## Persistence of Poverty, and Increasing Marginal Utility

I finally got the chance to read The Persistence of Poverty by Charles Karelis. Here is Tyler Cowen’s review. I can’t recommend this book enough. It’s deeply informative, and quite challenging to how we think of ordinary economic decision making theory. It’s a fun ride, and can easily be read in an afternoon.

Karelis proposes we start to distinguish between pleasure goods, and good that are relievers, and realize that some goods can act as both. His thesis is that there is diminishing marginal utility in pleasure goods, but that relievers have increasing marginal utility. “…paying the first bill in a stack of overdue bills does little to relieve a guilty conscience.”

Cake, Screaming

I didn’t quite understand what was going on with it from the book reviews, so let’s do the story with a teensy bit of math.

Here’s the normal story. Picture you are in a room with 10 people. Each of them has a slice of cake. How much you are willing to pay for a slice of the cake is the ‘marginal utility’ of having it, and the more cake you have the less any more cake is worth to you. You’d be willing to pay a \$1 for the first slice of cake, but you’d only be will to pay 90 cents for the second slice. You’d only be willing to pay 10 cents for the 9th slice, and a penny for the 10th slice. Eating the 10th slice of cake in that room would probably make you sick, hence you want it a lot less than the first slice, which is delicious. That’s declining marginal utility.

Now picture you are in a room with 10 people screaming. You hate it when people scream, and you can pay a person to get them to stop screaming. Would you pay in a similar way to the cake example? Would you pay a \$1 to get the first person to stop screaming, and a penny for the 10th person to stop screaming?

No. Getting one person to stop screaming would make very little difference in how much you dislike being in the room. Modern psychology tells us you might not even notice it. You’d probably only pay a penny to get that first guy to stop screaming. However getting the second guy to stop screaming might be worth 10 cents. And the last guy, the difference between some screaming and no screaming, might be worth the full dollar to you. The more quiet it got, the more a marginal difference in how quiet it is would be worth to you. There’s increasing returns to this good; the 10th guy not screaming is worth more than the first guy not screaming, which is the exact opposite dynamic of the 10th cake being less delicious than the first.

For those not involved with economic theory this might just elicit a shrug, but this mechanism turns everything on its head. Let’s say that instead of money, you are given 20 tokens to be used over 4 days, and each token gets you one slice of cake in room #1, and one person to stop screaming in room #2. In the cake room, the optimal decision is to consumption smooth – eat five slices of cake each day, so you use the tokens {5,5,5,5}. In the screaming room, all the enjoyment is not in getting a room with half screaming but in getting a quiet room, and instead of consumption smoothing the optimal choice is to binge – pay 10 people to stop screaming the first two days, and deal with a loud room the last two days – {10,10,0,0}. This will hold even with ‘nudges’, say offering two extra tokens if you have people consumption smooth, since the marginal utility isn’t increasing that much. The utility of {10,10,0,0} is greater than that of {5,5,5,7}.

(And most interesting, instead of tokens, let’s say you could work an hour for 1 token or take 65 cents in leisure over a 5 hour day. In the cake room, you’d probably work 3 hours, and relax 2 hours, as around that time you’d have the marginal return from cake equally the marginal return from relaxing. In the screaming room, you probably wouldn’t work at all – it’s impossible enough to make enough to stop the screaming to the point where it is worthwhile to try. Hence the persistence of poverty.)

His other point is that many goods have both characteristics. Let’s say you have 5 children. In a large house, where each child has his or her own room, a child leaving the house to go out into the world gives you diminishing marginal utility. The first room turns into an entertainment center, the second into a hobby room, and the third just sits empty. But if you are in a cramped, small 2 bedroom place for all of you, the first child leaving might only make a slight bit a difference compared to the second child leaving. By the time the 5th child leaves the home, you get the most marginal enjoyment of having your small place less cramped. Karelis point is that this inflection point is where we should be thinking about poverty, because as the token example above mentions, normal policy mechanisms based on neoclassical microeconomic theory won’t necessarily hold.

Intellectual History

Karelis takes a moment to do some intellectual history digging and finds that the current economic obsession with decreasing marginal utility comes from Jeremy Bentham’s equating happiness with the absence of unhappiness. Bentham, and the Mills, thought of happiness as reciprocal to unhappiness, like the relationship between tall and short. So to increase happiness is the same exact thing as to decrease unhappiness. Maybe, maybe not. But the problem is that this relationship is carried over to the goods that effect happiness and unhappiness.

Bentham: “utility [is] that property in any object whereby it tends to produce…pleasure…or happiness..or (what comes to the same thing) to prevent the happening of mischief, pain, evil, or unhappiness.” Stanley Jevons cites that passage 80 years later when he lays the foundation of what Alfred Marshall will later use to create modern economics.

