Price segmentation

About six months ago, I encountered a blog on price discrimination at hair-salons^e. With one late-comer stating that “This is an aspect I hope to explore in my research on gender-based price discrimination for my microeconomics class at Harvard University.”, it is high time for me to write a long-planned post on price segmentation—which is the true explanation behind this discrimination: Women, as a group, are willing to pay more, and that is the reason for the difference in prices. (See also below and some of my comments in the original discussion.)

To illustrate the principle of price segmentation, assume that a company manufactures a three-geared bicycle and wants to determine the right price: If a higher price is chosen then each bicycle sold will give a higher profit—but fewer people will be willing (or, at all, able) to buy it. Assume that the number of bicycles sold at a certain price in Euro is n(p) = 100,000 – 200p and that the total cost of manufacture, marketing, etc. amounts to 300 Euro/bicycle. (These are unrealistic and simplistic assumptions, but they serve well as an illustration.) We can now write the profit as (100,000 – 200p) (p – 300 ) = 160,000p – 200p^2 – 30,000,000

Starting with a price of 0, we have a pleasing 100,000 bicycles “sold”—but a horrifying loss of 30,000,000 Euro. No wonder: Each bicycle gives a severe minus. Using the realistic minimum price (= the cost) of 300 Euro, we see a profit of 0, at 40,000 units sold. Now, by increasing the price by 1 Euro, we can increase the profit by almost 40,000 Euro—gaining 1 Euro from each of 39,800 bicycles, instead of 0 Euro from 40,000. Another price increase brings almost the same amount (39,400), for a total of 39,600 bicycles at a gain of 2 Euros each and 79,200 Euro in all. Another Euro gives another 39,000 and a total of 118,200. Etc.

Increasing the price further and further gives a growing profit—we have fewer buyers, but a greater profit per buyer. At a price of 400 Euro, a full 2 million Euro from 20,000 items is reached. Here, however, we have a maximum: Increasing the price further leads to a smaller profit, as the loss of customers has a greater effect than the price gain. Indeed, at 500 Euro, the profit is back at zero, because not one single bicycle is sold. (The mathematical function works for even higher prices, with an increasing loss, but is now entirely unrealistic—we cannot sell a negative number of bicycles.)

This makes the manufacturer very sad: He knows that there are people willing to pay more than 400 Euro—but he cannot charge them more without losing other customers and reducing his profits. He also knows that there are people who do not buy at all at 400 Euro who would be willing to do so at a lower price—but he cannot lower the price without lowering his profit on the existing customers.

Or can he? Yes, he can! This is where price segmentation comes in: People with different willingness to pay are charged different prices for varying reasons, some based on actual value added, some on different needs, some on stupidity or gullibility on behalf of the customer, some on border-line (or outright) fraud.

Among the many options available to the manufacturer, he chooses the following: He manufactures an ungeared basic model for 250 Euro to be sold at a price of 300 Euro, the old model at the old cost and price, and a “de luxe” bicycle with twelve gears at cost of 350 and a price of 500 Euro. Now he has his previous profit, plus the additional profit from those willing to pay extra, plus the additional profit from those who can now afford the inferior bicycle. (However, also with a minus from those who would previously have bought the mid-ranged bicycle, but now opt for the low-end one. Minimizing such losses is a question for another discussion, but take note of factors like perceived status, brand recognition, deterrents in form of artificial quality reductions, whatnot.)

To give an indication of how powerful price segmentation can be: What profit would result if every potential customer bought a bicycle at the highest possible price using the original function? We then have to add 200 * 0 at 500 Euro, 199 * 200 at 499, 198 * 200 at 498, …, 1 * 200 at 301, and 0 * 200 at 300—amounting to 4 million Euro, to be compared with the original 2 million. (Where we assume that all prices are integers. Allowing prices like e.g. 300.94 makes no change in the big picture, but would lead to more complicated calculations and, possibly, the need to discuss assumptions about fractional bicycles.)

Examples of price segmentation can be found everywhere: In the cereal aisle in a supermarket, in a computer store, at the hair-dressers, … Some examples can be less obvious, my two favourites being DVDs and books:

DVDs are originally sold at very high prices, often more than 20 Euros at release. Those very eager, irrational, or wealthy buy at that price. The price then drops by and by, with those less eager, irrational, and wealthy eventually buying at a lower price. In the end a DVD may be dumped for 5 Euros or less, before it disappears from the market—or is marked up again, because the decision is made that it is better to refocus on the true fans and late comers willing to pay a higher price than on the masses.

Books, OTOH, are divided into hard-cover and pocket books: They both have their advantages and disadvantages (and I, personally, consider the pocket book to be the superior format in most cases), but the former sells for thrice the price of the latter. Why then does anyone buy hard-cover? Easy: The hard-cover books are released about a year earlier, and the true segmentation (as with DVDs) is one of time: The customer pays for the privilege of reading the book earlier—not any inherit superiority of the hard-cover format.

Even rebates to seniors, children, and students are usually done with an eye at price segmentation (although altruism and PR can be factors): Customers who would otherwise be hard-pressed to pay are given a leg up; others still pay the full price.

Returning to the example with hair-cuts: Why would women be charged more? Because of a patriarchal conspiracy? No. The true reason is simply that men and women, as groups, are willing to pay different amounts of money for a given hair-related service (and that they often want different services). Correspondingly, it makes good business sense to segment the market based on the sex of the customer: Increase the price for men and they will desert to self-service land; do so for women and they will remain as customers—with the occasional complaint about too high or unfair prices. Similarly, women are more likely to go to a fancy “hair architect”, while men tend towards someone who admits to being a cutter of hair; women want extras of various kind; men want it plain and simple; etc.

As an aside, the issues of competition and niches is very important in practice. For instance, in the original example, the presence of a competitor selling an equivalent or superior bike at 390 Euro could give the function n(p) a radically different look when that price was approached, possibly making the original “ideal” price of 400 Euro entirely unrealistic. It would also be possible that the three given market segments would each be dominated by a different manufacturer.

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