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As for 1, the whole article is arguing a case where that is not true. They are illustrating a case where Mary's $130 is not worth much of anything: it doesn't pay half of her $250 liability and get her out of half of the downside. It's useless. But doubled, it has some utility.

Granted it's an oversimplification, because that $130 could be used for something, and yes, #2 and #3 are probably better. (Though with fees and multiple rollovers, the payday loan could be ouchy).

Still - declining marginal utility is not always the case. There are plenty of situations like this one, (especially for a corporation) where having half of the money necessary gets you nothing.

Of course, there are also almost always better ways of securing that financing, unless you're the only person that perceives the odds that way.

Here's an interesting example in my life - if I get a windfall, the marginal value starts off low (I don't change my lifestyle), rises somewhat (it becomes enough for me to take a breather from my job and spend more time working on my startup), and eventually declines as I no longer need more to work.

Or in other words, I can't retire because I got $10k. Not useful. But if I can make that $50k, I can survive for a year+ and try to launch a company - that's useful. The value of that $50k is more than 5 times as much as the $10k. (Though the $10k does get me that much closer to having enough...)

It's not useless. It still pays for groceries, gas, etc. It's still $130 less she needs to put on credit cards for whatever.

In the real world, where you're never faced with two simple options like retire on $10k or start a business for $50k, money's marginal utility is effectively always diminishing.

1. Money has a declining marginal utility. Winning that $130 isn't nearly as positive as losing it would have been negative.

I question this because you're already in the red: do nothing, and you'll be left with $130 in the bank but $250+$100=$350 in liabilities that eventually have to be paid, so you're at -$220 by default (even if you've still got $130 in your pocket, that's not really your money; as I commented elsewhere, I probably should have set up the example so that Mary had already purchased food for the week, to avoid questions of starvation).

When you're starting in negative territory the usual rules about marginal utility of money don't necessarily apply, I'd actually argue that there might be more utility gained when you go from -$50 to +$50 than there is going from -$150 to -$50 because of the debt spiral effects that you mention.

As for your other points, I agree, there are issues with the false dichotomy that I've set up, ones that I expected to be called out on. Perhaps I should have worked out a better example where there were fewer options available, c'est la vie.

No, I'm pretty sure declining marginal utility applies more when you're in debt, not less, because interest rates on loans compound. Someone who owes credit cards $150 is going to be FAR more in debt, as a percentage of earnings, after a year than someone who owes $50.

By that same interest rate argument, the marginal utility of money should increase on both ends the further you get from zero, since interest earned on the money you have compounds, too. That said, the interest rate is much larger when you're in debt than when you have money (actually, in this case that's not 100% true, because DMV suspension fees don't accrue interest, nor do tickets or court costs after the late fees max out, but in general, you're right), so this could be a real concern.

Even in the face of marginal utility differences, though, if you were to accept (unreasonably, of course; thought experiment disclaimer goes here) that you only had the two options given (do nothing and owe another $100 to the state, or take the bet, coming out $130 ahead or $230 behind), would you really suggest that doing nothing is the better option? How good would the odds need to be (and how little variance) for you to take the bet, if so?

If I laid out this payoff structure without placing it in a real world context where there are many other obvious potential solutions, I think you'd probably argue in favor of taking the bet - the expected loss is so much lower that I think it's difficult to make a marginal utility argument against it. I suspect that what's really making you argue against it in this example is that there are so many better ways to deal with the situation in real life that it's hard to even imagine having to make a choice between the two alternatives on the table.

Note: when you make a don't pass bet, not only are the odds still slightly against you, at least 10 other people at the table will hate you too :)

That's the most fun part.

All that you say is practical and true but it seems in this contrived example, the imminent deadline with a disproportionate-to-the-time-value-of-money late fee means that liquidity now, in the winning scenario, has an extra utility -- as if it had increasing marginal utility.

It doesn't though, because you're not considering the rest of life. Whether or not this person pays the BMV, they still have to buy groceries, pay off credit cards. That $130 is not useless at all.

The most likely result of gambling is that they will still have to pay the BMV bill plus now have to recoup $130 (which is hard for them to come by) to pay other bills.

The catch here that the author was trying to tease out is that marginal utility is not always a smooth curve. Sometimes it is a step function, which changes the rules around the step.

Tax brackets are another classic example. Sometimes you get much more by being paid a little less.

Edit: The tax thing was a brain glitch and not true IRL. Check Matt's comment below. There may be true life examples where you come out ahead but they are likely to be scholarships or insurance policies or something with similar hard cutoffs that form step functions.

No you don't. Earning more never causes you to take hom eless after taxes (at least in any country I know of). That's a common fallacy about them amongst people who don't understand the tax code.

Tax rates are marginal. So for instance if the tax rate was 20% up to $100k, then 30% afterward, you'd pay 20% on your first $100k, then 30% from $100,001 and up.

Hmm. You are right. All of the examples I was taught with used fictional examples of magical taxes. I though surely there must be somewhere... but no, just a clever fiction, repeated ad absurdum to make word problems for 5th graders and then glossed over by time until I took it for reality. Ouch. Harder still because with a moments reflection I should have seen its absurdity(1).

But the step function thing was the point, not the taxes. I'll put in an edit and get that last bit ignored.

(1) Be careful what you take as truth when young and don't rethink later.

Income tax is probably always marginal, but in the UK at least this kind of thinking does apply to selling houses - when a house is sold in the UK the buyer must pay "stamp duty", which is a percentage of the value of the house, with the percentage changing at certain thresholds. For example at £250,000 the stamp duty changes from 1% to 3% - but the percentage applies to the entire value of the house. So if you sell for 250,000 the buyer pays 250000 * 0.03=£7500, compared to 249999 * 0.01=£2,499.

That introduces some distortions into house pricing, making it very difficult to sell a house in the £250,000 to £265,000 range - because you are competing with houses just under the threshold which work out significantly cheaper for the buyer. As someone selling a house which falls into that price range, you might be better off asking for slightly less from the sale (versus asking for just over the threshold and waiting much longer to find a buyer).

Tax brackets do not work that way! http://www.youtube.com/watch?v=ZQg8JKo_3ZQ

You only pay the higher rate for income within that bracket.

Making an extra dollar pushing your taxable income to $34,001 as a single American in 2010 does not raise your Federal taxes from $5100.00 to $8500.25 by naïvely applying the higher rate — it actually raises your taxes by 25¢ from $4681.10 to $4681.35.

Is that a safer bet than blackjack, or are you defining blackjack as "a game of skill"?

(I know it's a smaller house edge than roulette by some way, but not too familiar with craps)

Don't pass is a much safer bet if your goal is to bet once and double your money. Blackjack can have a positive expectation (craps cannot, absent some unusual promotion) but that requires much skill. Even with knowledge of basic strategy though, which can get the house edge very low (assuming rules that favor players, like what you'd find on the Vegas Strip) it's not a good all-in wager. A significant amount of the EV from blackjack comes from doubling down and splitting, which require you to put up extra money, so if you're playing it all-in, you're much more likely to go bust than at roulette or either line bet in craps.

Also some of the EV comes from blackjacks (typically paying 3:2) so there is some chance you'll end up with more money than you need. You could walk out with $325. Again since marginal utility is diminishing the extra risk is bad.

#3.5) or decent Texas Holdem player. I won a couple hundred bucks in a 10 man tourney in Vegas. Final showdown hand: Ad, 7d. His hand, As, Qc. I pushed all in, he called.

Diamond flush for the win! It's better to be lucky than skilled :D