An Example of the Possible Divergence of Willingness-To-Pay and Preference

In a previous post, I suggested that I thought it reasonable to not be willing to pay the full price that would entirely offset the perceived benefit of a possible exchange. Some of the comments effectively suggested that if I was willing to pay only 80% of the price that would offset the perceived benefit I was either violating a definition or inadvertantly re-valuing money. Let me start with an example which attempts to address these issues.

Assume that I drink both Diet Sprite and Diet Pepsi at the same constant rate. Also assume that I subjectively value them both the same under all conditions and that I do not consider one as a possible substitute for the other.

In fact, there is only one thing that distinguishes one from the other.

If I go into a supermarket, I find that the price of the Diet Sprite is sometimes $1.50 for a 2 liter bottle and sometimes $0.79. In contrast, the price of a bottle of Diet Pepsi is always $1.50.

To simplify, we will only consider the trips to the supermarket at times in which I have a stock of exactly one bottle of each drink remaining in my refridgerator.

The purpose of buying either drink is to assure that I do not run out of either drink.

My purchasing rules are as follows:

1. If the price of Diet Sprite is $1.50, buy one bottle.
2. If the price of Diet Sprite is $0.79, buy six bottles (the limit, as it happens).
3. Always buy six bottles of Diet Pepsi at $1.50.

It should be clear that these rules are an attempt to economize on the use of money and still fully satisfy my ongoing desire for both drinks.

If the price of a Diet Sprite is $0.79, I buy six of both drinks. Every drink that I buy, one through six, demonstrates a preference for that drink over the price that it requires. Since all six of the Diet Pepsis have a price of $1.50, they are all preferred to $1.50. Since the two drinks have the same subjective value by assumption, all six of the Diet Sprites are preferred to $1.50 as well, even though the actual price paid is $0.79. There is no anomaly to be explained in this case.

In contrast, if the Diet Sprite price is $1.50, only one bottle is purchased. We know that Diet Sprites two through six are preferred to $1.50, but we don't purchase them. The money used to buy the two drinks comes from the same place, so there's no question of the value of money changing. What explains the restraint from purchasing?

The problem is a logical error in the understanding of demonstrated preference.

If a purposeful action (exchange) is undertaken, this correctly demonstrates an underlying corresponding preference. However, the lack of an action doesn't necessarily indicate a reversal in the order of preference.

Every purposeful action must be preceded by a preference. But the universe of possible preferences is infinitely greater than the number of possible actions. There are many reasons why a given preference may not be demonstrated in action. There may be no counterparty with reverse order preferences to trade with. In fact this has to be true for all ordered preferences that are shared by all humans. For a purposeful
action to occur, it is necessary for a corresponding preference to exist. It is necessary, but not sufficient.

If all preferences do not result in action, then some of them can remain unsatisfied as potential, but unrealized exchanges.

Since not all preferences are satisfied, there is no reason that the gating factor that blocks a satisfying action cannot be a voluntary refusal to realize the satisfaction of preferences of too little perceived benefit. This allows us to economize on the use of money and not require us to make every beneficial purchase opportunity that comes along, no matter how minimal the perceived benefit.

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We know that Diet Sprites

We know that Diet Sprites two through six are preferred to $1.50, but we don’t purchase them.

No, we don't know that. You are forgetting that marginal value decreases with each additional can bought. It's not necessarily true that the marginal value of each additional can stays above $1.50 all the way through the 12 cans.

Suppose you have gone to the store and have found the Cokes and bought them and put them in the car, and are now heading back to the grocery store to buy the Sprite. You get to the store and you see:

a) The Sprites cost $1.50. Well, your marginal value for your first can of Sprite is at this point slightly above $1.50. But it dips below $1.50 at the next can, so you buy only one can.

b) The Sprites cost $0.79. In this case, your marginal value for your first can is slightly above $1.50, and your value for the second dips below $1.50 but is still well above $0.79, so you buy the second can as well, and you continue all the way through the 6 cans of Sprite. The marginal value of the 6th can of Sprite is, say, $0.80.

Make that bottles, not cans.

Make that bottles, not cans. Add "diet".

If all preferences do not

If all preferences do not result in action, then some of them can remain unsatisfied as potential, but unrealized exchanges.

