# Economists Do It With Models

## The Most Compelling 5.882% Discount Ever…

#### August 15th, 2010 · 8 CommentsBehavioral Econ · Buyer Beware · Fun With Math

Consider the following problem from Choices, Values, and Frames*:

Imagine that you are about to purchase a jacket for \$125 and a calculator for \$15. The calculator salesman informs you that the calculator you wish to buy is on sale for \$10 at another branch of the store, located 20 minutes drive away. Would you make the trip to the other store?

In this example, 68 percent of respondents said that they would drive to the other store to save the \$5. On the other hand, when the question was rearranged so that the calculator cost either \$125 or \$120 and the jacket cost \$15, only 29% of respondents reported being willing to drive to the other store.

From a pure utility-maximization perspective, this is, well, dumb. In both of the question setups, the total expenditure options are the same- \$140 versus \$135. Despite this fact, people seem to be making judgments based on the percentage discount on the particular item, and a 33 percent discount on the calculator sounds a lot more appealing than a 4 percent discount on the calculator.

I am willing to buy that people think in terms of percentage discounts, even when it’s not economically “rational,” if for no other reason than we’re so used to seeing sales of this form. As such, I get very perplexed when I read about the economic impact of sales tax holidays. For example, this weekend is the sales-tax holiday in Massachusetts, and it’s going just swimmingly, according to the Boston Globe:

After a year’s hiatus, the retail tax holiday made a roaring return yesterday, with customers flooding Boston-area stores and plunking down their plastic and cash to buy iPads, sofas, and cases of wine.

At the CambridgeSide Galleria, consumers waited for an available sales agent in a line that snaked outside the Apple store. At Copley Place, store managers reported that by early afternoon, foot traffic was substantially higher than what they had seen earlier in the lazy, hazy summer. And at the M. Steinert & Sons piano salon, where baby grands make beautiful music on Boylston Street, four pianos had been sold by midday.

Shoppers like Joe and Melissa Gilburd of East Boston had marked their calendars for this day — even if there was not always accord about what, precisely, to spend hard-earned dollars on.

“We came to buy,’’ Melissa Gilburd said. “It’s got to be something.’’

Ah yes, the outlet mall “we’re gonna be pissed if we don’t buy something” mentality. Let’s think about this for a second- the effective discount due to the sales-tax holiday is only 5.882 percent. (To convince yourself of this, consider that an item that costs \$100 without the tax usually costs \$106.25, and the percentage decrease in going from \$106.25 to \$100 is in fact 5.882%. Don’t make the naive mistake of thinking that it’s a 6.25% decrease.) So there are two main options for what could be going on in consumers’ minds:

1. Consumers could be wising up in their thinking and considering absolute rather than relative discounts. This is entirely plausible since the article specifically highlights that consumers are interested in big-ticket items such as computers and mattresses. (In case you are curious, there is a cap of \$2500 per item that is tax exempt, but even with that you could save \$156.25 in taxes on a single item.)
2. Consumers could be unreasonably swayed by the marketing of this “holiday.” If this is the case, then stores simply announcing a 5.882 percent discount wouldn’t have nearly the same effect. I am watching television as I write this (men’s gymnastics- don’t judge), and I notice that Bob’s Discount Furniture seems to have caught onto the marketing schtick: “Remember- there was no tax holiday last year, and you can never know if they’ll do it again!” To investigate this possibility, I would like to know how sales of clothing are affected by the tax holiday, since items of clothing under \$175 are never taxed anyway.

In terms of real impact, this sort of program has the same problem that cash for clunkers had- it’s difficult to tell how much of the increase in sales is an actual increase and how much is just a timing shift on items that consumers would have bought anyway. On a similar note, the state of Massachusetts estimates that it forfeits up to \$23 million in tax revenues- if the increase in sales used to calculate this figure is a true increase, then the notion of “forfeit” is meaningless, since the purchases wouldn’t have taken place (and thus no tax would have been collected) if the tax break wasn’t there. Who do I have to talk to to get come clarification here?

