### Would Toyota sell fewer cars if they raised the price by a penny?

Last post (which I'm about to delete), I asked this question:

**Suppose that for the last ten years, Toyota had priced a Camry one cent higher than they did -- so, for example, a $23,000 model would have been $23,000.01. How many fewer cars would they have sold in that time?**

I asked a couple of my friends, who answered zero -- Toyota wouldn't sell any fewer cars at all -- because nobody would change their mind about buying a Camry for a single penny. And in the comments to the blog post that led me to ask the question, many commenters also believed the answer must be zero.

But I don't think it can be.

Suppose a typical price of a Camry is $25,000. Now, suppose that Toyota had raised the price to $45,000 instead.

You can be pretty sure that Toyota wouldn't sell a lot of Camrys at $45,000. There's too much competition in the midsize sedan market. Few people would pay an extra $20,000 to get a Camry instead of, say, an Accord or a Malibu. Some Toyota loyalists might, but, let's suppose 95% of them would not.

From 2000 to 2009, it looks like Toyota sold close to 4 million Camrys in the USA and Canada. At a $20,000 price hike, we assume they would have sold only 200,000 of them.

So a $20,000 increase results in a sales drop of 3.8 million units.

In other words, when they increase the price 2 million pennies, they lose almost 4 million sales. That's an average drop of two cars per penny.

That's a reasonable first estimate, that if Toyota had bumped the price by a single penny, they would have lost two sales.

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Now, you may object. You may say, why should I assume that *every* penny costs two sales? Maybe sales only start dropping when the price gets very unreasonable, like, say, $35,000?

Well, yes, that's possible. If you redo the argument on that assumption, you have to conclude that if Toyota raised the price from $35,000 to $35,000.01, they'd lose *four* sales.

That's possible. But ... do you have a basis for your assumption that consumers only start caring at $35,000? There's a strong basis for assuming that's *not* the case. If raising the price the first $10,000 had no effect on sales, Toyota would have done it! Their revenues would have increased by $10,000 a car, or $40 billion dollars over 10 years. To make that argument stick, you have to assume that you're forty billion dollars smarter than the people at Toyota who actually study this stuff.

Furthermore ... it seems more likely, to me, that the early pennies are more important than the late pennies. At $44,900, there are so few buyers left -- less than 6% of the original -- that a single penny can't eliminate two of them. It seems more likely that, at the actual price of $25,000, a single penny might eliminate at least three buyers, and at $30,000 it might eliminate only one (since there are fewer left to eliminate).

In fact, my best guess would be around 3 fewer sales per penny. Maybe even a bit higher.

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Another argument might be: consumers aren't actually responding to a single penny. They might be responding to, say, $100 increments. No buyer will change his mind over one cent, but maybe 20,000 buyers will change their mind over $100.

That sounds reasonable when I write it, but, when I think about it, it doesn't hold up. When do the 20,000 buyers change their mind? If it's only at $100, then it's the single penny between $99.99 and $100 that makes the difference! There's no way to plot a decrease in sales without SOME penny making a difference.

Here's a graph, with price on the horizontal axis and sales on the vertical axis. Connect them any way you want -- but you'll find that there has to be *at least one time* that a penny difference has a difference in sales. And you'll find that the average penny difference has to be around two cars, no matter how you draw the graph.

Now, maybe it's not every single penny that's the problem, but specific pennies. Maybe pricing the car at $30,000 leads to many fewer sales than $29,999.99, for psychological reasons. So, yes, that one penny makes the difference, but only because consumers are irrational.

But ... consumers are rational in not wanting to buy a $45,000 Camry, right? So the total sum of the sales drops is rational. Could it really just be the sum of a bunch of irrationalities?

And, we'd probably all agree that there would be fewer sales at $28,999 than $27,999. So it can't just be that.

In any case, not every potential buyer sees the same number. Many people have trade-ins, of differing values, so the actual bottom line is fairly random compared to the total price. An irrational consumer might pay $18,999.99 after a $6240.50 trade, but not $19,000.00 after the trade. In terms of the price of the car, the difference is between $25,239.49 and $25,239.50.

Factor in sales taxes and fees (which vary by state/province), and the fact that there's also a "99" effect in monthly payments (which vary by trade-in, interest rate, term, and dealer extras), and it becomes hard to argue that only certain pennies can be important.

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What we have, I think, is a very strong argument that a penny makes a difference. But, still, we can't imagine a consumer walking away on the basis of a single penny (I certainly can't). So what's going on?

