Dynamic pricing and market segmentation at the theatre (and the hospital)

This post is about theatre pricing, from a unlikely source. Today’s New York Times has a piece by Austin Frakt on hospital pricing, and whether and how changes in funding of patients through public sector programs might change hospital charges to privately insured patients. Mid-way through, the article looks for an analogy from the arts:

The theory that hospitals charge private insurers more because public programs pay less is known as cost shifting. What underlies this theory is that a hospital’s costs — those for staff, equipment, supplies, space and the like — are fixed. A procedure or visit simply takes a certain amount of time and requires a specific set of resources. Therefore, if Medicare, say, does not pay its full share of those costs, a hospital is forced to offset the loss with higher prices demanded of private insurers. …

[A] weakness of the cost shifting theory is that it runs counter to basic economics. Hospitals that maximize profits, or even maximize revenue to fund charity care, would not raise private prices in response to lower public ones. In fact, such a hospital would already be charging the highest possible prices to all payers. And, instead of raising them to one insurer if another paid less, they’d do exactly the opposite. Prices charged to two types of customers would move together, not in opposition, for the same reason it does so in other industries.

If a theater finds that bulk ticket purchasers are unwilling to pay as high a price as expected — perhaps because demand by tourist groups and corporations is down — it wouldn’t raise ticket prices for individual purchasers. Because it had filled fewer seats than anticipated from bulk sales, it would reduce prices to others in order to increase sales volume. With seats to fill, when bulk purchasers pay less, so do individual ones. Likewise, retailers charge lower prices to clear inventory, not higher ones to make up for less revenue from early purchasers. Economists have shown that the same logic applies to hospitals: They shift volume from Medicare and Medicaid to privately insured patients by lowering private prices in response to lower public ones — a spillover effect.

On twitter, Jacob Bacharach takes issue:

Theaters may offer targeted discounts to fill vacant seats, but very rare to see broad discounting across price cats. post-onsale.

In fact, often see dynamicpricing: high-price seats *increase* even with low overall sales, while cheap seats further discount.

Mr Bacharach raises an interesting point. Let’s consider two sorts of cases.

First, let’s look at the example used in the Times. Bulk sales and individual sales are fairly separate market segments. With any segmented market, optimal prices are set according to the demand conditions in each of the individual markets. If it is revealed that demand is lower than had been anticipated in one market, it does not necessarily mean it is down in all segments. The strategic price-setter will respond to new information in the segment where shifts in demand have been revealed, but unless that signals something about other segments she won’t change prices in other segments, where prices are already at their optimal level (note that doesn’t mean ‘highest possible prices’ as the Times story has it – I’m not even sure what that phrase means in practical terms).

Suppose I have published a textbook on arts pricing, to be sold in Australia and Canada. Suppose I discover there is a competing text in Australia for my book, specific to Australia, lowering demand for my book there. That might cause me to discount the price of the book in Australia. But unless there is news about demand for my book in Canada I have no reason to adjust my Canadian price.

Second let’s consider Jacob Bacharach’s case, between high-priced seats and cheap seats. This is slightly different than market segmentation, because the demand for one type of seat is dependent in part on the quality and price of all the other sorts of seat. My willingness to pay for a seat in the orchestra section depends in part on the quality and price of balcony seats. Suppose, as an example, we thought we had the price differential set pretty well to maximize ticket revenues from a show, but balcony seats are selling less well than we had expected, while sales of orchestra seats are on target. A decision to discount balcony tickets will decrease demand for orchestra seats at current prices – customers previously on-the-fence between orchestra and balcony seats will now lean towards purchasing balcony. Other things equal, that will lead to a decision to look at discounting all seats.

So, I think Jacob Bacharach is correct to point to a flaw in the reasoning of Austin Frakt at the Times, but the good seats / bad seats dynamic pricing problem is not the best example to show that.