I agree, but I think this is a commonplace and I don't think it gets you what you want. I'd rather date Rachel Weisz than Jennifer Lopez, but they're both way out of my league, so I won't be exchanging Lopez for Weisz any time soon.

Constant, No, we don’t

Constant,

No, we don’t know that. You are forgetting that marginal value decreases with each additional can bought. It’s not necessarily true that the marginal value of each additional can stays above $1.50 all the way through the 12 cans.

Yes we do. We always buy 6 bottles of Diet Pepsi at $1.50 and the two drinks always have the same value relative to each other. Since the sixth bottle of Diet Pepsi is preferred to $1.50, the sixth bottle of Diet Sprite must be as well. The first bottle could have a benefit offsetting price of $10, but there is no way to tell from the problem, nor any need to know.

Remember that the two drinks are not substitutes for one another. The drinks satisfy separate demands for Sprite and Pepsi, not a general thirst.

Regards, Don

Since the sixth bottle of

Since the sixth bottle of Diet Pepsi is preferred to $1.50, the sixth bottle of Diet Sprite must be as well.

No. If you first buy six bottles of Diet Pepsi and then you start with the Sprite, then the first bottle you buy of Diet Sprite after that is as valuable to you as the seventh bottle of Diet Pepsi, were you to buy a seventh. That is what you assumed: "I subjectively value them both the same under all conditions." Under the condition that you have just bought 6 Diet Pepsis, then buying one additional bottle of Diet Pepsi *or* buying your first bottle of Diet Sprite must have the same value for you.

Thus, after you have bought 6 Diet Cokes, then the 6th bottle of Diet Sprite is as valuable to you as the 12th bottle of Diet Pepsi would be, if you bought 12 bottles of Diet Pepsi.

Think of it this way: since you are indifferent between Diet Sprite and Diet Coke, they are from the point of view of your preferences the same product. You could call them Diet Sproke.

Remember that the two drinks

Remember that the two drinks are not substitutes for one another.

That contradicts your other statement. (“I subjectively value them both the same under all conditions.”)

Maybe you want to try again.

Constant, No. If you first

Constant,

No. If you first buy six bottles of Diet Pepsi and then you start with the Sprite, then the first bottle you buy of Diet Sprite after that is as valuable to you as the seventh bottle of Diet Pepsi, were you to buy a seventh. That is what you assumed: “I subjectively value them both the same under all conditions.” Under the condition that you have just bought 6 Diet Pepsis, then buying one additional bottle of Diet Pepsi or buying your first bottle of Diet Sprite must have the same value for you.

No, my intent is to say that the first Pepsi has the same benefit as the first Sprite, and the same for 2-6. Also, that a Pepsi cannot satisfy a desire for Sprite, and vice versa. If you claim that I cannot unambiguously express this, you are probably right. Feel free to suggest something that does.

Thanks, Don

Don, No, my intent is to say

Don,

No, my intent is to say that the first Pepsi has the same benefit as the first Sprite, and the same for 2-6. Also, that a Pepsi cannot satisfy a desire for Sprite, and vice versa.

In that case, then what you are doing with Pepsi is what you would have done with Sprite had Sprite always been $1.50 every time you went to the supermarket.

So, if Sprite were $1.50 every time you went to the market, then your practice would be that you would always buy 6 Sprites on every visit. But in the current situation, where Sprite is sometimes $0.79 and sometimes $1.50, your practice is that you buy 1 Sprite when it is $1.50 and 6 when it is $0.79.

It is not clear to me that this would happen outside of very exceptional circumstances. Essentially you have something like a negative sloping demand curve. The average cost of Sprite drops and your response is to reduce your overall purchases of Sprite. Suppose this price fluctuation happens on alternate trips. Then every two trips, you buy a total of 7 Sprites (6 + 1). Whereas if Sprite had been $1.50 all the time, you would buy a total of 12 Sprites every two trips (6 + 6).

It doesn't seem to me a very likely scenario. I can of course come up with explanations of the behavior which violate your assumptions - for example I might hypothesize that if Sprite is cheaper it loses its cachet and so loses its value. But that violates your assumptions.

