OT - What is money worth?

[QuikSand]

When economists and other similarly-inclined people talk about the concept of "decliing value of money" they (we) sometimes lose other more sensible-minded people. Economists hold dear to the notion that for almost anything, the more you have, the less you value more of it.

Sure, some examples work fine. After you've already eaten three slices of pizza, you probably aren't as hungry for a fourth as you were for the first, right? But what about money? It just seems tough to get people to accept the idea that the more money you have, the less each additional dollar is worth to you. (Many of my students still desire to measure "value" or "utility" in monetary terms, which is a bit like measuring mass as weight -- usually it works out okay, but it's imprecise at best.

Here's an example that I'm toying with... I'd like some feedback. Try to answer this question as honestly as you can - even though it's pretty hypothetical.

- - - - -

I am going to offer to let you play a game. I'll give you one dollar. Then, if you like, I will give you a chance to bet that dollar on the toss of a fair coin, with the hopes of winning X dollars. For what value of X would you be willing to play?

Well, most people would probably say that anything more than $2 makes this a worthwhile bet. The math is easy, let's use X=$2.50 as an example.

Cost to take the bet = $1
Expected winnings from the bet = $2.50 x 50% chance of winning = $1.25

Since the expected winnings are greater than the cost, this is a winning proposition, and most people would take the bet at X=$2.50, or perhaps any value greater than $2.00. Implicityl, we are saying that $2 is worth twice as much to us as is $1, and we assign a linear amount of "value" to each dollar: dollar #2 is worth just as much as dollar #1 was.


Now, let's look at the same game, framed a bit differently. In the new game, I'll give you $1 million. Then, if you like, I will give you a chance to bet that $1 million on the toss of a fair coin, with the hopes of winning X dollars. For what value of X would you be willing to play?

Our logic from before suggests that any value of $2 million or greater woudl make this a worthwhile bet. for $2.5 million, we could do our exactl same analysis as before -- and see that the expected winnings of $1.25 million are greater than the cost to play.

Would you be willing to play for $2.5 million? Or would you need to have a greater possible reward to risk this potentially exciting $1 million that you have just been given? How much greater?

[cthomer5000]

I'd walk away with the money.

[Subby]

How much money do I already have? If I am already wealthy, then I am going to let that one million ride.

Otherwise, I would walk away with the one million.

[QuikSand]

I guess the working theory is that I selected $1 million as a figure that would be enough to "change your life."

Ideally, given that, I'm looking for you to put a value on it. How much would it take to get you to accept the bet?

What if it was "risk $1 million to have a 50% chance at getting $100 billion?" Would you accept the bet then? or is there no amount of money at all that would get you to risk the newfound million?

[bryce]

Originally posted by Subby
How much money do I already have? If I am already wealthy, then I am going to let that one million ride.

Otherwise, I would walk away with the one million.

agreed. if i'm wealthy already, i'll let it ride. otherwise, there's NO amount that would make it worth my while to risk the mil.

[Daimyo]

I'd walk away. The first million buys me a decently comfortable life, the second million just a little extra luxury.

[cuervo72]

I'm taking the cash.

[Bee]

I don't see how your example really demonstrates the principle you mentioned: the more you have, the less you value more of it.

It seems to me the example indicates more about the fact that people aren't willing to risk losing an amount that would change their lifes just to get more. Maybe I'm missing something in the translation to the example?

Edit:

I think a better example (if I may be so bold) would be something like this:

I'm going to give you $100 Million dollars. That's yours. Congratulations!

I will also give you another $100,000 , but I want you to spend a week digging ditches from 5 am to 5 pm every day to earn that money. Would you do that after I gave you the $100 million?

[Subby]

Originally posted by QuikSand
What if it was "risk $1 million to have a 50% chance at getting $100 billion?" Would you accept the bet then? or is there no amount of money at all that would get you to risk the newfound million?

No amount of money could make me risk the "life changing" amount. Once my life is changed, it's changed. Maybe if you increased the odds? Not even sure then.

[Chubby]

Originally posted by bryce
agreed. if i'm wealthy already, i'll let it ride. otherwise, there's NO amount that would make it worth my while to risk the mil.

so you're telling me that if given the opp to risk $1,000,000 and have a 50% chance at winning 100 billion you wouldn't do it?

i'd have to say anything over $10 million I'd risk it.

Besides, how long is a million going to last you? a couple of years? I know damn that most people will blow through the money (including myself) after say 3-5 years and then be back to square one.

[HornedFrog Purple]

If I needed money I would go earn it, so if you give me money to bet no matter the amount given I would gamble it under any conditions. Wouldn't bother me in the least if I lost.

If I had to put up 1 million of my own money then forget it. In that case the invested time I put into earning that money myself far outweigh the risk/reward. With 1 dollar, sure I play the lottery every week anyways.

In short, I'll play with your money all day long.

