Brett Rants

Cost Benefit Analysis

Cost < Benefit,
then a purchase is made.

Or in other words:

If BV = Buyer's Valuation
& SV = Seller's Valuation

then BV >= SV
is a prerequisite
for a sales transaction.

Introduction to the Problem

I read a magazine article (yes, I both can and do read) and the author of said article (although claiming to have studied economics for far longer that I) blatantly misconstrued the idea behind a Cost Benefit Analysis to the point it appeared (to me, at least, probably not to them) that they did not have the slightest understanding of the underlying nuances of the tool that is the Cost Benefit Analysis.

The Cost Benefit Analysis in Brief

Of course, the truth is that I have a rather low tolerance, understanding and valuation of technical jargon. And it is quite possibly that you, I, or some idiotic third person (you know who you are) may (indeed) have a different conception of what a Cost Benefit Analysis actually is. So, let me be explicit and define my terms. This is my website, after all, and if you don't like how I define my terms... um, tough.

In a Cost Benefit Analysis all the costs are added up. We shall call this Cost. I know, and here I said I didn't like jargon.

Then (assuming we don't have the attention span of a flea and are still working on a Cost Benefit Analysis) we add up all the benefits. And (wait for it) we shall call this the Benefit... or Total Benefit, but really, that seems a bit wordy to me, so why don't we leave it at Benefit?

And to me that's pretty straightforward, because it is entirely abstract. Or in other words, so far, all we (or I, but I like to think you are joining me on this little mental escapade) have done is made a pair of terms: call it a deuce of definitions.

And the assumption (and this is the only assumption made, because everything else in this formula is Do as thou wilt) is that if given the possibility of a transaction and, also, that the benefits exceed the costs (Benefit > Cost), then a rationale actor will make the trade; and if not, they won't.

And before you start putting together your list of objections, please pause for a moment and realize that I have presented the idea of a Cost Benefit Analysis, as a tautology. It is something that is always true. For, it is impossible for it to not be true.

A Tautology

A tautology is something that is logically true and never false, something that follows from the assumptions involved.

And my first assumption is that the following formula holds (always, everywhere):

If (Benefit > Cost), then Transaction

And that may not shed much light on the beauty of it all, so please realize what I, also, mean (and therefore, assume) is that:

If Transaction, then (Benefit > Cost)

And that's a tautology, because I can always make up some cost or benefit, so that the equation balances. And this is what my esteemed colleague (not that we are collegiate in any sense of the word) failed to understand.

Costs & Benefits

Costs are everything that might make a person (the particular person we are talking about and it is always a particular -- if hypothetical -- person) not want to go through with the transaction.

This includes such things as the purchase price (in dollars if you please), the time involved (rounded to the nearest second), negative social factors (and seriously, don't ask my how one measures this, so it truly is a Do as thou wilt situation), the time value of money (individual results may vary), and so on and so forth until you I and everyone on the planet are blue in the face.

And Benefits are all the good things a person (a specific person, as we are not talking about averages, here, but a specific transaction, rooted in reality) might get from indulging in the transaction.

This would include the purchase (ownership of some new item or experience), the joy of spending money (I think they call that Retail Therapy), any social signalling (the value to be had from keeping up with the Joneses), along with any secondary benefits (such as doing or not doing my part for the environment... or thinking 'I'm going to live it up because my friends ditched me'; and so, I need a pick me up), and so on and so forth... until, once again, we are all blue in the face.

So, it's not like this soda costs a dollar; and thus, because I made this purchase all sodas are worth a dollar for everyone, for all time, everywhere on the planet.


For instance, I may have made a particular soda purchase, because (just as a for instance):
  • Thirst
    • I presume this is the usual reason for buying a soda.
  • Sugar
    • I usually drink milk or juice, so craving soda tends to mark a low blood sugar moment for me.
  • Immediacy
    • I want it. I want it now. And it is a lot easier to get soda in this world than a chocolate milkshake, which is maybe what I really want.
  • Ego Enrichment
    • Believe it or not, drinking soda is an indulgence for me, so it tends to make me feel rich.
  • Social Factors
    • Hey! This is a special occasion, so let's live it up!
Note: this is not intended to be a complete list. And truthfully, by its very nature, it is unlikely any list of this sort could ever be truly complete.

