Wednesday, February 18, 2009

The Power of Discriminant Pricing

Imagine that every time you went shopping, prices of the items you bought depended on your ability to pay. If you were flush with cash, a cheeseburger might be $7, if not, you might get it for $5.50. It sounds terribly unfair, doesn't it?

Now think of the same question in a different context. The public schools that our kids attend typicially get a large portion of their funds from property taxes. But this tax depends on the value of the property, which is a good proxy for ability to pay. Rich folks live in McMansions and pay a lot more than the owner of a more modest home. Is this fair? It's the same question.

It's easy to see the downside (unfairness) aspect of this discriminant pricing, and perhaps that is psychological. But think for a moment about the inherent cost of fixed pricing. Imagine that you want a soft drink, but only have $.50 in your pocket. The machine requires $.55. It won't give you the time of day unless you pay full price. Suppose, however, that it were sentient, and you could negotiate with it. You could sometimes pay a little more and sometimes a little less, perhaps averaging around $.55. Wouldn't that be more efficient for all concerned? You get more soft drinks when you want them, and the vendor has a steadier cash flow. If this were done to all consumers, not just you, the average price of the soda could perhaps even be lowered because of the increased volume and attendant economies of scale. Let's say it's possible to decrease the average cost to $.50.

Taking this one step further, there will be people who can always pay more, and will always be paying, say $.55 for each fizzy beverage. They are no worse off than before the smart vending machines arrived, but lots of people are better off than before. Is this situation not fairer than the one where everyone pays the full original price? That point is perhaps debatable, but it seems a bit mean-spirited to deny the discount to those who benefit most from it.

In practice, this kind of thing goes on all around us. Store issues coupons and have limited-time discounts. Those with less money to spend are more likely to pay attention to these opportunities than those with more money, for whom their time is perhaps more valuable than the savings. The same thing applies to where you shop. If you want an upscale shopping experience, plan to pay more for the same items (or functionally similar, anyway) than you would at Wal*Mart.

The same principle applies to institutional aid. I wrote an article about this some time ago, but had to present these ideas recently in meetings, and so I did a rethink to try to make it more comprehensible. It's hard to explain average probabilities and demographic slices--it all sounds too theoretical.

Imagine that we look at a sample of applicants to our institution and have insight into their willingness and ability to pay for costs of attendance. This is represented in the graph below. Each bar represents an applicant, and the higher it is, the more cash they'd be be willing to cough up to come to our fine university. Generally this will likely look like a power law distribution, but I didn't try to hard to reproduce that here. It won't matter.

In the ideal case, we could use individually tailored aid packages to collect 100% of the area in those bars if we wished. We'll ignore the marginal costs per student in this exercise and just think about revenue. So the total revenue possible is the sum of all the bars, which could only be attained through discriminant (i.e., individual) pricing. What happens if we have a fixed-price model? The graph below shows two variables that depend on the price we set.

If we set the price at zero, everyone can attend. This is the blue line, which starts at 100% on the left, and decreases as the price increases. This is an obvious effect--the higher the price, the lower the attendance with fixed pricing. Revenue (the tan line) is more complicated because it's enrollment times price. This increases to an optimum price, and then decreases again as enrollment drops toward zero.

Notice that the maximum amount of revenue that's attainable in this fixed-price example is between 50% and 60% of the total. That is, by using fixed pricing, we cut our possible revenue by almost half. This is a powerful demonstration of the cost of the inflexibility of a single-priced model. If you think about the kinds of things you can buy for thousands of dollars--real estate, cars, college tuition--these things are generally negotiable. There's a good reason for that, as we've just seen.

The discount rate is the usual way to talk about how much institutional aid is being given. It may be assigned for reasons other than to increase attendance or revenue. For example, applicants seen as particularly desirable may be given 'merit' awards. The discount rate is the amount of unfunded aid given divided by the cost to attend.

A 2006 report from Noel-Levitz puts the average discount rate for private institutions at about 33%. You can also use the IPEDS comparison tool to compare your college's institutional grant average to a peer group you choose (and a lot more).

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