[QuikSand]

Originally posted by Bee
I think a better example (if I may be so bold) would be something like this:

I'm going to give you $100 Million dollars. That's yours. Congratulations!

I will also give you another $100,000 , but I want you to spend a week digging ditches from 5 am to 5 pm every day to earn that money. Would you do that after I gave you the $100 million?

While that doesn't fill the exact niche I have in mind, I do like that as a good illustration of the point that I led with. Nice.

[cthomer5000]

Originally posted by QuikSand
I guess the working theory is that I selected $1 million as a figure that would be enough to "change your life."

Ideally, given that, I'm looking for you to put a value on it. How much would it take to get you to accept the bet?

What if it was "risk $1 million to have a 50% chance at getting $100 billion?" Would you accept the bet then? or is there no amount of money at all that would get you to risk the newfound million?

If I had to set a price at which I'd risk the million... 3 billion.

[heybrad]

Isnt the missing piece to this that you are talking about a percentage of what the person has to begin with. If you give me a dollar and I can double it through the bet, it doesnt matter either way, because thats an extremely small percentage of what I most likely already have. If you give me a million and I have to risk it, now I'm risking 100% of what I have (assuming I didnt have a mil to start with).

[Bee]

Originally posted by heybrad
Isnt the missing piece to this that you are talking about a percentage of what the person has to begin with. If you give me a dollar and I can double it through the bet, it doesnt matter either way, because thats an extremely small percentage of what I most likely already have. If you give me a million and I have to risk it, now I'm risking 100% of what I have (assuming I didnt have a mil to start with).

That's what I was trying to fit in with my example...I think most folks would be willing to do some hard labor (dig ditches) for a week for $100,000. That's a large amount of money for a week's time. Of course, give them $100 Million and that $100,000 becomes somewhat meaningless.

[JAG]

One reason this example may not work so well is that yes, over time your estimated winnings from playing this $2.5 million or nothing bet would be worth it to take the risk, but you only have one opportunity...so no matter how much you put on the other side of the equation, that 50-50 chance of losing a solid million is too much risk to contemplate.

Now, let's say the example was: Here's $1,000,000 dollars. You can either keep that or we flip a coin 10 times. Each time you get heads, you lose $100,000, but each time you get tails, you win $150,000.

I think many more people would be willing to take a chance in this case that they would increase their money. Or at least there would be a smaller value x needed to make this bet more worth while (I couldn't imagine anyone saying no to a winning of $1,000,000 for a single tails in 10 tries for example).

JAG

[HornedFrog Purple]

Originally posted by Bee
That's what I was trying to fit in with my example...I think most folks would be willing to do some hard labor (dig ditches) for a week for $100,000. That's a large amount of money for a week's time. Of course, give them $100 Million and that $100,000 becomes somewhat meaningless.

Over time maybe, but most people don't instantly lose their time invested/money ratio overnight. Just keep tabs on those lottery winners who became instant multi-millionaires, they generally keep doing the same thing they were doing before with a greater peace of mind in all likelihood.

[bryce]

Originally posted by Chubby
so you're telling me that if given the opp to risk $1,000,000 and have a 50% chance at winning 100 billion you wouldn't do it?

that's EXACTLY what i'm saying. i'm not an extravagant person. $1 mil will suit me just fine, and frankly, a modest 5% interest each year ($50,000) would enable me to live off the interest alone (which would actually be more than i make now), leaving me the mil to endulge in a few luxuries.

what's 100 bil reasonably going to buy me that 1 mil can't? i don't want my own jet, i don't want a 100,000 sq ft house in malibu, i don't want a yacht, etc etc. just give me a comfy home, maybe a fun, new car, and let me quit my job to pursue something i actually enjoy that may not pay as well, and i'm good to go.

[B & B]

Id risk the initial million of life changing money for a 50/50 shot at three million.

[cthomer5000]

Originally posted by bryce
that's EXACTLY what i'm saying. i'm not an extravagant person. $1 mil will suit me just fine, and frankly, a modest 5% interest each year ($50,000) would enable me to live off the interest alone (which would actually be more than i make now), leaving me the mil to endulge in a few luxuries.

what's 100 bil reasonably going to buy me that 1 mil can't? i don't want my own jet, i don't want a 100,000 sq ft house in malibu, i don't want a yacht, etc etc. just give me a comfy home, maybe a fun, new car, and let me quit my job to pursue something i actually enjoy that may not pay as well, and i'm good to go.

I agree completely. The only dream I couldn't fulfill with 1 million dollars is owning an NFL team.

[B & B]

What about two chicks at once?

[Senator]

Go on ...... take the money and run!

[Ufer]

I'd definately risk $1 million for $100 billion. I could change a lot of other people's lives -- look at Bill Gates.

