In response to a previous post on price discrimination by hospitals in India, commenters Apex and Chris L wondered how it is possible for price discrimination to make everyone better off, and even if you wanted to charge more to rich people, how could you do that in practice?

The general idea is that price discrimination allows firms to overcome fixed costs and thus offer products and services that they otherwise wouldn’t. But I’ll give a specific example using a really simple model.

Say there are four potential consumers of a hospital’s services. Three of them value the service at $5 and the fourth (the rich one) values it at $8. The fixed costs of a hospital are $5 and the marginal cost of treating one patient is $4. If the hospital charges a uniform price of $5, then all four will buy the service and the hospital will have revenue of $20, marginal costs of $16, and thus a total costs of $21. Thus the hosptial will not offer services at this price, since total costs are above total revenue.

At any uniform price above $5 and three of the four patients will not buy the service, and the maximum value the rich customer would pay ($8) is not enough to cover the total cost of treating him ($5 + $4 = $9). So under uniform pricing the services aren’t purchased by anyone, and thus everyone  is worse off.

However, if the hospital can price discriminate by charging $5 to the three poor customers, and $7 to the rich customer then the total revenue is $22, total cost is $21, and thus profit is $1.  In this case price discrimination allows the hospital to offer the services, and so being able to price discriminate makes everyone better off.

(The simpler case is where price discrimination doesn’t make all customers better off, but does increase overall welfare by making those with lower valuation and the firm better off by more than the higher valuation customers are worse off.)

How could hospitals do this in practice? They could do it rather directly by offering customers discounts if they can prove they are on food stamps (3rd degree price discrimination). Or they could allow customers to self-sort (2nd degree price discrimination) by charging a lot more for last minute reservations, better parking spots, or other “luxuries” and add-ons, which will tend to be demanded by people high time value of money (e.g. richer people).