How much money did you lose?

[dps]

Depends how you define "Lost".

I'd say €5, since that's the unneeded spending, but other people could say differently, depending on how they'd define it.

That would be how an economist would define it, assuming that the tickets were equal except in price, and assuming that no otherwise identical ticket was available at a lower price.

[Valmark]

That would be how an economist would define it, assuming that the tickets were equal except in price, and assuming that no otherwise identical ticket was available at a lower price.

There was another user who using finance rules (I have no idea what's the proper term) came out with 3.9L of loss. So that one would be the economist way, not the 5L. Assuming the calculations were correct.

I don't think those assumptions are relevant? Even if they were different if the usage is the same there's no point. Same thing with the presence of lower price tickets- though in this case I'm biased 'cause here a ticket for say, the train has the same cost anywhere you go.

[Knaight]

That would be how an economist would define it, assuming that the tickets were equal except in price, and assuming that no otherwise identical ticket was available at a lower price.

That's one economists option - the other one would be to note that you lost 8.9, gained a train ticket, and clearly value a train ticket at at least 5. 3.9 is the maximum loss in this paradigm.

[Khedrac]

On the question of did you lose E5 or E3.89, there's another way to look at this question which might help you work out your answer (as noted, different people will have different answers).

Suppose you bought a train ticket for E5 (the base price) and then noticed that there was an offer you could have got which would have allowed you to buy the ticket for E3.89, have you lost E1.11 or not?

[Valmark]

On the question of did you lose E5 or E3.89, there's another way to look at this question which might help you work out your answer (as noted, different people will have different answers).

Suppose you bought a train ticket for E5 (the base price) and then noticed that there was an offer you could have got which would have allowed you to buy the ticket for E3.89, have you lost E1.11 or not?

That is a different question though, not another way to look at it. In the first case you buy a ticket then have to buy an overpriced one because you forgot you had it with you and you can't refund them. The loss in this case is 5 €, if you apply logic.

In the second case you buyed a ticket and saw that there was one on sale but you don't actually buy an additional ticket wasting one of them. The loss in this second case is crearly 1,11 €, and I think it's that one no matter how you look at it, but I might be wrong.

[Aedilred]

I think Scarlet Knight is probably looking at it the right way. If it's your money, you can always write it off and say you've paid for the experience, or something. But if you're spending somebody else's money (or somebody else is spending your money) the question of how much is lost becomes rather more significant.

In that context it's hard to see how you've lost anything other than €5.

[jayem]

"How much money you lost" is not an unambiguous, well-defined quantity, and therefore there is no single unambiguous answer.

Seconded, I hope the economist textbooks have different precise names for the different losses (a bit like chemists have Gibbs Free, Enthalpy and the other two to talk about energies).

In this (moderately simple) case there are obviously multiple good cases for both $5.00 and $3.90
$8.90 I think already has 'expense', $0.00 and $1.10 require the unused ticket to still have functionality.
Other values (other than possibly $4.45) I think require an arbitrary valuation.

Of course the true accountants answer is $1045.96+my expenses explaining that if it's something they are claiming, and actually you saved $4357.32-my expenses if they are paying!

[Unavenger]

Other values (other than possibly $4.45) I think require an arbitrary valuation.

I don't see how the unnecessary spending is an "Arbitrary valuation". It is, exactly, the amount of money that you could have avoided paying while producing the same non-financial result.

Maybe I'm looking at this from a game theory perspective and not an economics perspective? I suppose I'm comparing optimal play to actual play and comparing the monetary values of each play. But I'm also asking the question of "How much money did you lose from making that mistake" pretty clearly.

[jayem]

I don't see how the unnecessary spending is an "Arbitrary valuation". It is, exactly, the amount of money that you could have avoided paying while producing the same non-financial result.

Maybe I'm looking at this from a game theory perspective and not an economics perspective? I suppose I'm comparing optimal play to actual play and comparing the monetary values of each play. But I'm also asking the question of "How much money did you lose from making that mistake" pretty clearly.

For those other values (I'm sure there's some I've missed), you need more than the numbers you have given, maybe you could have picked the $3.90 ticket up for a $2 bus fair, but you needed to protect yourself against the £60 ticket risk (as a story that doesn't make sense).
If it's the UK advance tickets come with a seat reservation, which you could still potentially use.
Maybe there's still a 50% chance you come back again, so how much value does the ticket remaining have.