I've thought about this question watching game shows like "Who Wants to Be a Millionaire": someone has put $100,000 in your pocket; will you risk it over a trivia quetion? I think some people get caught up in the game and the pressure not to look like a wimp and don't think about the economic reality. A friend of a friend (no, really) was on "Greed" and the team had won enough for her to win approx. $150,000. She's a single mom struggling financially, and she begged the team to take the money and quit. They lost it.

[Radii]

I agree with many of the others here that this is not really a question that will tell you about the value of money, or whether you value money less once you have a lot of it. I think the answer to the $1 million question will tell you more about people's willingness to take risk, or perhaps, the dollar amount that would signify the threshold where its simply not worth a large risk because of what you can do with it.

$1 Million won't mean I never have to work again, but $1 million will get me completely out of debt and get me into a very nice house, my dream house for my family even. That kind of a gift would be priceless to me and there is no return I could get on that money where I would be willing to take a 50/50 chance at losing it all.


On a muuuuch smaller scale, a local radio station is doing a contest where a caller gets to play for up to $10,000. They call it the "cash cow"... it starts very small, and slowly goes up, for example it might say $50... $300, $375, $500, $675, $1100, etc... the risk is that it can "explode" at any time, leaving you with nothing. You can say "stop" at any time and walk away with the last stated amount. Most people stop it right when it crosses over the $1000 barrier. Occasionally it gets to $1500, and one time I heard someone let it go over $2000 before stopping it.

It seems to pose an interesting(and possibly similar) question, this isn't life changing money, but it is some very nice spending money for any middle-class income family. At what point would you stop this thing? At what point, if you lost all the money, would you cease to say "it was only $500, it was worth the risk" but rather say "I just lost $2000 because I got too greedy and lost" ... Personally, I think I'd stop it at $1500, even if I knew there was an even distribution and I have a 50/50 shot of it going above 5 grand.

[albionmoonlight]

Part of me thinks that I would stay at $1,000,000. That amount seems like enough to make life more comfortable, but not so much to really complicate my life by making me change it a lot. I would not change my career path if I had $1,000,000. I just would not have to worry about putting my kids through college.

If I had much more than $1,000,000 (say $10,000,000+), then I think that my life would fundamentally change. I would be able to live as a really rich person without working at all--I am afraid that my interactions with my friends and family would change--and I don't know if it would be for the better or the worse.

In short, I like who I am and the life I am living right now. $1,000,000 would sweeten that life, but leave it pretty much unchanged. Lots more money would necessarly (sp?) change that life, and I don't know if I want that change.

That said, there is a certain temptation to being able to own sports franchises and establish billion dollar foundations to shape geo-political policy in the ways that I believe are best.

So, I don't think that I would risk the $1,000,000 for any amount. However, if I did, it would have to be for $3 billion--That would be enough to allow me to effect the kind of worldwide political change about which I am talking.

Strangely enough, the middle ground is not as tempting. I would rather $1,000,000 than $10,000,000 for the reasons given above.

[Raven Hawk]

Originally posted by cthomer5000
If I had to set a price at which I'd risk the million... 3 billion.

Why does this remind of that Hooker joke . . .

A: Would you sleep with me for $3 billion?

B: Well . . . yeah . . .

A: How about $2?

B: What do you think I am, a whore?

A: We've already established that, now we're just negotiating price . . .

----------------

I hate to say that it's all relative . . . but it IS all relative. If I was given an amount to wager with that is between .001% and .002% of my annual salary, I'm more free to spend it how I like because I know that it would take me a matter of minutes/seconds to make that up.

However, if you give me an amount that is 13x-15x my annual salary, I'll look at it and say . . . hmmm . . . do I really want to work that extra 15 years to make up this loss . . . no.

If 1,000,000 dollars truly represented .001% to .002% of my annual earnings. Hell, yeah. I'd put it down on the chance to win 1,000,005 dollars.

[kcchief19]

I think the point that money has less value when you have more of it has been made by the sheer number of people who would walk away with a million dollars.

But instead of changing the payoff, what if you lowered the initial payout? What if someone gave you $10,000? What would it take to make the bet pay off now? The example above would say $25,000.

Personally, the payout on the bet for me would increase exponentially to what I was given. If you gave me a $1, I'd bet the dollar on any amount because it's pocket change. The more money I'm offered, the more the payout would have to be for me to risk it. If you gave me a $10,000, I'd probably have to have at least $100k to risk it.

I think the point that gets made is that as you have more money, it takes more money for you to risk.

I, too, hold the notion that the more you have of something the less you value more of it. The catch is that human nature is the volatile variable in the equation. Logic and human nature are not necessarily synonymous.

[wbonnell]

Originally posted by B & B
What about two chicks at once?

I'd relax, sit on my ass all day. I would do nothing

[wbonnell]

Without thinking too deeply (sorry, I have a paper to avoid, err, I mean write), if the initial windfall event was "life changing", I would simply walk away. For I'm perfectly happy with my current lifestyle (which, admittedly, is extravagant compared to most of the world); I abandonded rampant consumerism quite some time ago.