Two things seem clear to me:

a) alternative soft drinks are very good substitutes for each other in the real world. They both quench thirst, both accompany a meal, etc. If you drink too much of one, you're not going to want to drink the other until for a while. This is a reality which you can say you assume away in your scenario but it's hard to forget it, and so I think it plays a role in making your thought experiment seem credible, even if you are trying to rule it out by fiat.

b) if we assume that alternative soft drinks are very good substitutes then your thought experiment is obviously correct, but in the way that I explained it - it demonstrates decreasing marginal value.

negative sloping demand

negative sloping demand curve

I mean positive sloping demand curve. As price goes up, demand goes up.

Constant, From the problem

Constant,

From the problem statement:

To simplify, we will only consider the trips to the supermarket at times in which I have a stock of exactly one bottle of each drink remaining in my refridgerator.

In general, my scenario seems to me at least somewhat plausible given only a tendency to buy more of a given good when it is on sale. Some goods have routine large discount sales and others never have sales.

If this is true, it seems to me inevitable that I will sometimes refrain from making positive benefit purchases in the expectation of future sales with larger benefits, and that this is NOT a function of a varying value of money.

Regards, Don

Then every two trips, you

Then every two trips, you buy a total of 7 Sprites (6 + 1). Whereas if Sprite had been $1.50 all the time, you would buy a total of 12 Sprites every two trips (6 + 6).

The frequency of the trips must remain the same. Yeah, I know if you increase the frequency of trips then you end up with the same amount of Sprite (or even more) for less money. I'm reasoning from what's done with the Pepsis, and the Pepsi trips and Sprite trips simultaneous, the same trip - therefore, same frequency.

Don, What you’re missing

Don,

What you’re missing is that there are two distinct forms of economic value, exchange-value and subjective use-value.

The value of the two drinks is entirely subjective to me, and derives from the satisfaction that I experience in their consumption. ...

Can you really determine that value, even in non-monetary units without a market context of alternate pleasures and their respective costs?

The subjective use-value to me of a good humor ice cream bar is normally much lower than the cost, in that I can get top notch fresh creamery ice cream at a reasonable price in about a dozen places within a 10 minute drive of either my home or work, and normally keep a quart of such in my freezer. But the other day, when the truck came by the softball field and I was on the bench for an inning in 95* heat, there was sufficient subjective use-value that I chose to purchase a toasted almond bar.

What you say would be true if I bought the bottles with the purpose of exchanging them at a profit later.

But you are buying them with the purpose of exchanging them later in some fashion, because you do not actually need more than 1 bottle sprite to satisfy your current consumption between now and the next grocery trip (if you did, given its subjective use-value, you should choose to buy more than 1 bottle at $1.50per). If there is sprite available at a cheap price (lower than the expected average future price), then you "stock up" by buying more sprite than you intend to consume between now and your next grocery trip.

So in essence, when you buy 6 sprites now, you are buying sprite that you don't need now, to exchange it to yourself when the market price goes up (it's no longer on sale).

With pepsi, buying 6 bottles, you are really doing the same thing, just with transaction costs. The transaction cost of putting it on the grocery list and in your cart is not zero, so having it in stock is worth something. How much is worth having in stock when the price is completely stable depends on your storage costs and capital costs vs. the transaction costs. You've determined that 6 is your equilibrium. Given that, it normally will be the case that your equilibrium on sprite on sale is higher than 6 bottles, but there may be some unusual constraint (more likely, you just didn't think about that :)).

Michael

Don, you appear to be trying

Don, you appear to be trying to define "value" outside of the context of a market.

I'm not sure that's feasible to do.

What's going on here is that other people's actions (willingness to sell diet sprite for less than $1.50 on some occasions) is affecting the value you place on marginal bottles of diet sprite. If nobody was ever willing to sell diet sprite for less than $1.50, then the marginal value of your sixth diet sprite would be >$1.50, since by the terms of your assumptions you would be buying six in that situation.

But the presence of a market where you can sometimes buy diet sprite much cheaper, *changes* the value. In the same way that the mmarket price of a stock going down or up, changes its value even if I consider the long terms prospects to be unchanged.

