# It's the Language of Action, Not a Trick

Mises Daily: Wednesday, February 03, 2010 by

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In the last several months, retail stores have sales on all sorts of products. Discounts go as far as 90% off. Some of these widespread price reductions can be attributed to the holiday season behind us, while most of them, it seems, were triggered by the recent fall in consumer demand due to the macroeconomic downturn.

This might induce some individuals to be concerned that sellers are now highly inclined to use little tricks to compel us to buy things we don't really need or want. For example, the "buy-one-get-one-half-off" deal, where, as the name says, the buyer pays the whole price for the first unit of a good but only half of the price for the second unit.

Some writers caution against buying something one does not really need just because it is offered under the buy-one-get-one-half-off deal. Some describe it as "slick marketing," and others advise people to beware of such deals because they are just 25% discounts in disguise. The purpose of this article is to shed some more light on this issue in the hope of showing why this type of discount is as popular as it is.

## The Popularity Puzzle

Typing the phrase "buy one get one half off" in Google search, results in about 7 million hits (for the exact phrase), while the number of hits for "25% off" is about a tenth of that (i.e., somewhat more than 700 thousand). This could be interpreted as a rough indication that the first discount option is much more popular than the second.

But, cutting the price of the second unit of a purchased good by 50% is arithmetically equivalent to reducing the price of both units by 25%. Why wouldn't the sellers just offer a buy-two-for-25%-off deal instead of going through the hassle of pricing different units of the same good differently?

One might think there is no difference between buying two units for 25% off and buying the first unit for the full price and the second pair for half price. As a result, one might think that this is a trick to make the buyer feel like he or she made a good deal when he or she really didn't. What's the "trick?" What do these "sneaky" sellers know that we don't? How is it that they are able to "manipulate" us over and over again?

Similar hints of negative ethical judgment can be found in some economic literature, resting on the works of Alfred Marshall. This type of deal would be characterized as price discrimination. According to this interpretation, the seller tries to charge the highest possible price a buyer is willing to pay for a product and thus transfer some "amount" of "consumer's surplus" (i.e., consumer's benefits from an exchange) into his own hands.[1]

However, this approach still fails to explain why sellers would prefer to offer buy-one-get-one-half-off instead of buy-two-for-25%-off. The average per-unit price would be the same. It must then be that this type of deal is offered because consumers prefer it.

But, what is the merit of such deals for consumers? Is this just an illusion? As it will become apparent in the remainder of this article, there is a much more plausible explanation than a persistent inability of buyers to recognize the "trick."

The fact that the buy-one-get-one-half-off deals have existed for quite a while, and that there are many people who continue to participate in them, suggests that this is not simply a trick. If it were, one would expect people to learn from their experience and to start avoiding such deals the same way most people learn to recognize and avoid con artists. Thus, it seems that this particular exchange arrangement has evolved simply because it tends to work well for both parties involved.

## The Economic Explanation

First, we need to know about the law of diminishing marginal utility, formulated by Carl Menger, further elaborated by Ludwig von Mises and Murray Rothbard, and recently clarified by Art Carden. This law states that a person values the first-acquired unit of a good the most.

"Value scales are purely ordinal. Thus, no meaningful comparisons in distance between pairs of points on one's value scale are possible."

Each next unit is valued less than the previous one. This is because humans rank their wants and needs. The higher the rank, the higher the value attached to the unit of a homogeneous good used to satisfy that want or need.

With the first acquired unit, we satisfy the most highly ranked want or need. Thus, the first-acquired unit of a good is valued the most. The next unit goes to satisfy the next want or need, which is, by definition, ranked lower than the previous one and higher than the next one.

The other fundamental element is to realize that human decisions are made at the margin. Whether one will acquire an additional (i.e., marginal) unit of some good is determined by the value of whatever needs to be given up in order to acquire that unit.

As long as the last unit of a good acquired is valued more than anything else that needs to be given up in return, a person will keep acquiring additional units of that good. Since each additional unit of a homogeneous good is valued less than the previous one, there is a point at which the value of the next unit that could be acquired becomes less than the value of something else that needs to be given up.

In our everyday life, money is generally seen as the good that is being given up in return for consumption goods and services. Actually, what is being given up is the alternative use of that money.

