### Price discrimination is economically efficient

Daniel Hamermesh reminded me of a subject I have been planning a post on.

In case you made the mistake of thinking cutthroat price competition is always efficient, I have a small demonstration for you.

Imagine a market where there are three consumers of sausages, A, B and C.

A derives £5 of benefit from a sausage; B gets £10 and C £15.

Suppose now there is a single butcher in town, and he has to charge a fixed price. The variable cost of producing a sausage is £4 and the fixed cost for the period is £5.

If the butcher prices his sausages at £15 he'll sell one unit at a cost of £9 and make a profit of £6.

If he prices at £10 he'll sell two units at a cost of £13 and make a profit of £7.

If he prices at £5 he sells three units at a cost of £16 and makes a loss of £1.

Naturally then, the butcher will set the price to £10, make £7 profit and generate consumer surplus of £5 (all of which goes to lucky C).

However, imagine that he develops the ability to price-discriminate and charge a different amount to each consumer. If he can charge £5 to A, £10 to B and £15 to C he sells three units at a cost of £16 and makes £14 profit. He can even offer some extra incentives to the customers, by setting prices to £4.50, £8 and £12 - still making £8.50 profit but now with £5.50 of consumer surplus. Better for everyone (except C, but she still does better than either A or B so we shouldn't feel too sorry for her).

Incidentally, competition between firms does not change this result much. The exact results depend on the nature of the fixed costs under competition, but price discrimination - if it can be maintained in a competitive environment - still enables the companies to sell product to more people and thus generate more consumer surplus.

The point is that there is no single price point which allows all three consumers to buy the good and the producer to stay in business. Thus price discrimination is the only way to achieve an outcome that's stable and beneficial for all parties - as well as maximising total welfare.

Good ways to achieve price discrimination include structured pricing, value pricing and various other mechanisms. We've also created a capability within our CVM software which manages price discrimination to maximise revenue (consumer surplus, though not a short-term concern of most suppliers, is worth maintaining in the long term - the theory of repeated games again).

So, price discrimination is an economic free lunch. Who said competitive markets were a good thing?