If it's anything like the real world case when I was in this situation:
I went to the park and ride, expecting to pay a moderate amount
Found it was free travel (Salisbury was desperate for visitors)
Collected my free return ticket and went to town centre
Saw the Cathedral
Didn't find HMV
Couldn't find my ticket
Bought a single ticket
Found the ticket while still on the bus
Got to Old Sarum (technically just after closure but close enough to see the outside)
Then there are a lot of "how much do you really value" questions to ask. I could easily have got off the bus and re-searched bags and pockets but then I would have been even later for old Sarum. And except for seeing how I behave, in lots of experiences, there isn't much way to know.

[Unavenger]

For those other values (I'm sure there's some I've missed), you need more than the numbers you have given,

No, you don't? You just need to know how much the ticket you needed cost, and how much the ticket you didn't need cost. None of this stuff about buss fares and $60 risks that you're making up. And if there were a 50% chance of you coming back and using the second ticket, that would equally affect your figure of half the total!

[jayem]

No, you don't? You just need to know how much the ticket you needed cost, and how much the ticket you didn't need cost. None of this stuff about buss fares and $60 risks that you're making up. And if there were a 50% chance of you coming back and using the second ticket, that would equally affect your figure of half the total!

It's a three post conversation.

If you just used those numbers then you'd end up with one of the numbers I'd stated as being derivable from those numbers (if I've missed one that makes sense feel free to pick it up) These are the 'easy answers' for the problem as stated, and depending on the exact wording each are IMO equally justifiable.

Personally I think it's quite fair to say you can't decide which ticket was the wasted one, and the wasted value was somewhere between. But to do that we need some sort of weighting value, the simplest being 50% (which gives the case mentioned). Others values I can't see a way to decide other than out of a hat.

From personal experience I also know quite well that value is complicated.
In this case the $3.90 ticket is quite possibly on offer because they know some people will not make use of it. Our cheaper tickets are normally tied to a particular train, by buying an anytime ticket I'm buying insurance against the meeting running late, by buying the early ticket I'm taking a bet that it finishes on time. I would consider taking that into account quite reasonable, but to do that I'd need more information and at the end of the day there's probably not a good reason to choose one value over another, which again get back to my initial claim. It's harder to do for the transactionally identical example given (but even then I know that is rarely RL experience).

[Unavenger]

Personally I think it's quite fair to say you can't decide which ticket was the wasted one

I can decide quite easily: it's the one that I could have gone without getting, but got because I made a mistake; ie the $5 one. And the money wasted is the amount of money I could have avoided spending, but spent: that being $5. It's not hard to work out how much your mistake cost you: you lost $5 because of your mistake, therefore your mistake cost you $5.

[Valmark]

You are approaching the subject in two different ways- Unavenger like a math problem, which it is (and I agree with them) and jayem is trying to put it into a real life contest with additional factors.

I agree with Unavenger on the basis that, well, the question is quite clear. Adding factors not mentioned by the OP or by the text doesn't really make much sense to me (of course this is my personal view, I'm not pretending that it's wrong by default)

[jayem]

You are approaching the subject in two different ways- Unavenger like a math problem, which it is (and I agree with them) and jayem is trying to put it into a real life contest with additional factors.

I agree with Unavenger on the basis that, well, the question is quite clear. Adding factors not mentioned by the OP or by the text doesn't really make much sense to me (of course this is my personal view, I'm not pretending that it's wrong by default)

Although partially true. It clearly wasn't seen as being quite, quite clear (otherwise the post wouldn't have been made, and the initial answers would have been different).
And I think that the argument that it was "clearly" the $3.90 ticket that was unused has some merit, as well as Pelee's take.
FWIW in my first post (one page 1) gave £5 (which has the wrong units) as my instinctive choice for the particular story as we heard it.

On the basis that it's not a primary school textbook trying to justify subtraction exercises (if so it ought to at least have a subtraction in it), I think prodding at why, and nudging things, to be valuable. Is that $5 dollars special because it was the last purchase or the highest? As I say, I hope it's something that has been covered in more subtlety by economists because otherwise they are going to get caught out when they try applying those rules.
___
I used the chemical potentials, but actually the averages (mode, median, a-mean, g-mean, h-mean, ...?) are another example where there're slightly different definitions (of average) for slightly different purposes.