I may think for various fundamental or speculative reasons that GOOG is in some sense worth $500/share, but I would be a fool to pay more than the $398.36 that I just saw it quoted for, and I would have a hard time justifying more than $398.36 as its "value" to a would be creditor for whom my shares are offered as collateral.

Similarly, if I thought GOOG's fundamentals only justified a price of $250, I would nonetheless be *delighted* to purchase shares for $350 from someone ignorant of the current market price. I would not, of course, purchase those shares for $398.35, but my reasons have to do with transaction costs, the value of my own time and uncertainty. If I had enough money to play with, and enough knowledge to determine my arbitrage risks down to the penny of EV, so that I had the opportunity to make such a trade with millions of dollars, I would surely be willing to pull the trigger on a trade that generated only a few pennies per share of expected risk-adjusted profit.

Value is only well-defined in the context of a market. You're trying to come up with a definition of value that doesn't depend on market conditions, and I'm pretty sure that's just not going to work.

Michael

Michael, Value is only

Michael,

Value is only well-defined in the context of a market. You’re trying to come up with a definition of value that doesn’t depend on market conditions, and I’m pretty sure that’s just not going to work.

What you're missing is that there are two distinct forms of economic value, exchange-value and subjective use-value.

The value of the two drinks is entirely subjective to me, and derives from the satisfaction that I experience in their consumption. For subjective-use value, no markets are involved except in that my demand for consumption may impact a market, if one exists, by bidding up the emergent market price.

What you say would be true if I bought the bottles with the purpose of exchanging them at a profit later.

Regards, Don

Constant, I don't think

Constant, I don't think there will be an upward sloping demand curve, because he's almost certainly not buying pepsi every time he goes to the store. For this hypothetical, he's extracting only those particular situations when he has exactly one bottle of each in storage at home.

But if his subjective use-value is the same for each, then presumably his consumption level is roughly the same for each (flat demand curve), or he might choose to consume more of the sprite because of it's lower average price. In any case, since he's buying only 1 bottle of sprite at the high price, I presume he does not expect to consume more than 2 bottles between grocery trips, so if he buys 1 sprite and 6 pepsis this trip, he will probably buy zero pepsis next trip (but either 1, 2 or 6 sprites depending on consumption and price). Over multiple trips, I expect the consumption to show either a flat or slighhtly downward sloping demand curve, as expected, and nothing in Don's assumptions make that impossible. It's only the short term effects of price volatility that make things look odd in a given grocery trip.

You assume that the value of

You assume that the value of money doesn't change, but is that the case. I would think that the value of money changes depending on what you can buy with it. As a thought experiment: you are standing next to a vending machine full of soda which you value at $2 (assume constant value). You have $3 in your pocket. How many soda's do you buy? For some bizarre reason steve jobs walks up to you and offers you as one time, take it or leave it offer to sell you as many iPods as you like for $1. Do the number of soda's that you buy change? Clearly. You could say that the opportunity cost of the soda's went up, but the cost is still $3 (i.e. 3 green pieces of paper). The opportunity cost of the green peices of paper have changed. Likewise in your example, doesnt the availability cheap diet sprite changes the value of your dollars?

Imagine another example.

Imagine another example. You can purchase the two drinks from either of two stores. You do not prefer either store to the other for any factors other than the products they sell and the prices they offer them at. Both stores sell Diet Pepsi for $1.50 per bottle. The regular price for Diet Sprint is $1.50 per bottle at both, but one has it on sale for $0.79 per bottle. It is clear in this case that choosing to make your purchase at the store with the lower price does not indicate that you prefer the $1.50 to a bottle of Diet Sprint.

The difference between this example and yours is that the prices are not at two different stores, but at the same store at two different times. As such, your example does indicate something important about your time preference. Specifically, you are expressing a preference for a bottle of Diet Sprite at $0.79 at a time when it is available at that price to the same bottle of Diet Sprite at $1.50. The difference between the two transactions is not just the price, but when they occur.

You are also making use of your knowledge of the market. You know that historically, Diet Sprite is offered periodically at a lower sale price. You are taking advantage of the store's mechanism for price discrimination to get a lower price than you are otherwise willing to pay, because your preferences are:

1) 6 bottles of Diet Sprite at $0.79 each, $4.26 that you didn't spend and one trip to the store.

