the price to $18, the probability the seat will sell rises to y%. Your expected revenue from G-7 if you keep the price constant is $20 times x%. Your expected revenue if you lower the price is $18 times y%. If the former is the bigger number, keep the price constant. If the latter is the bigger number, lower the price. If x is something close to 100% (you are anticipating a sellout), then lowering the price is not going to make much sense, since y is going to be barely different from x.
You can do the same exercise for whether to raise the price. Raising the price lowers the chance the unsold seat will sell, and you are trading off the increased price if you do sell with the increased risk of not selling the ticket.
That’s the calculus of the problem. What are the nuances?
First, recall an earlier post of mine of why dynamic pricing is rarely used – it entails the problem of potentially signalling low quality of the product when price is reduced (thus killing sales altogether), and it has the problem of unwelcome surprises for customers when the price is raised. This is especially a problem for theaters since price changes, and differential prices for different customers, will be visible in a way they are not for hotels and airlines.
Second, remember the goal is to get the menu of prices right at the beginning. Changing prices mid-stream is something to do when demand is not going as anticipated, it should not be something planned upon. If a dynamic-pricing using organization is always finding itself needing to lower prices during the final week of sales, then it needs to revisit how it is setting initial prices, and why the initial price is biased upwards.
Third, and related to the second point, if price changes become a regular occurrence and in a predictable direction, consumers will respond by anticipating when prices are likely to be lower. The last thing you need your audience to think is that they just need to wait until the last week before the performance to buy their seats.
Finally, if used prudently, there is nothing inherently wrong with nonprofits using dynamic pricing – there is no rule I know of that states commercial firms can change prices in response to new information about demand but nonprofit prices are unchangeable. Nonprofits need revenues, and if admission prices are going to be charged at all, there is no compelling reason that the initial price must be the final price regardless of revealed demand.