* Technically, this is from a paper called “Choices, Values and Frames” by Daniel Kahneman and Amos Tversky that was published in the journal American Psychologist in 1984. Now Google like the wind.

### 8 responses so far ↓

• 1 John F. Opie // Aug 15, 2010 at 4:02 pm

Men’s Gymnastics? Don’t judge?

Sorry: East German judge: 2.4

🙂

• 2 Tristan T. // Aug 15, 2010 at 4:08 pm

Sad to say that the first thing I thought of was, “hey, so a 20 minute drive there + gas means I’ll probably lose money on the deal anyway.” Add my time preference for time (time>money considering the traffic and long term health effects) and you can say no deal to that.

Now make like a google and go on for practically forever!

• 3 Warren J // Aug 15, 2010 at 4:09 pm

I’d say there’s a significant “screw the government” mentality influencing consumers’ decisions, here, but that’s only a guess. We don’t have sales tax holidays in California, so I’ve never had the pleasure of studying one.

• 4 judgeetox // Aug 15, 2010 at 4:52 pm

I’m with Tristan on that. Why would a 20 mile drive (each way) come up to a \$5 discount when you are standing in the store?

• 5 Joao Pedro Afonso // Aug 15, 2010 at 4:57 pm

If people are committed to maintain their original intention purchase (Jacket+calculator), I agree, it is dumb. We can even think it double dumb, because they only have the word of the clerk about it… what would happen if they reach the other store and found the price the same, wasting travel time and gas? There is also the question of the support: the first store was likely chosen because it was the most accessible, I guess… so, each time the purchased articles have problems, I can surmise the necessity of another 20 minutes travel.

However, it is only dumb if there is that commitment of buying that and nothing else. Can we not see here the same effect (and more) we saw when you discussed the effect of free products? While the same discount of \$5 in both situations shouldn’t change the propensity to take the decision of traveling more, a 33 percent discount on the calculator versus 4% is a lot different.

First, it means the same money will have 50% more purchase power. That means that with the same money I buy 2 calculators, now I can buy 3. Maybe, I’ll buy one for me, and several more for friends and relatives. Maybe I can fill my Christmas List of presents to give earlier. The possibilities are tantalizing.

Second, there is our curiosity about the motive behind the seller. As a rational purchaser, my reaction will be, why the stores are different? Can the second store have more things at such a discount? Curiosity leads to knowledge, and knowledge leads to more informed choices, and nothing of this is dumb. So, unless there was some strong constrains in the mind frame allowed to the people sampled (kind of, asking if he would travel but enforcing the idea that it will only allowed to buy the same he would buy in the first shop), which I suspect not, because that would had contaminated the experience, with weird interferences to their natural decision process, I do not see anything odd in the observed results.

About tax holiday’s, I kind of agree with you. Nothing below 20% discount moves me these days. However, that kind of discount means a 6.25% increase in my purchase power for a time… as if I was raised that value in my work. Considering how in my country (and others), the different of one percent in salary raise’s discussions between unions and employers, can lead to general strikes, I can only suppose it is more important than I personally feel.

• 6 econgirl // Aug 15, 2010 at 5:15 pm

@ Tristan and judgeetox: The experiment was performed a while ago, so it’s not necessarily \$5 in today’s dollars. The relevant takeaway is that people’s choices can be affected by the framing of a transaction even when the underlying payouts don’t change.

• 7 sheila // Aug 15, 2010 at 5:45 pm

The consumer already has a surplus in purchasing a \$15 jacket therefore an additional \$5 savings has a lower utility than the calculator.

• 8 Greg // Sep 26, 2010 at 9:39 pm

My guess is that it’s less a ‘consumers are irrational thing because they don’t max utility/min cost the way that theory says they should’ problem than it is a ‘this is kind of a stupid question’ problem. If you were to just ask people whether \$125 is a reasonable jacket price, most would say yes. If you ask people whether \$125 is a reasonable calculator price, most people would say no. Most people will never see themselves getting \$125 worth of use out of a calculator.

This is likely the ‘meh whatever.’ response that you’re seeing coming from people being forced to make a decision within a world that doesn’t match their own day-to-day reality.