David R. Henderson  

Clarification on Consumer Surplus

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Commenters on my previous post on consumer surplus (CS) raised some questions that I want to respond to.

1. Philo points out that in figuring out our consumer surplus, our baseline matters crucially. So, for example, my CS from one package of Advil, given that I can buy another only an inch away for the exact same price, is zero, even if the Advil instantly cures a splitting headache. But my CS from that Advil, if my baseline is having no other Advil and no other pain relief medicines, could be very large indeed.

This matters for companies pricing their products. One of my longest-time friends has made a really good living helping firms price their products. He has pointed out to me that often the other consultants and company decision-makers he consults to make an elementary mistake by not understanding the issue of the baseline. They will see what a great product they have and then shoot for the moon by wanting to charge a high price that captures much of that large CS. The problem: if there's another company with a product that's almost as good, that apparently large CS is not so large and the price premium they can charge is roughly equal to the difference in the consumer's valuation of the two products.

2. Philo also points out that when a product is given away, there is no trade. He's right. I should have stated that CS is almost always a measure of the consumer's gain from trade. When the product is given away, though, there is no trade but there is still CS.

3. Robert Johnson, after complimenting me on the post (thanks, Robert), raises an interesting question:

If I'm starving, then I might be willing to spend everything I have for a loaf of bread. But if everything I have is one dollar, and the bread costs $2, then it's definitely the wrong conclusion to say that my consumer surplus from buying the bread is minus one dollar. If the bread costs $1 then it's still the wrong conclusion to say that my consumer surplus from buying the bread is $0.

Suggestions for how to solve this problem?


Here's my answer. First, if all you have is $1 and the bread is priced at $2, then you don't have negative CS because you don't buy the bread. (I'm assuming away the possibility of borrowing to buy the bread.)
Second, if you have $1 and the bread is priced at $1, and you buy it, your CS really is zero. How do we know? Because if it had been priced at $1.01, you wouldn't have bought it.
This gets to the issue of "willingness to pay." We economists use that term very differently from how almost everyone else uses it. By "willing to pay," we mean what other people mean when they say "willing and able to pay." So, for example, if someone says, "I'm willing to pay $10 but I have only $1," then (again, assuming no possibility of debt), the economist will respond, "No, you're not willing to pay $10." I think non-economists sometimes think we're being smart asses or, even worse, callous people, when we say that, but I don't think we are. We're just sticking with this peculiar use of language.


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CATEGORIES: Business Economics



COMMENTS (28 to date)
Daniel Kuehn writes:

People talk about microfoundations of macro all the time, but this is precisely the circumstance where we need to think more about macrofoundations of micro.

If microeconomists had a way of thinking about distinguishing "effective demand" from "demand" we'd probably have much better responses on these willingness to pay glitches.

Consumer surplus is still a valuable idea. I was glad to see you post on it yesterday because the concept has been conspicuously absent from the conversation about consumption bundles and innovation with Cowen's new book. It's a valuable concept, but it's really shaky to understand what "optimality" really means if a lot of the downward slope of a consumer demand curve is due to ability to pay, rather than just willingness to pay.

I'm not smart enough to say exactly what we should do about it all.

Robert Johnson writes:

Prof. Henderson,

Thanks for replying to my question. I understand that consumer surplus *is* defined in dollars, and that definition means that relevant information about willingness to pay (e.g. how much I have available to pay with) is sort of folded into consumer surplus. My complaint is that this relevant information is *obscured* because it is not made explicit.

I guess I just want consumer surplus to reveal more about utility or improvement to welfare, since that's where the rubber meets the road.

david writes:

Two points:

In standard consumer theory, one can alter an agent's willingness-to-pay by changing the price of other goods or income. Not only the price of close substitutes but generally of any good; thus, any definition of "consumer surplus" that discludes such effects is missing something.

(it may help to think of it this way; suppose the consumer values an apple at $10, and has $10; the apple is priced at $1. The consumer surplus is "$9", but what it actually is, is what the consumer then goes on to spend $9 on. That's what gives the consumer utility! Of course the consumer surplus of the first n-1 Advils is $0, if the consumer simply buys the nth Advil, or if the only things available in the world are Advils and you only need one. Isn't this a much better way to think of it than an allusion to baselines which are not, in fact, constant baselines?)

Second - "willingness to pay" is a partial-equilibrium sort of intuition, and you're trying to making a general sort of point, which is why you're running into nonintuitive behavior. How's this: capture the notion of gains from trade directly and invoke the exchange economy. Here's your initial endowment. Here's your post-trade endowment. The difference is your surplus; goods which you net sell generate producer surplus and goods which you net buy generate consumer surplus. And we're done!

david writes:

*note
surplus = producer-surplus = consumer-surplus
in that last paragraph; as far as exchange economies go, producer and consumer is a matter of perspective. Everyone who exchanges stuff with you is a producer to you.

