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You mentioned Cracked, that's awesome.

It's not false that you can use unit pricing to compare brands in all sizes of packages. It's just that in thie instance you must calculate the unit price yourself, which is annoying. I have noticed that many stores no longer display any unit prices, and those that do often omit them from sales tags (which seems odd...would think you'd want to direct the price concious consumer to the on sale items).

I was having a chat with my 10 year old niece over the weekend about the importance of math. She eventually agreed with me that I was right and fractions (her current nemesis) are useful in the real world. Not sure that that'll help her be any more motivated to learn to do quick calculations in her head though, which is a really important financial literacy skill to have.

Neil "It's not false that you can use unit pricing to compare brands in all sizes of packages"

But the statement that you can *easily* use unit pricing is false. I can't do 150/2.82 in my head very quickly.

On fractions and other aspects of the mathematics generation gap, see this old post http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/05/bridging-the-mathematics-generation-gap.html.

Stephen - John Cheese is my favourite columnist, though David Wong is sometimes brilliant also.

Great post!

For another interesting example, I was in a Shopper's Drug Mart yesterday where they advertised one bottle of water for \$1.99, and 2 for \$4.00! It costs two cents extra to buy two at once. I was wondering how many "deals" of two they sold.

Frances,

A bit off-topic (or maybe not). Why is the regular price of popcorn "\$1.99", but the sale price "2 for \$3.00" and not "2 for 2.99"? Or, even better, "2 for \$2.98...Save \$1.00 when you buy two"? As far as I can tell, supermarkets still predominantly use ".99" pricing. But they seem to prefer integer prices in cases like this. I wonder if there's some marketing psychology reason for this.

Giovanni,

Good question. I suspect its because consumers don't like doing math (and are bad at it), so 2 for \$3 is an easier sale than 2 for \$2.99 ("half of 9, carry the 1, 17 dollars? WTF?"). Customers already think they're getting a deal, so the benefit of pricing at \$2.99 vs. \$3 is off the table.

Whitfit, while I'd like to think that the pricing you saw at Shopper's was evidence of clever marketing strategy, I wouldn't be surprised if that isn't a function of Shopper's employees being just as bad at math as their customers.

Bob,

"...2 for \$3 is an easier sale than 2 for \$2.99 ("half of 9, carry the 1, 17 dollars? WTF?")"

Good point. The store manager is constrained to write the price as "2 for..." because they want customers to buy two units at a go, but at the same time they want arithmetic-challenged consumers to easily see they're getting a substantial markdown relative to the regular price.

I know that a lot of consumers are annoyed by these types of promotions. You have to be careful because sometimes 2/\$3 is really just \$1.50 each, and ohter times it is first one for \$1.99, the second for \$1.01. And the fine print on the other is usually literally in painfully fine print.

I agree wholeheartedly that financial should focus a lot more on sensible consumer behavior and encourage a little more basic intuitive math. Most people under-save and -invest because their income efforts are focused on consumption, and a lot of consumption is stimulated by wish-fulfilling perceptions of bargains.

A good financial literacy question would be: Your benefits plan allows \$400 a year for massage with a 20% deductible. If you have a choice between a \$110 massage today versus a \$70 massage tomorrow, what does the higher priced item cost you? Most people would answer (110-70)/5 = \$8--only eight dollars! But the real cost is of course \$40, with \$32 depleted from your benefits resource.

Financial literacy is probably improved less by technical knowledge than it is by teaching people to make the full costs of decisions visible.

Andrew F: " You have to be careful because sometimes 2/\$3 is really just \$1.50 each, and ohter times it is first one for \$1.99, the second for \$1.01. "

Yup. So perhaps the "correct" answer to this financial literacy question is: it's almost impossible to know, so take a couple of packages to the cashier and ask. If it turns out that there's a 2 box minimum purchase, buy two, otherwise buy one.

I am horrible slow at such basic calculations, but doesnt matter, i just stick to hard discount stores which do not play those games. Every store manipulates customers, but not with those two for one and similar "take now discount" signs. The per unit price is always there, in readible sice easy to find. In my experience only overpriced brands and overpriced stores play those games. In the end, no doing fractions in ones head fast is not an important skill in todays everyday life.

Reading the terms at a video game sounds rater irrational, far too much effort for that amount of money. In addition, at least in Europe the terms are always in breach of basic consumer law - now that is something good to know which is typically only taught at University here, so who cares what one "agrees".

Wholehartedly agree that the most important skill is to get as cyninical, in particular about all finance companies. One basically needs a degree in law and math to compare the price of many products sold, only knowing to stay away from them is a way out there.

"The terms are in breach of consumer law"; I remember a court case some years ago, at the time when programs whre still distributd on diskettes. A guy had a fire in his office and computer and diskettes were destroyed. Some companies sent rplacement but on asked that he buy new copies. He got them to court and won because their terms wer clearly that he had bought a license. The judge agred that the fire didn't terminate the agreement.