2) 6 bottles of Diet Sprite at $1.50 each, no change left over and 6 trips to the store.

3) $9.00

There are several intermediate cases between the first two.

Constant, I don’t think

Constant, I don’t think there will be an upward sloping demand curve, because he’s almost certainly not buying pepsi every time he goes to the store. For this hypothetical, he’s extracting only those particular situations when he has exactly one bottle of each in storage at home.

Then it's an upward sloping demand curve when we restrict our attention to the situation where he has exactly one bottle each in storage at home. The point is, he responds to a reduction in price ceteris paribus by decreasing the overall quantity he buys. That's unlikely. I want to warn you against trying to bring in stuff outside of the conditions of the hypothetical, which you seem to do by alluding to the times when he has more Pepsi in the fridge, because I think that violates the spirit of thought experiments. Maybe, outside of the hypothetical, someone kidnapped his grandma and told him to behave this way in order to see her alive. In order to avoid that, let's think of the hypothetical as the only thing that's happening. That is, every week like clockwork he has one bottle left in his fridge of Pepsi and Sprite.

Of course, that may be a problem with his hypothetical. But I think if you're going to speculate on what happens outside of the conditions of the hypothetical then you can pretty easily come up with explanations of his behavior, e.g. his kidnapped grandma.

he might choose to consume more of the sprite because of it’s lower average price

My point was that in the confines of his hypothetical he consumes *less* Sprite because of its lower average price. If you want to say that outside of it he might consume more and so inside of it he might be reacting to that higher consumption by compensating, then I think my kidnapped grandma has the virtue of being funnier and no less valid.

But the presence of a market

But the presence of a market where you can sometimes buy diet sprite much cheaper, changes the value.

Yes, I agree, and that was my initial gut reaction. I didn't pursue it because the numbers of Don's example are all wrong.

Specifically, suppose I would buy 6 bottles of Sprite per week if the price were $1.50. Suppose the price starts fluctuating, $0.79 one week and $1.50 another. Then in the real world what I'm going to do (what I actually do) is stock up when the price is low, which has the effect of decreasing my consumption when the price is back to normal. The result is that I buy *less* than normal when the price is back up to $1.50, but I buy *more* than normal when the price is $0.79.

But Don's numbers don't support that interpretation.

Michael, I think Don's

Michael,

I think Don's trying to set up unchanging initial conditions - one bottle of each in the fridge, same set of preferences each time. So the history is not supposed to affect each iteration. These are supposed to be causally independent.

That's why I think it misconceives the experiment to start talking about what happens outside it. By design, that's not supposed to matter.

Michael, Can you really

Michael,

Can you really determine that value, even in non-monetary units without a market context of alternate pleasures and their respective costs?

Subjective values are not and can never be measured, only ordinally ranked in preference order.

So in essence, when you buy 6 sprites now, you are buying sprite that you don’t need now, to exchange it to yourself when the market price goes up (it’s no longer on sale).

I don't accept this use of 'exchange'.

Without trying to find an appropriate quote, an interesting point of this problem is that successive bottles purchased lose value not because of normal diminishing marginal utility, but because their consumption will sucessively occur further in the future.
This brings time preference of consumption into play, being reflected in a lower discounted present value.

... Given that, it normally will be the case that your equilibrium on sprite on sale is higher than 6 bottles, but there may be some unusual constraint (more likely, you just didn’t think about that ).

There is a very usual constraint, a purchasing limit of six bottles when on sale.

Regards, Don

On further reflection, Don's

On further reflection, Don's hypothetical is blatantly self-contradictory. If history does not matter, then the fact that Sprite is sometimes $0.79 will not affect Don's behavior when it is $1.50. Since by assumption Don's preferences visavis Sprite are perfectly parallel to those visavis Pepsi, and since there is no substitution between them, then on the occasions when there's one Sprite and one Pepsi in the fridge and Don buys 6 Pepsi, then he will necessarily also buy 6 Sprite - since any other behavior violates the assumptions of a perfect parallel and no substitution.

Dale, The difference between

Dale,

The difference between this example and yours is that the prices are not at two different stores, but at the same store at two different times. As such, your example does indicate something important about your time preference. Specifically, you are expressing a preference for a bottle of Diet Sprite at $0.79 at a time when it is available at that price to the same bottle of Diet Sprite at $1.50. The difference between the two transactions is not just the price, but when they occur.