Robert Johnson writes:

"The consumer surplus is "$9", but what it actually is, is what the consumer then goes on to spend $9 on."

"...capture the notion of gains from trade directly..."

These are really helpful. Thank you!

MikeDC writes:

I don't like your final anecdote (your CS is $1 if you pay $1 and that's all you have) at all. You're going back on a point you (rightly) made in your prior post. CS can't be measured for certain, but it must be >=$1. We can estimate consumer surplus as the most we'd pay minus what we do pay, but we shouldn't forget it's really a non-monetary concept.

Rather than dicker over terms (because non-economists rightly laugh at us), simply admit that and accurate estimate and trade is contingent upon parties having enough medium of exchange to make their demand effective.

However, without money, there's still CS. Obviously. Folks can barter many other things besides money. "Look, I've only got $1 in my pocket, but if you give me that $2 loaf of bread, I'll clean your store. Or do your dishes. Or give you my watch".

In any case, the CS generated by the trade is still an estimate, but it's perfectly valid to say the bread is worth an hour of my time cleaning your store, for instance.

Peter writes:

I think the problem with measuring the consumer surplus is that amount I am willing to pay will be anchored by the price of the good.

Consider the story in this blog post: http://www.knowingandmaking.com/2009/12/applications-of-behavioural-economics.html

How can you measure consumer surplus, when someone's willingness to pay is not developed independent of the price?

Julien Couvreur writes:

Regarding point no. 2, why don't you consider gift giving as a subset of trade?
All the conclusions you reach about voluntary trade, namely that both participants gain in the exchange, still hold in the case of voluntary giving. There is no difference.

Regarding point no. 3, I don't agree with the analysis. If you buy the bread for one dollar, but don't buy it for one dollar and one cent, that doesn't show that your CS from buying the one-dollar bread is zero.
In terms of preference scales, bread ranks higher than 1$, and that's it. Since you don't have 1.01$, your preference scale simply does not provide a comparison between the two options. In particular, you don't have any upper cap.

David R. Henderson writes:

@MikeDC,
You misstated my point. If you're willing to pay $1 and you do pay $1, then your CS is zero, not, as you say, $1. And CS is a monetary concept, although, as you noted, if there's barter, we could estimate CS in terms of the bartered good.
@Julien Couvreur,
It's true that both participants gain whether someone gives a gift. I'm simply saying that we don't normally think of that as a trade. You could, of course, stretch the concept of trade. I don't understand your last point, or, if I do understand it, it's the point that item #3 in my post to refute.

Sridhar Loke writes:

I don't agree with the baseline point that Philo made. If there is a perfect substitute at the same price, then it doesn't matter which one you purchase, the consumer surplus is the same. If you have an ailment that you would pay $10 to get rid of, and there is a product that will help you achieve that goal for $1, then there is a surplus of $9, period.
Now, if the product is not a perfect substitute, then your surplus will change. IF there is a pill that costs $2, but cures only 90% of your headache (implying that you would pay $9 for that product), then the surplus in that case is $7.
Irrespective of the number of products out there, you would only purchase one, and that will decide what the surplus is.
Robert Johnson's issue can also be addressed (in fact, it is already addressed) in the same way. There has to be a trade for surplus to exist.
I think surplus can surely exist in case of a $0 trade (giveaway). Can't see why not. In this case, your entire willingness (and capability) to pay is your surplus.

Joe writes:

You can measure consumer surplus where you can accurately graph a supply and demand curve.

If you draw a supply and demand curve, then a horizontal line through the competitive price point where they meet, then the area bounded at the bottom by the competitive price and bounded at the right by the demand curve represents the consumer surplus.

If that's not practical, you can usually demonstrate a consumer surplus where there is a price change. Let's say product X costs $2, and 1000 people buy it every day. Then market conditions change, X costs only $1 and 2000 people buy it every day. You can say that 1000 people are getting at least $1 in consumer surplus.

MikeDC writes:

Oops, yeah, I botched the numbers, but I don't see how the misstatement is germane to the point, which was that, if I trade the $1 in my pocket for $1 of bread, the consumer surplus is >=0. Not 0.

Viewing CS as a monetary phenomenon seems both arbitrary and incorrect. It certainly exists in barters, whether anyone calculates it back to dollar values or not. Two cavemen swapping fire and water would generate surplus value.