[Unavenger]

On the basis that it's not a primary school textbook trying to justify subtraction exercises (if so it ought to at least have a subtraction in it)

If you still don't see why it's really obvious, then the correct thing to use isn't subtraction so much as game theory (although, it's more really shockingly easy game theory). We're comparing two plays, one where you spend an extra $5 and one where you don't. How much does spending an extra $5 cost you?

To be clear, I'm only actually interested in the real-world problem of "How much money did you lose by making a mistake", which is the amount of money that you wouldn't have lost if you didn't make the mistake, rather than any weird way of number-crunching the problem and being armchair-philosophical about what it is for a mistake to cost you money.

[Aedilred]

I wonder if this disagreement is founded in part on a misunderstanding.

I don't see how the unnecessary spending is an "Arbitrary valuation". It is, exactly, the amount of money that you could have avoided paying while producing the same non-financial result.

Unavenger objects to the reference to arbitrary valuations in determining what the unnecesary spending is. But if we go back to jayem's original post:

In this (moderately simple) case there are obviously multiple good cases for both $5.00 and $3.90
...
Other values (other than possibly $4.45) I think require an arbitrary valuation.

(my bold, and with one line removed for clarity). I don't read that as jayem's saying that €5 is an arbitrary valuation or that to reach that answer you have to perform one. Indeed, both seem to be in agreement at least that €5 is a correct answer.

Unavenger may disagree that there is any case at all for the loss being €3.90, but the bulk of the subsequent disagreement seems to stem from a misconstruction of jayem's original post. I read jayem's post as saying that if you want to value the loss at anything other than those values, you have to do an arbitrary valuation, and/or introduce additional factors into the question.

Everything else is jayem playing around with the question and introducing additional factors to reach different results. Unavenger isn't interested in that, but it doesn't mean that jayem has misunderstood the question or is answering it incorrectly.

[jayem]

I

Thanks, that was very clear (much better than my attempt).

On my side I'm not sure about how much of the disagreement comes from being distracted by that, and how much from something else.

Just to pre-empt another misunderstanding regarding the subtraction. I was making the point that the OP presumably asked the question for a reason.
It is superficially similar to questions in a child's exercise book, but I don't think that was the point of the OP. Even ignoring the questions of what the OP planned to gain from such a post, (as we both agree) the question doesn't really lead itself into that kind of arithmetic.
Clearly* we are meant to engage with the wording/situation in some way.

*that's going to bite me back later

We've got to weigh up the game theory approach with the equally easy and obviously true "I bought a ticket for $3.90, I lost the ticket. [Something not about that ticket]. How much money did I lose?". Literally just reading the question.

___(going from $3.1 to $5.0)

The obvious thing to say is that "I bought a new ticket for $5", changes things in a way that "and to cheer myself I bought a $5 lunch then walked". You need to conclude that the new ticket you bought, actually bought a $3.90 train journey, whereas buying lunch you got a $5 lunch.
That is that the problem actually consisted of the two statements "I bought a ticket for $3.90, I lost the ticket", "I bought a ticket for $5.00, which I could have bought for $3.90", and the question "how much did I lose". Which pretty smoothly does this, unfortunately it now has a great big hypothetical in it.

When Bob says "I bought a ticket for $5, how much did I lose", do we now say $1.10 (because we now think we know of the other game-plays) or $0.00

___

Going back to the game theory, again it actually comes to an having chosen to set the value of train ride=$3.90, before you go into the straightforward application of game theory
So the payoff matrix goes

early ticket	late ticket	both tickets
0.0	-1.1	-5.0

Rather than e.g.

early ticket	late ticket	both tickets
+1.1	0.0	-3.9

The behind the scenes logic is exactly the same in both cases. You decide the answer going in.
Then whether you use the simpler argument that if one ticket is the train ride the other is the loss (or vice versa)
Or if you go flexibly via the game theory approach makes no difference

[Unavenger]

Let's rephrase the question a little to see why the price of the original ticket isn't part of the answer.

Say for the sake of argument you have one train ticket. Believing that you've lost that ticket, you pay $5 to get a new one. It turns out that you still have the old ticket, given which the new ticket is useless. How much money did you lose by buying an object with no value for $5?

I think it's relatively easy to see that you've pretty unambiguously lost $5 no matter how you look at it, and irrespective the original cost of the first ticket. The only real difference between the scenario in the OP and my rephrasing, you're actually getting a new item with the same use as your old ticket, and instead rendering the old ticket - but either way, you're still up one pointless ticket, and down $5.