Yes, but the time preference relates to the time of consumption, discounted to present value. Also, the key point is the refraining from buying a second Diet Sprite at $1.50 when it is known that it is valued at more than $1.50.

You are also making use of your knowledge of the market. You know that historically, Diet Sprite is offered periodically at a lower sale price. You are taking advantage of the store’s mechanism for price discrimination to get a lower price than you are otherwise willing to pay, ... (truncated)

Yes.

Quotes in reverse order, but not worth correcting.

Regards, Don

Constant, My point was that

Constant,

My point was that in the confines of his hypothetical he consumes less Sprite because of its lower average price.

No, my consumption is at a constant rate as long as I don't run out.

Regards, Don

netziq, You assume that the

netziq,

You assume that the value of money doesn’t change, but is that the case. I would think that the value of money changes depending on what you can buy with it. As a thought experiment: you are standing next to a vending machine full of soda which you value at $2 (assume constant value). You have $3 in your pocket. How many soda’s do you buy? For some bizarre reason steve jobs walks up to you and offers you as one time, take it or leave it offer to sell you as many iPods as you like for $1. Do the number of soda’s that you buy change? Clearly. You could say that the opportunity cost of the soda’s went up, but the cost is still $3 (i.e. 3 green pieces of paper). The opportunity cost of the green peices of paper have changed. Likewise in your example, doesnt the availability cheap diet sprite changes the value of your dollars?

To make my point I need to accomplish only two things.

1. To present a set of purchasing rules that is both plausible and effective.

2. To demonstrate that I have declined an exchange which is beneficial, in the expectation of a more beneficial one later.

For 2. above, the critical declined exchange is the failure to buy Sprite #2 when the price is $1.50.

At that time, we know that the subjective value of Sprite #2 is identical to the subjective value of Pepsi #2.

Since the purchasing of Pepsi #2 has demonstrated that it is preferred to $1.50, so must Sprite #2 be prefered to $1.50.

Even if we worry about the small increase in marginal utility of money as each $1.50 is spent, the result is still the same as follows:

We buy,in order, Pepsi #1, Sprite #1, Pepsi #2, not Sprite #2, Pepsi #3, etc.

Since both Pepsi #2 and Pepsi #3 are preferred to $1.50 even if the marginal utility of $1.50 has increased, the intermediate Sprite #2 must also be preferred to $1.50.

Regards, Don

Constant, On further

Constant,

On further reflection, Don’s hypothetical is blatantly self-contradictory. If history does not matter, then the fact that Sprite is sometimes $0.79 will not affect Don’s behavior when it is $1.50. Since by assumption Don’s preferences visavis Sprite are perfectly parallel to those visavis Pepsi, and since there is no substitution between them, then on the occasions when there’s one Sprite and one Pepsi in the fridge and Don buys 6 Pepsi, then he will necessarily also buy 6 Sprite - since any other behavior violates the assumptions of a perfect parallel and no substitution.

Doesn't follow.

History does matter because it guides my expectations for the future.

The valuations of Pepsi and Sprite are assumed to be identical under all equivalent conditions. But this doesn't take away my free will to decline an even beneficial potential exchange, which is the whole point of the example. See my comment to netziq above.

Regards, Don

Don, The valuations of Pepsi

Don,

The valuations of Pepsi and Sprite are assumed to be identical under all equivalent conditions. But this doesn’t take away my free will to decline an even beneficial potential exchange

Seems to me you're back to saying that free will means people are free to do what they don't want to do. But it seems to me that violates the meaning of "want to do".

History does matter because

History does matter because it guides my expectations for the future.

Fine, it matters in some vague way which you haven't explained. I think you need to start over. I'm tired of trying to make sense of your current scenario.

To demonstrate that I have

To demonstrate that I have declined an exchange which is beneficial, in the expectation of a more beneficial one later.

When you decline X in expectation of Y, the fact of Y is affecting your preference visavis X.

