Challenging the Certainty in the Claim I often Make

I recently made a comment about a pricing article that recommends doubling prices.

The article under question claims,

Higher prices simply work better. Here’s seven psychological reasons why… (and gives seven reasons)

You may think I make similar claim too. Well, am I on solid ground making a comment like this with bold claim?

If one price is good, two are better.

It states that if it were possible to sell a product profitably at one price, it is certain that there will be higher profit from two prices.  Note that the profit here means Price less marginal cost and does not include fixed cost. You might find there are other cost components that make the second price untenable. But that is a factor you can control.

Some time back I did take a critical look (to an extent I can suppress my own biases) at this claim.

It is impossible for me to re-do years of economic research on consumer surplus, price discrimination and other economic works. The  statement I make relies on those works first started by Pigou.

The point to note is that my claim is not inductive logic. It does not follow from this statement,

“if two prices are good, three are better”

Yet, I did not address adequately the certainty in this claim. Shouldn’t this claim be more like,

“if one price is good, two are likely better for most situations”

No.

Let us rely on the works of  Thomas Bayes for this (P is the probability)

What I am stating with my claim is,

P(2 are better | 1 is good)  = 1 and not

P(2 are better) = 1

That is a huge difference.

The first probability statement is conditional probability. It is the equivalent of stating, “you picked a random card from the deck, if it is Jack of Spade, then we are certain that it is a face card).

It states that if it were possible to sell a product profitably at one price, it is certain that there will be higher profit from two prices. Either a moment’s reflection will convince you or you need to dwell into tomes of economic research.

The second probability statement is false. To see that we have to expand it

P(2 are better) = P(2 are better| 1 is good) . P(1 is good) +
P(2 are better | 1 is not good) . P(1 is not good)

As you can see from practice, P(1 is good) is a much small number than 1 and hence the it is not at all certain “two prices are always good”.

Ignoring all these, the net of these to you the marketer/entrepreneur/product manager is

If you find a market for your product at one price, you will find bigger market (measured in $$) at two prices.

2 thoughts on “Challenging the Certainty in the Claim I often Make

  1. Leigh
    Correct, if there exists one price, then there exist two prices (both of which could easily be different from the single price) which are better.
    It is guaranteed in the Price discrimination lit starting in early 1900s.
    I would be very interested in hearing the counterexample that does not include externalities.
    Of course I will be happy to find the two prices for any marketer, for a price (or two).
    -Rags

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  2. You have left undetermined the actual two prices that you should use. I assume you’re not asserting that any two prices are better, but that there exist some two prices which are better?

    And do you claim that this is guaranteed always to be true by economic theory, or just that it is true in all practical situations? The latter I intuitively agree with; but I suspect I could come up with a counterexample to the first. Interesting, anyway.

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