Put another say, the $3.90 was already spent and gone long before you made the mistake. There was no opportunity to gain, lose, fail to gain, or avoid losing that $3.90 at any point during the actual proceedings in question, and you never even lost the item that you bought for that $3.90 either. All that happened while you were at that station is that you gained an item you didn't need, and you lost $5.

[jayem]

Let's rephrase the question a little to see why the price of the original ticket isn't part of the answer.

I think this is where it gets interesting

All that happened while you were at that station is that you gained an item you didn't need, and you lost $5.

This is where it gets paradoxical:

Say for the sake of argument you have one t

That all makes perfect sense, score 1.0 for the $5 loss

Say for the sake of argument you left it entirely at home. That mistake has been made and is lost regardless of whether you buy a new train journey or walk. So you've clearly lost $3.90 whatever happens next.
In this case you then clearly valued the new ticket, you spent $5 and gained an item you valued.

Say now we do a similar variation but rather than realising the mistake between the ticket booth and train, you find the old ticket at home (this is just as indistinguishable from the OP as your variant), but it is also (from the subjects experience) to the above

That makes sense to me, score 0.5 for the $3.90
I've rated it less firstly because it differs from the OP experience. There is a material change to the tickets location. However I don't see why the if anything bigger mistake should have a lesser loss though. How did you lose $1.10 more by having it in your pocket?
Secondly because (in the absence of other information) it sounds like spending $3.90 was the plan (even if you theoretically clearly value the journey at $5, you've cashed that profit already)

With that story, I'd definitely go for the £5
If you changed it so the £3.50 ticket stayed at home, then I might go for the £3.50.
...

If the £3.50 was an advance and the £5.00 was on the day and I wasn't sure. Then I'd say I 'lost' £3.50, but actively feel I'd spent it on insurance (against changing my mind).

But if such small narrative details make a difference, I think I'd rather have a range of different 'losses' defined, and then argue which is the relevant one for the situation. Because it doesn't matter too much when the subjects a train journey, but when it's a shipload of goods, it impacts lives.

[Aedilred]

Put another say, the $3.90 was already spent and gone long before you made the mistake. There was no opportunity to gain, lose, fail to gain, or avoid losing that $3.90 at any point during the actual proceedings in question, and you never even lost the item that you bought for that $3.90 either. All that happened while you were at that station is that you gained an item you didn't need, and you lost $5.

In the scenario, though, you did need that item, because you had mislaid or forgotten about the first item. You used that item to get on the train and then discovered that you still had the first item, thought lost.

As has been noted by a couple of people, you go on to use the €5 ticket, so if the loss is calculated on the value of the wasted item, it's the value of the unused ticket, the €3.90 one. Yes, you could in theory have used the cheaper ticket, but things didn't work out that way.

Presumably, had you not bought the second item, you would have missed the train altogether, so you did in fact need it even though you shouldn't have done. This is why I think a strict logical approach doesn't provide a watertight solution, because the purchase of the second ticket is both illogical and contextually necessary.

If we change the scenario slightly then we get a choice: you realise before you get on the train that you now have two tickets. (Assuming here that they're non-refundable, and that you can't sell one of them on). In that case you have a choice as to which ticket you use, and which is wasted. In which case can you decide how much you lose, by choosing one of the tickets? Do we say that each ticket is now of equal value (in which case we go back to the €4.45 loss)? Or is the loss always €5 whichever ticket you use?


I mean, all in all I think the loss is €5 whichever way you look at it, but I do think there is room for differences of opinion.

[jayem]

Reminded of this thread by another recent real world situation (I'm not sure about the answer, I don't care, I'm sharing it for the story)

I wanted to buy some compost £10
The Garden Center switched to mail delivery only
(I thought the supermarkets would be more restrictive, in practice I could have possibly got away with it, there's a whole raft of secondary factors you could squeeze here)
Delivery is £10 or free if the order is over £20
There was £6 of stuff I half wanted, and a pot for £5 which I didn't care for much
Looking at the pot on Wednesday, I saw it still has a big sticker (presumably from just before) "Was £5 now £3"

[JNAProductions]

Reminded of this thread by another recent real world situation (I'm not sure about the answer, I don't care, I'm sharing it for the story)

I wanted to buy some compost £10
The Garden Center switched to mail delivery only
(I thought the supermarkets would be more restrictive, in practice I could have possibly got away with it, there's a whole raft of secondary factors you could squeeze here)
Delivery is £10 or free if the order is over £20
There was £6 of stuff I half wanted, and a pot for £5 which I didn't care for much
Looking at the pot on Wednesday, I saw it still has a big sticker (presumably from just before) "Was £5 now £3"

So, you got:

£10 Compost
£6 of other stuff you wanted
£5 of a useless pot

For a total of £16 value, effectively, for £21

Whereas, had you gotten the compost alone, it would've been:

£10 Compost
£10 Shipping

For a total of £10 value for £20

You spent more, slightly, but got more relative value out of it. The actual price of the pot is insignificant-you can donate/throw out the pot and just treat it as a £5 shipping charge.

