Economic Research, Decomposed

In a previous post, an economic puzzle was published.

Rather than bury it in the comments, I will decompose and dispose of it below the line.

Think of the 10% credit card charge as a user fee for the use of money and a penalty for not doing your duty to boost the economy by spending at least every last penny. Since this precedes the choice, it is a sunk cost and not relevant.

Money is an economic good in its own right and the service that it provides is helping to provide for an uncertain day to day future, dealing with both emergencies and opportunities. As with any other economic good, it is subject to the law of diminishing marginal utility. For money, this is important as the value of each sequential dollar spent from a ready cash balance becomes more and more valuable.

Not only are checking accounts considered part of the money supply, but they also augment your actual ready cash balance in dealing with emergencies and opportunities. This is more true in terms of using your debit card in an ATM than writing a check, but both apply. When your debit card is cut in two, you have temporarily lost the ATM part of this augmentation and the value of every dollar in your actual ready cash balance has increased. Once again, since this precedes the choice, it is not relevant.

Since your credit cards can sometimes augment the use of your ready cash, they reduce your demand to hold money and reduce its value, even if you never borrow. Therefore their temporary loss increases the value of your money holding. Again, it is not relevant to the later choice.

If you make choice 2., you are effectively betting 80% of your cash balance. If you win, your new cash balance is 180% of the original. If you lose, it is 20%. Since the odds of winning are 50%, the expected value is 100%.

The first approach is to evaluate your risk tolerance. with respect to the stakes involved. If you are risk-seeking you may take this double-or-nothing bet. If you are risk-avoiding, you may not.

Even if you are risk neutral, and the potential risks and rewards are the same in dollars (80%), the real risks and rewards are not equal. This is because the dollars given up are more valuable than the ones returned due to diminishing marginal utility as above. As a result, most people, most of the time, should choose #1.

In an exceptional case, where you were expecting to visit an ATM to get a rent payment in by 5PM to prevent eviction, the gamble might be worthwhile.

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Diminishing marginal utility

Diminishing marginal utility explains loss aversion! The scales fall from my eyes, and all makes sense! Thanks for the insight, Don.

[...] s Nose by Matt

[...] s Nose
by Matt McIntosh

I just had a big “HOLY DUH” moment reading this post by Don Lloyd. For years behavioural economists have point [...]

Glen, Thanks. I think this

Glen,

Thanks.

I think this is getting it backward. If you have diminishing marginal utility of dollars, that will cause you to pick #1 over #2 – and that’s what it means to be risk averse. If you had constant marginal utility of dollars, then you would be risk neutral and be indifferent between #1 and #2. To say someone’s risk neutral and yet has diminishing marginal utility of dollars is just a contradiction.

That was really my point, i.e. that it was the diminishing marginal utility of dollars that was the determining factor.

(If you have to pay the rent check or get evicted, and there’s no way you can afford the rent without winning the bet, then you have increasing marginal utility of dollars: the last dollar required to pay the rent has value much greater than all the previous dollars that don’t keep you from being homeless. Increasing marginal utility of dollars leads to risk-loving behavior.)

According to Rothbard, this would not be a proper marginal analysis. The marginal unit is always the unit under consideration. If you were talking about tires and a car, the marginal unit would be a set of four tires, not a single tire.

Regards, Don

Wow, that's a very

Wow, that's a very convoluted way of describing an oversimplified theory. Why bother with the percentages and holdbacks? Just have a thug steal all your ready cash and cards, and ask about desirability of various options ($100 now or 50% chance of $200). Oh, and unless the mean outcome of the gamble is higher than the non-gamble, it's not really risk-aversion.

There is a bunch of research showing that loss aversion in most people is far stronger than can be explained by diminishing marginal utility. Entitlement effects are very real. This means that many folks would choose differently in the following two situations:
1) you lose your cash and cards, but find $100 in your sofa. Your friend offers to flip a coin, offering $210 if you win, costing your $100 if you lose.
2) you lose your cash and cards, and your sofa had no money in it. Your friend offers you a risk-free coinflip, $210 if you win, $0 if you lose.

A lot more people will take the coinflip in #2 than #1.

Mark, Thanks for your

Mark,

Thanks for your comment.

There is a bunch of research showing that loss aversion in most people is far stronger than can be explained by diminishing marginal utility. Entitlement effects are very real. This means that many folks would choose differently in the following two situations:
1) you lose your cash and cards, but find $100 in your sofa. Your friend offers to flip a coin, offering $210 if you win, costing your $100 if you lose.
2) you lose your cash and cards, and your sofa had no money in it. Your friend offers you a risk-free coinflip, $210 if you win, $0 if you lose.

