It's the Same Five Dollars!

by Z_M_Davis1 min read8th Mar 200932 comments

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EconomicsHeuristics & Biases
Personal Blog

From Tversky and Khaneman's "The Framing of Decisions and the Psychology of Choice" (Science, Vol. 211, No. 4481, 1981):

The following problem [...] illustrates the effect of embedding an option in different accounts. Two versions of this problem were presented to different groups of subjects. One group (N = 93) was given the values that appear in parentheses, and the other group (N = 88) the values shown in brackets.

[...] Imagine that you are about to purchase a jacket for ($125) [$15], and a calculator for ($15) [$125]. The calculator salesman informs you that the calculator you wish to buy is on sale for ($10) [$120] at the other branch of the store, located 20 minutes drive away. Would you make the trip to the other store?

The response to the two versions of [the problem] were markedly different: 68 percent of the respondents were willing to make an extra trip to save $5 on a $15 calculator; only 29 percent were willing to exert the same effort when the price of the calculator was $125. [...] A closely related observation has been reported [...] that the variability of the prices at which a given product is sold by different stores is roughly proportional to the mean price of that product. The same pattern was observed for both frequently and infrequently purchased items. Overall, a ratio of 2:1 in the mean price of two products is associated with a ratio of 1.86:1 in the standard deviation of the respective quoted prices. If the effort that consumers exert to save each dollar on a purchase [...] were independent of price, the dispersion of quoted prices should be about the same for all products.

This one's a killer. Money is supposed to be fungible, but these observations really highlight how difficult it is to really behave as if you believed that. So, aspiring rationalists, how might we combat this in ourselves? Maybe it would help to consciously convert between money and time: if you value your time at 25 $/hr, then the cost of a twenty-minute drive is 25 $/hr * (1/3) hr = $8.33 > $5, so you buy the calculator in front of you in either case. So this heuristic at least takes care of the calculator problem, although I would guess it fails miserably in other contexts, I currently know not which.

Another takeaway lesson is to ignore advertisements boasting that a product is currently such-and-such percent off. We don't care about the percentage! How many minutes are you saving? 

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There's a heuristic at work here which isn't completely unreasonable.

I buy $15 items on a daily basis. If I form a habit of ignoring a $5 savings on such purchases, I'll be wasting a significant fraction of my income. I buy $125 items rarely enough that I can give myself permission to splurge and avoid the drive across town.

The percentage does matter -- it's a proxy for the rate at which the savings add up.

It's also a proxy for the importance of the savings relative to other considerations, which are often proportional to the value of what you're buying. If you were about to sign the papers on a $20000 car purchase, would you walk away at the last minute if you found out that an identical car was available from another dealer for $19995? Would you try to explicitly weigh the $5 against intangibles such as your level of trust in the first dealer compared to the second, or would you be right to regard the $5 as a distraction and ignore it?

But if the time to drive across town is worth more than $5 in the $125 case, it's worth more than $5 in the $15 case, and forming that habit loses big. (Unless driving across town once allows you to save on more than one item, but that completely breaks the example.)

Other than cognitive cost, I don't see any reason to speak in terms of habits rather than case-by-case judgments here.

In the car case, you know the cost of walking away is very high; this screens off the informational value of the price.

It seems to me like it shouldn't matter how often you buy the $15 items, technically. Even if you always bought $125 items and never bought $15 items, your heuristic still wouldn't be completely irrational. If you only buy $125 items, you'll only be able to buy 4% more stuff with your income, as compared to 33% more stuff if you always buy $15 items.

I've had to consciously adjust my reactions on this sort of thing a few times, by reminding myself that the amount I should care about saving 1 euro on a product should not depend on the total price - but only and specifically on how frequently I will buy the product.

Put another way: it helps to have the right formula to replace the wrong one.

[-][anonymous]12y 1

Certainly

[-][anonymous]12y 1

Good point

One reason that I would do the 20 minute trip across town for a $5 saving is to reward the store with the good deal and punish the store with the high price.