[Valmark]

With the change of price you tecnically saved money- had you waited until wednesday the pot wouldn't have been pricey enough to avoid delivery prices.

Of course if you didn't care about the pot you could have just picked something else in it's place, but that is based on numbers we have no knowledge of so they aren't relevant here.

If you did care about it (which you seem to do, even if only in the slightest) then it's saved money period.

[jayem]

With the change of price you tecnically saved money- had you waited until wednesday the pot wouldn't have been pricey enough to avoid delivery prices.

Of course if you didn't care about the pot you could have just picked something else in it's place, but that is based on numbers we have no knowledge of so they aren't relevant here.

If you did care about it (which you seem to do, even if only in the slightest) then it's saved money period.

On Monday[sic] I noticed that the pot I'd bought had that sticker on. It had arrived on Friday, so it clearly wasn't my first thought
It's a nice blue pot but slightly smaller that I thought it would be. Now I know how the actress feels.
(I wasn't paying too much attention as the next size up was £10), had it not been for the delivery I'd probably have been happy to pay £2 as I didn't need it).

Spoiler: more boring details

Show

I know I said Wednesday before, it was a few days ago and tomorrow may be the weekend but it's not Saturday
1) I wasn't sure how long it would remain open for, or what other options would be available. Other centers had straight out shut.
2) The website had been hurriedly converted (it's been extended a bit more since, but even Sunday it didn't really have anything I wanted more)
3) It's a localish business, I want to encourage it to be there when lockdown ends.
4) But it's not a charity, I wanted my "money's worth", which I'm happy I got.
5) I'm guessing they either had a pre-lockdown sale which they didn't remove the sticker after
5b) (in which case I 'lost out' by not prioritising driving there the week before but did other stuff instead
5c) although then I would just have bought the compost, and I am more pleased by the £6 thing than I thought I would be

7) The amusement I got when I looked at the label, and thought back to this thread was worth twice the difference.

[lio45]

There's one piece of information missing in the OP if we want a definitive answer.

If the €5.00 ticket is exactly the same as the €3.90, and only cost more due to the fact that it was bought at the last minute / at the gates, then the wasted/lost money / unnecessary expenditure is €5.00.

If the €3.90 ticket was a more economical class of ticket, and by the day of the trip those were all sold out while higher-end tickets including more services (say, complimentary snack, more comfy seat, window seat, etc.) were still available at their usual price (including in pre-sale) of €5.00, then the lost money is €3.90 in this case.

(In the absence of that information, I'd lean to the former scenario as the default case.)

[Asmotherion]

1.10... provided you can sell the other ticket at face value latter.

If you manage to sell at a higher price, under the right circumstances, for exaple the ticket value being higher than 5 at location of selling, you may even manage a small net gain (let's say at location, ticket sells for 6, and you sell your 3.9 one for 5.20. A win win situation for both, and you still get a 20 cent net gain.

[Lvl 2 Expert]

You have bought a train ticket for €3.9. However, right at the last moment, you forget that you have bought the ticket, so you buy a new one for €5. Then you remember the first ticket, but it's already too late. You're already on the train, and you can't cancel the tickets.

How much money have you lost?

€8,90, plus several hours of my life for a stupid train ride and wherever lame place it is I'm going.

[Studoku]

£8.90, compared to hiding in the bathroom when ticket inspections happen.

[Not]

This thread amuses me.
But am I the only one wondering how the same ticket jumped in cost by £1.10, in the time it took to wait for the train?
Which ticket is the "real" price of a train ticket?

[Peelee]

This thread amuses me.
But am I the only one wondering how the same ticket jumped in cost by £1.10, in the time it took to wait for the train?
Which ticket is the "real" price of a train ticket?

There are no "real" prices. A price is simply what both buyer and seller agree is acceptable.