A lot more people will take the coinflip in #2 than #1.

It seems to me that the biggest thing to be explained is why anyone would not go for standalone situation #2.

The background of Behavioral Economics is so pathetic that a simple assertion about diminishing marginal utility is of little value by itself. But, yes, diminishing marginal utility is just one part of a bigger problem.

Regards, Don

"There is a bunch of

"There is a bunch of research showing that loss aversion in most people is far stronger than can be explained by diminishing marginal utility."

How would one establish that without knowing the precise utility curve of each person in the experiments?

"Even if you are risk

"Even if you are risk neutral, and the potential risks and rewards are the same in dollars (80%), the real risks and rewards are not equal. This is because the dollars given up are more valuable than the ones returned due to diminishing marginal utility as above. As a result, most people, most of the time, should choose #1."

I think this is getting it backward. If you have diminishing marginal utility of dollars, that will cause you to pick #1 over #2 -- and that's what it means to be risk averse. If you had constant marginal utility of dollars, then you would be risk neutral and be indifferent between #1 and #2. To say someone's risk neutral and yet has diminishing marginal utility of dollars is just a contradiction.

(If you have to pay the rent check or get evicted, and there's no way you can afford the rent without winning the bet, then you have increasing marginal utility of dollars: the last dollar required to pay the rent has value much greater than all the previous dollars that don't keep you from being homeless. Increasing marginal utility of dollars leads to risk-loving behavior.)

I'm also pretty sure this experiment says nothing about loss aversion, but I'll have to think a little more about that.

"That was really my point,

"That was really my point, i.e. that it was the diminishing marginal utility of dollars that was the determining factor."

Okay, we agree then. Do you agree with Matt that your thought experiment says something about loss aversion?

"According to Rothbard, this would not be a proper marginal analysis. The marginal unit is always the unit under consideration. If you were talking about tires and a car, the marginal unit would be a set of four tires, not a single tire."

That's just Rothbard making his usual objection to thinking about underlying preferences as distinct from the act of choice; it's the same argument that leads him to reject the concept of indifference and to insist on stair-step demand and supply curves. I could argue against Rothbard's perspective, but it doesn't really affect the point in this case. There are two relevant "chunks" of dollars: the difference between 20% and 100% of your original wealth, and the difference between 100% and 160%. If the rent check is 160% of your wealth (meaning you can only afford to pay it if you win the bet), then chunk #1 has lower marginal value than chunk #2. That's increasing marginal utility.

Glen, Okay, we agree then.

Glen,

Okay, we agree then. Do you agree with Matt that your thought experiment says something about loss aversion?

Yes, I think 'something' is broad enough. Diminishing marginal utility invalidates the argument that equal amounts of money are necessarily of equal importance and that is illogical to not treat them the same. However, there's still plenty of room for loss aversion not tied to those considerations.

That’s just Rothbard making his usual objection to thinking about underlying preferences as distinct from the act of choice; it’s the same argument that leads him to reject the concept of indifference and to insist on stair-step demand and supply curves....

I am not inclined to agree that it's the same argument. Variable marginal unit sizes depending on the circumstances seems to me to successfully stand on its own.

...I could argue against Rothbard’s perspective, but it doesn’t really affect the point in this case. There are two relevant “chunks” of dollars: the difference between 20% and 100% of your original wealth, and the difference between 100% and 160%. If the rent check is 160% of your wealth (meaning you can only afford to pay it if you win the bet), then chunk #1 has lower marginal value than chunk #2. That’s increasing marginal utility.

I disagree with your "chunk" selection. The proper marginal unit is the number of dollars required to pay the rent check. A subsequent "chunk" of the same size is nowhere near as valuable, thus marginal utility still diminishes.

Regards, Don

Diminishing marginal utility

Diminishing marginal utility invalidates the argument that equal amounts of money are necessarily of equal importance and that is illogical to not treat them the same. However, there’s still plenty of room for loss aversion not tied to those considerations.

Okay, we agree then. I think loss aversion is a real phenomenon, but not everything that has been dubbed loss aversion really is.

I am not inclined to agree that it’s the same argument. Variable marginal unit sizes depending on the circumstances seems to me to successfully stand on its own.

