Recommendations, Discounts, and Discrimination

A discount can be real and still fail to settle whether a pricing system benefits customers overall. That sounds like an evasion until we ask the obvious next question: a discount from what?

The advertised price is one possible comparison. The price available yesterday is another. A price the seller would choose without personalization is a third. Those comparisons answer different questions. If an argument begins with one and ends with another, the apparent conclusion may be doing little more than changing the baseline.

The same care applies to recommendations. A recommendation can save time by showing a suitable product. It can also change spending by making one option easier to notice than another. We should measure relevance, cost and the customer’s eventual outcome separately. The word personalized is not a welfare result.

More beneficiaries can coexist with a larger loss

Dubé and Misra estimate that 63 percent of prospective employers would receive lower prices under theoretically optimal personalization than under the optimal uniform price of $327, while aggregate consumer surplus falls 25.01 percent. Comparing implemented capped personalization with the implemented $249 uniform price instead gives an 11.45 percent reduction. These model-derived welfare estimates concern one business-to-business setting. Dubé and Misra, Table 8, pp. 166–167

An average effect and a count of people helped should therefore travel together. We should also ask whether the largest losses fall on people with the least ability to absorb them. The study’s model cannot answer every moral question about the distribution. Nor can a slogan about discounts.

An economy small enough to inspect

For this brief, I use an independently coded example with deliberately simple assumptions. It illustrates established price-discrimination theory, particularly the information-design analysis of Dirk Bergemann, Benjamin Brooks and Stephen Morris. It is not new evidence about consumers.¹ Their 2015 paper

There is one seller and one product. Each buyer wants at most one unit. Forty percent value it at 2, forty percent at 5, and twenty percent at 9. These are invented units of value. The product costs nothing to supply in the baseline. Buyers know their value and buy if the price is no greater than it. There is no resale, no competitor, no privacy cost and no future response.

The seller first chooses one price for everyone. At a price of 2, everyone buys and revenue per potential buyer is 2. At 5, sixty percent buy and revenue is 3. At 9, twenty percent buy and revenue is 1.8. The seller chooses 5. With zero supply cost, revenue and profit are equal.

The buyers who value the item at 9 retain a benefit of 4 after paying 5. Their population share is one fifth, so average consumer surplus is 0.8. Buyers who value it at 5 receive the item but have zero surplus in this model. Those who value it at 2 do not buy.

Now give the seller perfect information and let it charge each person exactly their value. Everyone buys. Profit rises to 4.6 per potential buyer. Consumer surplus falls to zero. Total surplus rises from 3.8 to 4.6 because previously excluded buyers now receive the product.

That is why the phrase “the market became more efficient” needs explanation. Here, it means more mutually valuable trade took place. It does not mean customers kept more of the benefit. In the model, they kept less.

A different use of information

There is a third arrangement. Instead of revealing everyone’s exact value, put some buyers into a deliberately mixed group. In that group, the population masses are 0.4 of value-2 buyers, 8/45 of value-5 buyers and 4/45 of value-9 buyers. The remaining buyers form a second group.

For the first group, prices 2 and 5 each earn the seller 4/3 in revenue per member of the original population. The baseline rule breaks this tie in favor of the lower price. The second group receives price 5. Everyone buys. The seller still earns 3 per potential buyer, while consumer surplus rises to 1.6. The newly served value-2 buyers receive zero surplus under the assumed purchase-at-equality rule; the additional consumer surplus goes to higher-value buyers who receive the discount.

Information has now supported a different division of the gains. The seller retains its uniform-price profit and buyers retain more. The inputs are the same people and values. The grouping and decision rule changed.

This example makes a possibility visible. It does not show that a profit-seeking intermediary would choose the consumer-benefiting arrangement. If the seller can obtain more detailed data and earn 4.6, it needs a reason to accept a rule that earns 3. A contract, competing offer, public rule or different institutional objective would have to do some work. The arithmetic does not supply that institution.

The theory behind the illustration characterizes possible divisions of surplus under a particular monopoly structure. Our numerical example is a teaching implementation of that established result. It is not evidence that every market can achieve the same outcome, and the favorable allocation should not be described as the natural consequence of better algorithms.

Check the fragile assumption

The price tie matters. If the seller chooses the higher price in a tie, the same grouping produces the uniform-price result: output 60 percent and consumer surplus 0.8. We cannot hide that decision in a footnote and keep celebrating the better result.

A revised grouping makes the lower price strictly more profitable in the low-price group. The code does this by reducing that group’s higher-value members by ten percent and moving them into the other group. Profit becomes 3.08 and consumer surplus 1.52, with everyone still buying. Some consumer benefit has been given up to create a strict incentive for the seller.

The accompanying sensitivity calculations also change supply costs and introduce a specified kind of error in group labels. These calculations ask whether the same design still works. They do not estimate the frequency of such errors in real services.¹ The results show why a policy should be evaluated under plausible implementation changes, rather than only at the exact assumptions that make its chart attractive.

The conclusion I take from this is demanding but hopeful. A more informed market can produce a better bargain for buyers. It can also transfer more of the gain to sellers. We should ask which arrangement is being built, what keeps it in place and how its promises will be checked. Calling the technology efficient is only the beginning of that conversation.