Keep it up Frances.

We love 'hot' and unhot economists downunder.

Seriously I hope you are getting some people down here reading this great blog now

The other thing about unit pricing is that there are often no agreed upon units. I have been in a supermarket where there were three brands that each had different per-unit prices on the supermarket label (one say per pound, one per ounce, one "each", etc.).

Financial literacy classes aimed at introducing people to concepts of investment should also start not with bond pricing, but with management fees and Helaine Olen.

http://helaineolen.com/books/pound-foolish/

John

John - my pet peeve is the paper towels, where the per unit price might be "per sheet", but every brand has different size sheets. And then to make things extra-complicated, sometimes the per unit price is given in per roll terms.

Different size? It's even diffferent thickness. And absorbency varies even with the same thickness...
Scott Adams (of "Dilbert" fame) coined the concept of "confusopoly".

From Wikipedia:
"Adams introduced the word confusopoly in this book. The word is a portmanteau of confusion and monopoly (or rather oligopoly), defining it as "a group of companies with similar products who intentionally confuse customers instead of competing on price". Examples of industries in which confusopolies exist (according to Adams) include telephone service, insurance, mortgage loans, banking, and financial services."

My pet peeve (perhaps not surprisingly) is pizza. Why is it that nearly every pizzeria in the world uses diameter to describe the various sizes they offer...when even 2500 years ago Euclid knew the volume of pizza one gets is proportional to the square of the radius. Honestly...they should be forced to state their prices per square-centimetre (as well as rigourously respect a minimum-acceptable-amount-of-pepperoni-per-hectare-of-pizza rule).

Giovanni,

:-)

Jacques Rene, confusopoly - I'll remember that.

Giovanni - yes, you're absolutely right!

Principle of the thing, Frank...principle of the thing. Besides, I still have to do length x width and then divide into price (granted, your approach does save me from having to remember the value of pi to six decimal places).

Thank you, Frances. I cannot fathom how such a blatantly deceptive practice has persisted so long without challenge. I ascribe it to global conspiracy orchestrated by a shadowy group I call the "Pizzarati".

But then there are pan pizza, deep dish pizza and thin crust pizza. Back to paper towel territory. ( And a good many pizzas taste like cardbord anyway.)

I agree, Jacques...it is an ineluctably multidimensional problem. But I say we go with price-per-cm^2 until the people at MIT, the Culinary Institute of America and/or Dominos can come up with a more exact standardized measure of pizza-borne deliciousness.

No wonder we are mystified. For years, seeing in my TVHebdo (the QC equivalent of TVGuide) a PBS sation listing "Cooking lessons from the CIA", I asked myself ?!?. Till I understood there are many CIA...

Not sure the distinction between the two CIAs is all that clear. I once watched a Culinary Institute of America video about installing listening devices in a Christmas turkey...

My pet peeve (perhaps not surprisingly) is pizza. Why is it that nearly every pizzeria in the world uses diameter to describe the various sizes they offer...when even 2500 years ago Euclid knew the volume of pizza one gets is proportional to the square of the radius. Honestly...they should be forced to state their prices per square-centimetre (as well as rigourously respect a minimum-acceptable-amount-of-pepperoni-per-hectare-of-pizza rule).

So what? It thus rises proportionally to one quarter of the square of the diameter.....

Sorry, that was my Engineering Degree talking.

And Heaven has smiled on Delissio and McCain's, who brought true risen-crust frozen pizza to consumers everywhere. No more cardboard!

"So what? It thus rises proportionally to one quarter of the square of the diameter....."

Well, for one thing, the factor of proportionality is Pi...which to the average Canadians is a book about a dude and a tiger.

A response to an article in the Economist:

"SIR – You mentioned research which revealed that shoppers often prefer “50% extra free” to a notionally more generous 30% reduction in price, and you cited this as evidence of irrationality or poor mathematical ability on the part of consumers (“Something doesn’t add up”, June 30th http://www.economist.com/node/21557801). I think you may be wrong and consumers may be right.

There is, as the advertising sage Jeremy Bullmore observed, a significant difference between a bonus and a bribe. A price tells you much more about a product than merely what it costs. A price cut may be sensibly perceived as a mark of mild desperation on the part of the seller and it is not unreasonable to infer from a price cut that a product is an inferior good. Charging the full price but adding something extra does not convey the same desperation. In any case this whole debate is silly.

If people value 50% extra free more highly than 33% off, then that is an end of the matter. Since all value is subjective, what you are doing by offering the former is simply creating more perceived value at a lower cost. Whether or not the resulting behaviour conforms to some autistic neoclassical idea of rationality is irrelevant.

If the sole purpose of life was to be rational, we would have banned golf years ago."

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