Robert Johnson writes:

Just to be clear, my point is that there is something intuitively wrong with saying that the *willingness* of the starving man to pay is one dollar (everything he has), and his consumer surplus is zero if the bread costs one dollar. Obviously this statement doesn't sufficiently describe the man's options and preferences.

He is up against a hard limit, a discontinuity. He can trade everything he has for sustenance, or he can cease to exist and give up all possible future utility. Does it make any intuitive sense that all of his possible future utility (if he lives) is exactly equal to the one dollar he has now? If that is true, then shouldn't he be ambivalent about buying the bread?

Is it just me, or is there something troubling about this?

liberty writes:

I think the crux of the issue that some in this thread point to is this definition, which is presented differently by different economics courses and schools of thought:

"Consumer surplus is the difference between the maximum amount the consumer is willing to pay and the amount he actually pays. "

In neoclassical utility/welfare economics, this "willing to pay" is presented with utility curves that try to get inside the consumer's head. It is said that the person was "willing" to pay a lot more - even if we never look at his budget line. It may be assumed that he had the money to pay more, but we don't always talk about that. However, if we do assume that "willing and able" collapses to "willing" then we end up making Rothbardian assumptions: every transaction that people wanted to make they made, their preferences have been demonstrated in the market.

However, as Daniel Kuehn said above: "It's a valuable concept, but it's really shaky to understand what "optimality" really means if a lot of the downward slope of a consumer demand curve is due to ability to pay, rather than just willingness to pay."

And Robert Johnson (just above) demonstrates some of the absurdity that comes of collapsing willing and able.

Philo writes:

My thought was that consumer's surplus is a relative or relational quantity: it is a function with two (really, three) arguments, namely (1) a person and (2) a thing or situation that he possesses or enjoys (and (3) a *time*). The person's consumer surplus is the maximum amount he would have been willing to pay to possess/enjoy that thing/situation, minus the amount he actually is paying (at the time). (I mean "is paying *currently*; sunk costs are irrelevant. But non-monetary costs--depreciation, etc.--*do* count, so 'paying' may be too narrow a term.) The "baseline" is just the person's total situation *minus the thing/situation for which a consumer's surplus is being assigned*. (I assume, optimistically, that there is a unique way of subtracting this thing/situation from the person's overall situation.)

At any moment each of us possesses/enjoys a great many things/situations, for each of which he can be assigned a consumer's surplus (or deficit, if he is being compelled to buy something he considers overpriced). It makes no sense to add these numbers together; there is no *aggregate consumer's surplus for an individual* (at least, I can think of no way to make sense of such a notion). Care is advisable in specifying just which thing/situation we are talking about when we assign someone a consumer's surplus (and we also should specify the time); woolly thinking about consumer's surpluses is all too easy.

Philo writes:

@ Sridhar Loke:

". . . there is a surplus of $9, period." There is a surplus of $9 for *something*, but not for *obtaining just this packet of pain-reliever*--for *that* the consumer's surplus is (as I said) zero. The surplus of $9 is for *obtaining a pain-reliever (unspecified)*. Two different items, two different consumer's surpluses.

Tracy W writes:

Robert Johnston, consumer surplus is not the same as "all of his possible future utility".
I think, here, that you are expecting consumer surplus to do more than it can possibly do. People's options and preferences are complex, too complex to ever be fully described by one simple concept. But that doesn't mean that simple concepts are useless. Any person's preferences are far more complex than just food and water, but knowing that people consume roughly so many calories and need so much water a day is still useful information.

(Utility is just a name economists stick to the whole mass of what people want, like we use names like "Robert" and "Tracy" to refer to people rather than relating their entire life-stories, which we probably don't even know).

Robert Johnson writes:

Tracy,

I think David said it well. "...what it (consumer surplus) actually is, is what the consumer then goes on to spend $9 on. That's what gives the consumer utility!" See his comment (third from the top).

If I buy bread to avoid starving, my surplus is that I don't die. Minus whatever I paid for the bread.

Tracy W writes:

Robert - so you're not dying, but you don't have any more money in this case, so you can't get any utility from your consumer surplus.

Let's work through this again. I have only $1 in the entire world, and I spent it on bread to stay alive. I was willing to pay everything I had, and I paid that. I get all the future utility from staying alive, as you say but consumer surplus is zero because I have no left-over money.

Now, some new bread-making technology comes along, and the price of bread falls to $0.5, but nothing else changes, so I still have $1. My consumer surplus is now $0.5, I was willing to spend $1 on bread, but now I only have to spend $0.5 on bread. I still get all the future utility from staying alive that I did before (but we don't know how to measure it), and I get the utility from whatever I do with my leftover $0.5 (perhaps I spent it on some butter, perhaps I spend it on some booze, perhaps I put it on the ground and look at it admiringly).