Since a 20-minute trip is almost never worth $5 to me, it will really depend on how cranky I am.

In this scenario, given that they are different branches of the same store, the whole thing might make me so cranky that I go to another store completely or figure out a way to go a while longer without a calculator.

This is pretty much why I do not have colour ink in my printer right now. I was at a Staples recently and they had ink for a price I was willing to pay but I knew they were selling it online cheaper.

I know I'm not acting rationally about whether I have ink and how much I'm spending on it. I also know that I shouldn't assign moral values to Staples' pricing policies, but I don't think I'll be printing in colour until either I find someone with a pricing policy that doesn't feel all wrong to me or my girlfriend buys some ink because she doesn't want to wait for me to do it any longer.

[-][anonymous]7y 0

One reason that I would do the 20 minute trip across town for a $5 saving is to reward the store with the good deal and punish the store with the high price.

Very good point. I very often consciously or near-consciously think about that.

The seeming irrationality of the customers choice may disappear after the cost of decision-making is taken into account.

In our daily life we are constantly required to estimate trade-offs between things that are very difficult to quantify (e.g. pleasure of wearing a new jacket - money that has to be paid – extra hours of work to earn this money - …). Hence using simple subconscious heuristics (such as “improving the trade-off by 50% is worthy of your time, 5% is not”) is very helpful. A constant search for an optimal solution would make a nightmare out of our every decision, which is hardly worth an occasional 5$ saving.

In this specific example, I believe that increasing the price differentials would have justified an additional mental effort, leading more people to the “optimal choice”.

Good point. It's worth noting that those heuristics can use dollar values as well, although percentages are more cognitively natural.

When advertisements talk about percentage off, they're providing two prices. The higher price is meant to anchor your judgment of the item's value and your estimates of what other stores will charge, while the lower price is meant to seem cheap by comparison. However, the higher price is not required to be reasonable, and in fact, it usually isn't; stores often mark items up to ridiculous prices just so they can bring them back down again with sales.

Converting between time and money sounds like a good solution to this problem.

If you're interested in the broader psychological mechanism behind this bias, I highly recommend Jonah Lehrer' s blog post on irrational purchasing decisions: http://scienceblogs.com/cortex/2009/02/shopping.php

[-][anonymous]12y 1

good link

" Money is supposed to be fungible, but these observations really highlight how difficult it is to really behave as if you believed that. So, aspiring rationalists, how might we combat this in ourselves?"

I think there are some hidden assumptions in that question.

Money is supposed to be fungible, yes. But if we act otherwise, is it because money is truly fungible and we're failing to respond appropriately to reality? Or is money itself not fungible and our actions consistent with an understanding that denies our asserted beliefs?

If the unspoken understanding that guides our actions is correct, it's our explicit beliefs that need to be combated. If it's our explicit beliefs that are right, it's our intuition that must be fought. We can't determine the right course of action until we know where the error is.

Sometimes you buy more than one thing at a time. The heuristic might be something along the lines of, if that store is 33% cheaper on that calculator it might be 33% cheaper on other things, and you might end up saving a lot more than $5. If the calculator is only 4% cheaper, your savings will only work out to near $5, which might not be worth your 20 minutes.

I've come across this problem before - what the problem really is is the inappropriate use of proportional savings ($5 is a higher proportion of $15 than of $125) when the attention should be on the absolute savings ($5 in either case) because of the way the problem was framed. The way the problem was presented in this post actually obscures this point.

What use of proportional / absolute savings exactly is appropriate? Can you be more specific in which point is obscured by the framing?

3600 seconds in an hour, so if you value your time at $18/hour you should imagine a cent ticking away every two seconds, if $36/hour a cent every second, etc.