Ceteris paribus, your preference for Sprite on a given occasion would be the same as your preference for Pepsi on a perfectly parallel occasion. But ceteris is not paribus, because the relevant ceteris on the occasion of Sprite being $1.50 includes the fact that it's going to be $0.79. You yourself acknowledge that this is the reason, when you say "in the expectation".

The basic problem as I see

The basic problem as I see it is that Don makes an assertion about preference, and another assertion about behavior, doesn't bother to make sure they form a coherent pair, and then says, "see, behavior diverges from preference". Well, yeah, if you specify them separately and don't take care to make sure they're consistent, they're likely to diverge.

Constant, I think Don’s

Constant,

I think Don’s trying to set up unchanging initial conditions - one bottle of each in the fridge, same set of preferences each time. So the history is not supposed to affect each iteration. These are supposed to be causally independent.

That’s why I think it misconceives the experiment to start talking about what happens outside it. By design, that’s not supposed to matter.

You're right, but I claim that you are doing exactly that when you suppose (as you did in an earlier comment) that:

In order to avoid that, let’s think of the hypothetical as the only thing that’s happening. That is, every week like clockwork he has one bottle left in his fridge of Pepsi and Sprite.

In doing this you are making a supposition about what happens outside the hypothetical (that every week is like this). We are talking about "weeks like this", not "weeks like this when every week is like this".

We do not actually know what Don's consumption level is because he doesn't stipulate how often he goes to the store, or how often he gets in the situation described (of having exactly one bottle of each kind of drink), only his purchasing pattern in this particular situation.

What appears to drive the decision to buy more pepsi than sprite, despite the pepsi being more expensive is expected future price. There is no point buying less pepsi than fits in the fridge because he doesn't expect to ever see a lower price. With sprite, he only wants to fill up his fridge (or buy the sale-max) if the price is at a low point in the expected range. Don doesn't say that he would treat pepsi similar to the way he treats sprite if its price varied in the same way sprite's does, but the stated fact that his subjective use-value is exactly the same suggests that he would.

BTW, while sodas tend to substitute for each other in reality as you note, you could construct a situation where they don't easily enough. Model the problem as a person buying for a household containing two people, one who drinks sprite, and one who drinks pepsi, but neither likes the other at all. Now the two drink clearly wouldn't substitute at all. Of course in this case, you can only claim that the subjective use value is exactly the same if interpersonal utility comparisons are possible, which Don still doesn't if I'm following the battle lines correctly, but I think that they are (to an approximation anyway if not ever perfectly in principle).

You’re right, but I claim

You’re right, but I claim that you are doing exactly that when you suppose (as you did in an earlier comment) that:

That was just an intuition pump for you. I wasn't doing that earlier, I did that to help you get rid of it from your head.

What appears to drive the

What appears to drive the decision to buy more pepsi than sprite, despite the pepsi being more expensive is expected future price.

That reaches outside of the hypothetical, because the future includes other stuff. Therefore, *given* that it is important, *then* Don needs to specify it. Since Don did not specify it, I treated it as irrelevant - I treated the future as irrelevant to the preferences, because I had to, because if it was relevant then Don goofed by not specifying it completely. Don only specified the who-knows-how-rare occasions when there's only one Pepsi and one Sprite in the fridge.

*If* what lies outside is important, *then* it needs to be specified. Otherwise you'll be waving your hands forever not knowing what you or the other guy is talking about.

Constant, The basic problem

Constant,

The basic problem as I see it is that Don makes an assertion about preference, and another assertion about behavior, doesn’t bother to make sure they form a coherent pair, and then says, “see, behavior diverges from preference". Well, yeah, if you specify them separately and don’t take care to make sure they’re consistent, they’re likely to diverge.

In the problem specification, it was stated that both DP and DS would be consumed at the same constant rate. If it helps to have a number, assume two liters (one bottle) per day.

Now we know that the total cost of DP consumption will be $1.50 per day. We also know that the total cost of DS consumption will be, at most, $1.50 per day, and less if the $0.79 price is ever encountered.

Do you find it plausible that trying to buy more when DS is on sale will likely be at least partially successful in economizing on money over time?

Yes, questions about stock and store visits remain unspecified, but I can't see that worrying about them would be worth the trouble.

Is your view different?

What do you find inconsistent?

Regards, Don