This is my speculation, rather than a real part of the argument, but what I think is this: when a buyer is kind of on the verge of whether to buy or not, there's a certain amount of randomness involved, in terms of how the buyer feels at that moment. He might be seesawing between the Toyota and the Buick, which both seem like good values for the money. He's in the Toyota dealership, with his wife, looking at the final offer ... and, it might be 50-50 whether he goes for it or not.

I think that, unconsciously, if the price is a penny higher, instead of 50-50, it might be 49.9999/50.0001. I bet that's actually how it works.

I'd agree that for buyers who aren't on the fence, and know they want that car, a penny won't make a difference. If you *really* want a Camry, even after looking at the competition, then, to you, it's worth substantially more than the retail price (you have a high "consumer surplus"). The penny won't bother you. (But in that case, even $1000 may not bother you.)

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So: anyway, that's the argument. I think it's a strong argument, especially the part where you see you can't connect the two dots on that graph without individual pennies making a difference.

But, let me know what you think.

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Hat tips:

The commenters weren't completely convinced at this post from Brian Caplan, which makes a slightly different argument (and also brings up a point that I think also applies to sabermetrics (more on that here later)).

Also, the book "Mathsemantics" had a similar example, about how moving an airport ten miles farther from the city will reduce air travel (by 10 percent!!!).

## 8 Comments:

Very interesting; excellent work, Phil.

This sounds like an Austrian School of Economics article--inductive reasoning based on axioms we know *must* be true. (Incidentally, that is the approach I feel must be taken with economics.)

Phil: Totally agree with the argument. I would argue that you're saying something very similar to the mean value theorem.

Had to look up the Mean Value Theorem ... it says that if the average value is 2 cars per penny, then there has to be at least one penny where it's EXACTLY two cars.

Fair enough! Assuming pennies are continuous rather than discrete.

"Could it really just be the sum of a bunch of irrationalities?"

Darn straight it is.

Your unacknowledged assumption (shared my all macroeconomists) that also begs the question is that the demand curve is a line. But all the behavioral research we have shows that it is not a line, at all. Some parts of the demand curve are flat, some are quite steep, and there may be discontinuities, as well. In an economic model, we may approximate a demand curve as a continuous function, but that's a simplifying assumption that distorts reality when you are focused on something like the $.01 question.

Your latter question is interesting philosophically - it's the one grain of sand question. If you have a mountain and take off on grain of sand, is it still a mountain? If you keep doing that, is there the one single grain of sand that is the breaking point between a mountain and a hill or non-mountain? How could a single grain of sand by that difference?

This stuff is dealt with in Newton's discrete mathematics with derivatives and integrals, and is also a common philosophy puzzle. In fact, if I recall, your previous post had something to do with a well-known philosophical paradox relating to categories - seems to be on your mind!

I think you might really enjoy reading up on what people have said about very similar issues. The Stanford philosophy encyclopedia is a good resource. http://plato.stanford.edu/entries/sorites-paradox/

When I buy a car, the salesman doesn't use pennies- he is in whole dollars.

No, maybe adding a dollar to the price takes away unit sales of 200.

Well, I'm an economist, so I suppose I do have to comment on this.

It's always (what economists call) the marginal buyer who's affected, the one (or ones) who are just on the edge of buying or not buying a product, who change their minds when the price rises (or falls) a little. What "a little" means is difficult to quantify, unfortunately, for the purposes of this discussion, but, in general, yeah, even $0.01 on a $25,000 purchase is may to matter to someone. And the more competitive the market is, the more it will matter.

And the market for new cars has become a lot more competitive that it was 10 or 20 years ago (to say nothing of 50 years ago, when four companies sold over 90% of the new cars sold in the US). So that $0.01 price change will matter moe now than it did in 1960, when average car prices were much lower...

Interesting discussion here Phil,

But what about discrete changes in purchasing power of consumers?

I would think people tend to fall into minimum wage (mw) vs. mw + 5, mw + 10 etc... with a normal distribution about those means. (Under the assumption of the article, I understand that different tax laws might diffuse this discrete model into a continuous one, but I'll postulate that income tax laws follow a similar pattern as sales tax)

Thus, consumers are interested in cars within their price range (their purchasing power) and the price fluctuation is dependent on how valuable a car is relative to other commodities.

Therefore, certain pennies about the discrete purchasing power means are more influential than those most distant from the purchasing power means.

Assuming you are correct and one penny moves volume, why would every manufacturer I checked have all MSRP in multiples of $5?

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