When deciding on a purchase, a person assesses the value of an item and compares it with the values of other things that could be obtained using the money needed to make that purchase. To illustrate this marginality principle, I will present several scenarios involving a buyer and a seller.

Consider a person, Jim, buying shoes. Suppose that the price of a pair of shoes is \$100. Jim would be willing to pay \$100 for the first pair of shoes. The value that he attaches to the second pair of shoes is lower than for the first pair. This is because, as said earlier, the first pair goes for satisfying a more important need or want.

Jim is willing to pay, say, \$60 for the second pair, but not \$100. For him, the value of the second pair is less than the value of something else that he could acquire using the additional \$100. Thus, Jim decides not to buy the second pair.

Suppose that, prior to buying the first pair of shoes, Jim had \$150 in his pocket, and suppose that he knew that there was a sweater in another store priced at \$75 and t-shirts priced at \$25 each. Deciding to buy the first pair of shoes for \$100 implies that the \$75 sweater must be foregone in order to have the shoes. In other words, a pair of shoes was more important to Jim than the sweater. With the remaining \$50, he may buy two t-shirts. Suppose that he chose to do so. As a result he spent \$150 on one pair of shoes and two t-shirts.

Consider now a different scenario. Suppose that the shoe seller, Janis, realized that her sales were slow and decided to cut the price by 25%. Now shoes can be bought for \$75 a pair. Imagine that Jim is being faced with this choice instead of the one in the first scenario. He would be happy to buy the first pair of shoes for \$75 instead of for a \$100.

Now, he is left with \$75 to use for something else. Suppose that he chooses to spend the remaining \$75 on the sweater. This means that he valued the sweater more than anything else he thought of doing with the remaining \$75, namely, either saving the \$75 for tomorrow or exchanging it for either the second pair of shoes or for two t-shirts and \$25 left in his pocket.

Finally, suppose that instead of the previous two scenarios, Jim came to the store after Janis had realized that the 25% price reduction wasn't such a good idea. She was originally hoping that after the price reduction, people that were not willing to pay \$100 for a pair of shoes may decide to buy them for \$75 and that this increase in quantity sold would be more than enough to offset the reduction in price.

However, it turned out that this didn't work, and Janis's total revenue ended up lower than she had expected. This means that the price reduction did not attract enough people to be worthwhile. It seems that offering a deal where some customers would choose to buy two pairs of shoes instead of only one would be a better option.

"There is nothing inherently knowledge-concealing in the offer. In fact, the structure of the offer has important information built into it."

Now, Janis is considering offering the 25% reduction only to people who want to buy two pairs of shoes. This way, she would not lose out on those customers that would buy only one pair for \$100, regardless of the discount. Additionally, she may provide an incentive for those that would buy two pairs for \$150 to buy the second pair. She realizes that there are two ways she could do this: she could say, (1) "if you buy two pairs, I'll take 25% off the price," or (2) "buy the first pair for \$100 and get the second pair for half price."

Suppose she decided to use the second option. This means that the price of the second pair of shoes would now be \$50. Imagine that Jim is facing this offer. We know that he would buy the first pair of shoes because, for him, this is the most important item that he doesn't have, and it is more valuable than anything else that he could obtain in exchange for \$100.

Next, Jim has a choice between saving the remaining \$50 for tomorrow or spending it on either the second pair of shoes or two t-shirts. If the second pair of shoes is more valuable to him than either the t-shirts or having the \$50 tomorrow, he will buy the second pair. Suppose that this is exactly what happens: Jim buys two pairs of shoes, the first for \$100 and the second for \$50.

Note that the average price of the shoes did not change compared to the situation when all shoes cost \$75 a pair (or 25% off). As a result, Janis sells two pairs of shoes for a total of \$150. She is happy about selling more shoes at the same unit price — her total revenue is higher. Jim is happy because he exchanged \$100 for a pair of shoes worth to him more than \$100 and \$50 for a pair of shoes worth to him more than \$50. As a result, Jim and Janis participated in a mutually beneficial exchange. Thus, both benefit.