Consumer surplus != utility. Consumer surplus can be used to buy an increase in utility, but it's not utility in and of itself. It does not capture everything there is about a person's preferences and options. It's not intended to capture all of that.

Robert Johnson writes:

Tracy,

Right. That's what Prof. Henderson is saying also. He says, "We economists use that term very differently from how almost everyone else uses it."
Believe me I get it.

So if you embrace this definition of consumer surplus - literally defined in dollars, and not related to utility - then in some situations you're counting angels on pinheads. In some situations this concept of consumer surplus just doesn't tell you anything useful at all. That's the whole point of the story of the starving man.

Tracy W writes:

Robert Johnson, if you get it, then why does it trouble you so much? Yes, in some situations the concept of consumer surplus doesn't tell us much, including the situation of the starving man, but you seem to be feeling quite intensely about this.

By the way, consumer surplus is related to utility - the reason we care when consumer surplus rises is that then people have more money (or bartered goods) to spend on something else, and that something else will presumably bring them utility.

James Oswald writes:

Consumer surplus is determined by the alternatives consumers have - their opportunity costs. As Philo points out, your alternatives to buying aspirin determine your consumer surplus, not your total enjoyment of the product. A person will only be willing to pay as much the subjective value between one good and the next best alternative they have.

Consider Yoram Bauman's Snickers bar. If someone offers you a Snickers bar or nothing, your consumer surplus is the value of the snickers bar. If they offer you either one Snickers bar or another snicker's bar, your consumer surplus is zero - even if you really like Snickers.

Julien Couvreur writes:

@David

Let me try and clarify my reply to item #3.

You say: "... if you have $1 and the bread is priced at $1, and you buy it, your CS really is zero. ..."

I say, no.

If you have $1 and buy the bread for $1, then I conclude that you prefer the bread to $1. All I can establish about your subjective valuation is "1$

Also, I can not conclude to any upper bound (something like "bread

Generally, I think that consumer surplus is a very important notion, but I am wary of trying to quantify it (in dollars or otherwise).

Julien Couvreur writes:

Sorry, my most recent comment got mangled (special characters).

@David

Let me try and clarify my reply to item #3.

You say: "... if you have $1 and the bread is priced at $1, and you buy it, your CS really is zero. ..."

I say, no.

If you have $1 and buy the bread for $1, then I conclude that you prefer the bread to $1. All I can establish about your subjective valuation is "$1 < bread".

Also, I can not conclude to any upper bound (something like "bread < $X") because there is no observable information that would indicate such a subjective ranking (which only includes options available to and considered by the individual).

Generally, I think that consumer surplus is a very important notion, but I am wary of trying to quantify it (in dollars or otherwise).

Philo writes:

". . . in figuring out our consumer surplus, our baseline matters crucially." The baseline is just what is left over from the consumer's circumstances when the thing/situation that he possesses/enjoys--the consumer's surplus of which we are determining--is removed. Just in specifying this thing/situation we *automatically* specify the baseline.

Tracy W writes:

Julien Couvreur - but if you were buying bread at $2 a loaf, and then the price of bread falls from $2 to $1, and you keep buying the same amount of bread, we know that your consumer surplus has risen by $1 for each loaf of bread that you were buying.

And, to the extent that the fall in the price of bread induces new customers to enter the market, or existing consumers to buy more bread, we know that their consumer surplus per loaf is somewhere between $1 and $0.

Philo writes:

Originally I said (in a comment on the earlier "consumer's surplus" post) that the value of having auto transportation available to me today was pure consumer's surplus, since I had no out-of-pocket expenses today for it. That is correct if 'consumer's surplus' is defined in terms of *paying*, as being what I would be willing to pay less what I am actually paying. Rpl's objection--that I was ignoring costs other than overt payments--really amounts to suggesting a different definition of 'consumer's surplus', as *the costs I would be willing to incur less the costs I am actually incurring* (currently; I do think we should ignore sunk costs). I agree that this is a more useful notion, and so the definition in terms of *cost* is preferable to the definition in terms of *payment*. I wonder if David Henderson agrees.

James Oswald writes:

"Is it just me, or is there something troubling about this?"

That's why CS is not a measure of utility. The CS is zero in the bread example, but the starving man gets near infinite utility. CS is dependent on the alternatives people face. Strangely enough, the better alternatives someone has, the lower their CS, but choices left untaken have no impact at all on utility. Willingness to pay is not a good measure of how much someone values something because of budget constraints, as you note.

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