  • Money
    • I like money; and all things being equal, wish to part with as little of it as possible.
  • Future Value of Money
    • If I spend money on this, I cannot spend it on something else... nor earn interest on the money in the interim.
  • Worry
    • As above, spending money means I don't have it. This is a bad thing. I may need it for something else much more important than a silly can of soda... say, a candy bar.
  • Ego Erosion
    • Spending money makes me feel poor. It's a weird sort of give and take, as more or less the opposite was listed as a benefit. The fact remains, the more money I spend, the more I wish to put on the brakes. While, if I haven't been spending money for a while, I look for luxuries, in which to indulge.
  • Weakness
    • Do I really need this soda? Am I not strong enough to survive in this world just a little while longer until I find a drinking fountain from which to drink some free water?
In the end (it is my belief), that for any argument a person can make in favour of buying a soda, there is a (very close to equal) counter argument against buying said soda... and vice a versa.

Argument: Soda cans destroy the environment.

Counter Argument: I don't care. The Earth is dying anyway.

And that's why (as I define it) a Cost Benefit Analysis is a tautology. I'm smart enough that I can always make that equation work the way it is supposed to work, finding new benefits if a transaction was made or new costs if it was not.

I don't (well, very-very seldom) give money to bums, therefore (and this is the only thing a Cost Benefit Analysis will tell you) is that I would rather keep my money that give it to bums.

See how circular that is?

I won't give money to bums, I must value money more than giving it to bums.

I bought a soda, so in this situation, I must value a cool refreshing bubbly soft drink (boy, doesn't that sound good right about now) more than I value the dollar or two it cost.

A Cost Benefit Analysis is not predictive in the least (and using it as such is using it in the wrong way).

If I don't give money to bums, it's not because I don't value the life of bums... well, maybe I don't. But that's not what the Cost Benefit Analysis tells us. It merely tells us that I value something (by definition) that offsets whatever imaginary argument someone else might want to throw at me:

Bums need money -> I don't care

They'll starve without my help -> No they won't

I have a social duty to help -> ironically, some folks say my social duty is to not give any money to bums, as it's like feeding the pigeons in the park

And so on and so forth.

I'm not even trying to dig deep, here, because (for the moment) the exact rationales are not important. I'm just trying to show that the list of rationales (for or against any monetary expenditure of funds) is near endless.

Thus, another way of saying

If Transaction, then (Benefit > Cost)


People have reasons for doing the things that they do

which seems sort of obvious and non-controversial to me.

So, Why Bother?

Like everything else in the mental sphere (mathematical models, slogans, religions, ideologies, etc) a Cost Benefit Analysis is a tool. And the purpose of this particular tool is (ironically enough) to let you know when you haven't dug deep enough.

If you think you've found an exception to either:

If (Benefit > Cost), then Transaction


If Transaction, then (Benefit > Cost)

You haven't! You simply haven't looked at the problem hard enough.

It's a Zero Sum World

The world, actually, is not Zero Sum. The economy is growing. But most sales transactions have nothing to do with the growth of the overall economy; and rather, have everything to do with conflict and disagreement in the moment.

Remember, this equation must hold true for both the buyer and the seller:

If Transaction, then (Benefit > Cost)

And if that's the case, then that means:

Seller's Benefit > Seller's Cost

Buyer's Benefit > Buyer's Cost

Which brings almost no clarity to the issue at all, so let me point out that the Selling Price is the same for both the buyer and the seller. It's a cost to the buyer. And a benefit to the seller. Or in other words (and in the end), money tends to be the equalizing factor (sometimes there are other more important considerations, but usually not), flowing from one party to the other (typically, from the buyer to the seller), making up for any outstanding costs.

Or if that's still too complicated and you want the shorthand version, in a typical transaction (or in any pure transaction that relies mainly upon money as it's motive force), the buyer and the seller fundamentally disagree on the worth of the item: the buyer valuing it at a higher rate (i.e. for more money) than the seller.

Which means, folks don't come to The Market to agree. They come to The Market to disagree.

Seller: Transaction if Price > $
Buyer:  Transaction if Price < $

Or taken another (slightly different) way, sellers (by definition) must sell their wares for more than they think they are worth (i.e. more than they would buy them for), while buyers must do the reverse.

And that's both a reasonable and unreasonable concept all at the same time... as many of your high faluting intellectual concepts are.

It's easy to get such complicated ideas wrong... as you may feel that I have here, which is fine.

I mean, even if you still disagree with me (you stubborn mule, you), this is how I define a Cost Benefit Analysis and how I interpret Trades in the Market. And for whatever reason, I have found these ideas to be useful, allowing me to pull back certain layers of reality for closer inspection... while, no doubt, obfuscating others.

Thus, I give you free reign to do with these ideas as you may wish.

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