Cents and seconds are really too small to impact much on people's decisions. I've found it more useful to frame it in dollar or five minute increments - for every multiple of $12 an hour, that's $1 every 5 minutes. That is substantial enough that I (and probably people in general) will pay more attention to it.

[-][anonymous]12y 1

1 cent a second? It's almost depressing if you put it like that.

[-][anonymous]7y 1

To the extent that one buys $15 stuff way more often than $125 stuff, such a decision could make sense for reasons like these, but...

The same pattern was observed for both frequently and infrequently purchased items.

Oh. My.

(I myself used to have the same failure mode. What the hell, young army1987? If anything, after spending $120 I have $110 less than after spending $10, so the marginal utility of $5 should be larger in the former case. What the hell?)

[-][anonymous]12y 1

3600 seconds in an hour, so if you value your time at $36/hour you should imagine one cent ticking away each second, if it's $18/hour then it's a cent every two seconds, and so on.

[-][anonymous]12y 1

So, aspiring rationalists, how might we combat this in ourselves? Maybe it would help to consciously convert between money and time: if you value your time at 25 $/hr, then the cost of a twenty-minute drive is 25 $/hr * ⅓ hr = $8.33 > $5, so you buy the calculator in front of you in either case. So this heuristic at least takes care of the calculator problem, although I would guess it fails miserably in other contexts, I currently know not which.

So after I have the calculator I'll be set.

I've tried to combat this one by imagining the item at a variety of different price points, with the same saving. I don't know how you'd measure how much success you were having, though, because obviously no-one who understood this bias would exhibit it in a formal test setting, only in more informal settings where it's harder to compare. You need some way of mixing it up so you can't just do the sum, but the bias emerges from the noise all the same.

If you can't "just do the sum" then there is no apparent bias - you are just making an arbitrary choice if you can't compare them rationally.

What I'm hoping for is something akin to the racism tests which don't show you two candidates identical except for race and ask you to choose between them, but which mix up races and CVs and find the racism in the noise with statistical techniques.

[-][anonymous]7y -1

if you value your time at 25 $/hr, then the cost of a twenty-minute drive is 25 $/hr * (1/3) hr = $8.33

Am I the only person who is bothered by the US-centrism of assuming that the cost of fuel is negligible in calculations like those?

I don't think the cost of fuel is negligible in calculations like these even in the United States. At 3 USD/gallon, a ten- to fifteen-mile drive can cost enough to matter, especially if your car's gas mileage isn't great. Even the best-case likely scenario, a ten mile drive in a car that gets forty miles to the gallon, the gas price ends up being 0.75 USD, or an additional 16% cost. Worst-case examples could actually have somewhere between a quarter to a half of the true cost difference in fuel.

That's not as extreme as in other countries, where a twenty-minute drive could meet or exceed the time cost, true, but in many cases the distinction is rather extraneous. They're probably avoiding the fuel cost because it's far more complex to meaningfully calculate.

Don't forget depreciation on the car. Imagine that a car costs $20000 and lasts 100000 miles (it may last longer, but then you may have to pay to repair it, and 20000 is only a crude price estimate anyway, etc.) That's 20 cents a mile, and the ten mile drive adds another $2, which is 40% of the cost.

It seems pretty clear that the connotation of 'cost' in this instance is 'time cost' and not 'total cost.' Fuel cost is highly variable based on the price of fuel and the efficiency of your car.

[-][anonymous]7y 1

And why should it be time cost rather than total cost that matters?

Of course the total cost matters. However, the time cost is the point of the post, and including fuel cost in the calculation would be needlessly complex and generally unhelpful.

A 20 minute drive costs $8.33 in time given $25/hour time valuation. Depending on roads, traffic, etc. that might be about 10-12 miles. My car gets 45mpg on average, and gas costs around $3.30. My fuel cost is about $0.73. If gas cost $8/gallon and I drove a 25mpg car, then my fuel cost is $3.84. This variability makes figuring the total cost highly individual to situation, and not entirely relevant to the point of equating time and money.