Agreed, it's not precisely the same argument. But it tends to come from the same sentiment. Take the car tires examples. If the only thing I value is being able to drive, and I can only drive with four tires, then I would say the marginal value of tires 1, 2, and 3 is zero, and the marginal value of tire 4 is the value of driving. This is true even if tires are only offered in bundles of four; you can find my marginal valuation for the bundle by adding up the marginal valuations. (If you object to the cardinal utility language, you can think of it in terms of marginal rates of substitution. Add up the MRS's for each of the four tires.) So what's wrong with this approach? Rothbard says it's wrong because the only valuation that matters is the one that determines choice. I think that's silly. We can talk about my pre-existing preferences for tires without talking about how tires are sold, and then see how my preferences will interact with different sales regimes.

I disagree with your “chunk” selection. The proper marginal unit is the number of dollars required to pay the rent check. A subsequent “chunk” of the same size is nowhere near as valuable, thus marginal utility still diminishes.

It diminishes after the point where I can pay the rent, but it increases before that point. The two chunks I identified are chunks below that point. And these are relevant chunks because they're the ones I'm having to weigh against each other. If I take the bet, I'm trading in chunk #1 for a chance at getting both #1 and #2 (and a chance at getting neither).

Glen, Agreed, it’s not

Glen,

Agreed, it’s not precisely the same argument. But it tends to come from the same sentiment. Take the car tires examples. If the only thing I value is being able to drive, and I can only drive with four tires, then I would say the marginal value of tires 1, 2, and 3 is zero, and the marginal value of tire 4 is the value of driving....

This is certainly a valid description on its own terms. The marginal value of a tire 5 would then normally be the value of its insurance as a spare up until the point in time that it is needed, at which point its value becomes elevated to roughly that of tire 4.

The problem with all this is that it can't easily be reduced to a general statement that marginal utility is either increasing or decreasing. It's a complex situation that can't be accurately described in any simpler form.

... This is true even if tires are only offered in bundles of four; you can find my marginal valuation for the bundle by adding up the marginal valuations. (If you object to the cardinal utility language, you can think of it in terms of marginal rates of substitution. Add up the MRS’s for each of the four tires.) So what’s wrong with this approach? Rothbard says it’s wrong because the only valuation that matters is the one that determines choice. I think that’s silly. We can talk about my pre-existing preferences for tires without talking about how tires are sold, and then see how my preferences will interact with different sales regimes.

I agree that how the tires are sold means little or nothing.

The rest of the paragraph has too much interconnected content with which I can't be sure whether I agree, partially agree, or disagree.

When I go to google 'MRS substitution', I find indifference curves. It would appear that using MRS doesn't get us away from indifference curves and continuity assumptions. However, I suspect that almost all demonstrations that use indifference curves and continuity assumptions give pretty reasonable results.

I don't know where your pre-existing preference for tires comes from.

Economic value comes from the individual subjective ranking of desired ends, all of which cannot be satisfied by the available means which can be projected to be utilized to satisfy those ends. Diminishing marginal utility is nothing more than saying that the available means will be applied sequentially to the higher ranked ends first, and that the marginal utility of a given means will be related to the importance of the highest ranked end that has not yet been satisfied.

It is only when actual attempts are made to acquire the means to satisfy the highest ranked unsatisfied ends that the market for the means is hit with a particular unit demand. This is the first point where arithmetic comes into play, as the demand for a particular means can be added up for every individual attempting to access the market. Unit prices will then emerge as demand encounters supply.

Regards, Don

According to neoclassical

According to neoclassical economics, how does diminishing marginal utility determine the demand for a commodity? how should the fact that different people have different levels of income affect the demand for a commodity? And also according to neoclassical economics, how does increasing marginal disutility determine the supply of a commodity? How should the technology of production affect the supply of a commodity?
Please help me out with these questions. At least with one of them. I'm really confused. The answers are shattered into pieces and I can't figure seem to figure them out. I "really" would appreciate your help. Thanks.
Sincerely,

William, According to

William,

According to neoclassical economics, how does diminishing marginal utility determine the demand for a commodity?

I have no idea what neoclassical economics might say.

From an Austrian Economics view, every additional unit of a subjective use-valued good acquired will be ranked lower than each of the previous ones. For example, the subjective use-value of a second automobile will be far less important than the first which will enable you to commute to a job. This implies that total demand for automobiles is likely to be less than if the second automobile also had an important use.

how should the fact that different people have different levels of income affect the demand for a commodity?

Presumably, people with higher incomes are more likely to demand a second car, for example.

And also according to neoclassical economics, how does increasing marginal disutility determine the supply of a commodity?

You'll have to ask a neoclassical economist. This doesn't mean anything to me.

How should the technology of production affect the supply of a commodity?

A reduction of marginal cost enables a supplier to profitably satisfy additional potential customers who are either less willing or able to buy.

Regards, Don