But, one might say, "Wasn't Jim tricked into buying the second pair if he didn't want to pay \$150 for two pairs in the previous scenario?" No, and here's why:

Following the theoretical framework of Murray Rothbard, we can reconstruct Jim's scale of preference. This is shown in Figure 1, where money that he owns and objects that he does not own are ranked on a single scale in the order of decreasing importance. Exchanging his money for things higher on his value scale makes Jim better off.

Figure 1
A hypothetical individual value scale

According to this value scale, Jim would be better off if he exchanged \$75 for the first pair of shoes and the next \$75 for a sweater, when faced with a uniform 25% reduction in price. Since having either two t-shirts and \$25 for tomorrow or a second pair of shoes is lower on his value scale, these items are given up in order to obtain what is more important — one pair of shoes and a sweater.

In the buy-one-get-one-half-off scenario, Jim would still exchange \$100 for the first pair of shoes, because he values the first pair more than \$100. But now, only \$50 is left to be used for other purposes. He cannot buy a \$75 sweater any more. Note that he would not try to buy a sweater instead of the first pair of shoes, because the sweater is valued less than the shoes.

Thus, the sweater must be given up in order to have a pair of shoes. The next best thing Jim can do with the remaining \$50, according to his value scale, is to buy the second pair of shoes for \$50. The need for two t-shirts was left unsatisfied because it was less important than the need for a second pair of shoes. Again, Jim benefits because he exchanged something he values less (\$50) for something that he values more (a second pair of shoes).

## Benefits from Exchange Revisited

In all three scenarios, the buyer, Jim, did the best he could given the circumstances. The seller, Janis, also did her best to understand these circumstances and make the best of them for herself. Jim would choose to buy the second pair of shoes if it was priced at \$50, but he would buy a sweater if both pairs were priced at \$75. It is hardly Janis's duty to forego profit just for the sake of knowing that she induced Jim to spend his money in another store.

"Offering two pairs of shoes for \$150 would create an artificial unit for mental analysis. For most people, the appropriate unit of shoes is one pair."

In addition, we are unable to say whether Jim would benefit more from exchanging the first \$75 for a pair of shoes and the next \$75 for a sweater, compared to exchanging the first \$100 for the first pair of shoes and the next \$50 for the second pair. Murray Rothbard, in his Man, Economy, and State, points out that value scales are purely ordinal. Thus, no meaningful comparisons in distance between pairs of points on one's value scale are possible.

Thus, Jim was not tricked into doing something he would regret, given that his knowledge of his own wants and needs does not change later. Indeed, even if his knowledge does change, the deal itself had nothing to do with that. There is nothing inherently knowledge-concealing in the offer. In fact, the structure of the offer has important information built into it.

It turns out that the really interesting question is not whether Jim is better off or worse off in one or the other situation. The more interesting question is, why would Janis choose to offer a buy-one-get-one-half-off deal and not buy-two-for-25%-off?

The answer has much to do with the above described marginality principle. In short, Janis was wise enough to choose the language more palatable to Jim, the buyer. She eased Jim's assessment of the value of the two pairs of shoes by allowing him to assess each pair's value separately.

Offering two pairs of shoes for \$150 would create an artificial unit for mental analysis. For most people, the appropriate unit of shoes is one pair. People rarely have a single immediate end that would be satisfied by purchasing two pairs of shoes. Thus, when offered two pairs up front, people first need to disaggregate the offered two-pair unit into one-pair units and align them with different ends on their value scales, together with different combinations of money prices that add up to \$150.

This is an additional effort that can easily be avoided by specifying the price of each pair separately. Taking into account the law of diminishing marginal utility, Janis translated this offer into a more understandable language — the language of human action.

## Conclusion

Some buyers may be willing and able to take the additional time and effort needed to translate less-understandable offers into a more-understandable language. But there may be some that would not bother. It is in the sellers' best interest not to lose these buyers.

Equivalently, it is in the best interest of the buyers, the customers, to be offered a deal that is convenient for mental calculation so that they don't forego potentially beneficial purchases. However, expecting the seller to leave money on the table for no apparent reason would be unrealistic. After all, as motivated producers are necessary for providing marketable goods, so motivated sellers are necessary for delivering these goods to the willing buyers.

##### Notes

[1] For an excellent critique of quantifying benefits from exchange, refer to pages 257–268 of Murray Rothbard's Man, Economy, and State.