Bentham usually showed a more ambiguous approach, noting that there are often ranges of postive experiences and negative experiences that don’t necessarily net, but that ambiguity hasn’t transfered to the current theory where the marginal rate at which pleasers please is information on the rate at which relievers relief. And this approach, to see a cross-section within time and see that a baseline income can change incentives in a dramatic way, is a whole new dimension to think through. And one with very testable hypotheses.

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### 54 Responses to Persistence of Poverty, and Increasing Marginal Utility

1. roger says:

I loved this post. Interestingly, if you can get the screaming people to eat cake – which would quiet them – you could save on your tokens. I would like to see a bit more about the relation between pleasure and relieving goods in the economy. I could see how, in some ways, marketing might well be geared to making pleasure goods into relieving ones – which would be interesting in that neo-classical theory has no handle whatsoever on the function of marketing besides viewing it as information exchange.

2. Dismal says:

This is a pretty dumb argument if you ask me. It’s kind of like saying, what’s the point of practicing basketball if I’m not already Micheal Jordan, or, what’s the point of me going to work if I’m not going to be a millionaire. It doesn’t explain shit, especially not about poverty.

Poverty is increasing in this country, unsurprisingly at the same time as workers rights are decreasing. Poverty isn’t just some variable in a model, that will be true for some and false for others, it has causes, such as falling wages, disappearing jobs, increasing costs of living, increasing costs of education.

Poverty persists because it is convenient to have around. 3rd world countries are easier for multinationals to exploit if everyone in them is scared and hungry. Look at illegal immigration in this country, it persists not because it would be so fucking hard to fine managers and corporations that hire illegals or because we don’t have a berlin wall built on our Mexican border, but because in some fields, like meatpacking or construction, you want a cheap and disposable labor force that you have no responsibility towards.

Sorry to go on a little rant here, but the more I read about economics the more I start to think that the whole purpose of the “science” is to ask the wrong questions. How the hell is poverty like someone in a room screaming? Why are they screaming? Why do you have tokens to give them? To borrow a line from Lebowski, why does everything have to be a god damn travesty, economics!

• Will says:

It’s a thought experiment.

• cst says:

You are right in your own way.

The screaming people and cakes are thought experiments, not to be taken literally. They ares not about the wrong politics that you describe (weakening worker unions, etc.), but about why its is so difficult to poor people to abandon poverty, in the US and elsewhere.

It is a very good way to look at the problem, and I will definitely get that book.

3. Karl Smith says:

This basically take the “Poverty Trap” notion of S-shaped production functions and replaces them with S-shaped utility functions. In the traditional poverty trap what you need is a big push. What’s the recommendation here?

• reason says:

Wouldn’t a citizens income do the trick?

• Ano says:

If I remember correctly from the book, one possible solution is to just give suffering people some money, which moves you up the “increasing marginal returns” curve enough to make it worth it to the person to start relieving his own suffering through work.

4. reason says:

This made me think of applying the same thinking to pollution. Isn’t this basically explaining the problem with doing something about global warming very clearly. Doing a little is not much better than doing nothing, so there is no way to scale up to a solution.

• Russ says:

I was sort of reminded of that too. I said given 20 tokens and four days to pay people to stop screaming, I’d rather endure it for the first two days counting down to when I can have quiet. So (0,0,10,10). Why is “binging” supposed to be better?

But then I figured that economic theory would say I could drop dead at any time, so it’s better to binge; I wouldn’t be “discounting the future” enough. Which made me think of the economists’ wrangling over climate change mitigation, Stern vs. Nordhaus and Mendelssohn.

I guess they’d say spend all the tokens now since you’ll magically get more later, a lot more.

5. Interesting mental jigsaw problem.

Like all models, it only goes so far. In the room with 10 screamers, after noticing that you are paying for silence, the remainder of the screamers would start a from of reverse auction, the majority not wanting to charge too much to silence themselves. The last few screamers would have the silence buyer over a barrel.

Adding to the chaos would be silenced individuals deciding to start screaming again to gain more payments.

This is more of a shock model characteristic in reverse, much like the effects of depletion on purchasers of crude oil. The cost of silence does not follow an arithmetic path but ramps quickly.

More on the shock model here:

http://www.theoildrum.com/node/2376

Intermediated by credit, the ramp effect would become exponential, until credit was exhausted along with the ears of the listener.

Hmmm, interesting, I think I’ll buy the book, good tip.

Thanks.

6. Nate says:

Interesting, but the greater the “wow” factor of a thought experiment, the more I’m suspicious.

Lets start with a more formal definition of decreasing marginal return. Decreasing marginal return says as x increases by a constant increment, y increases by a diminishing increment (y = f(x)). In other words, second derivate of f(x) is negative.

With your cake argument, it’s all good. Each piece of cake is a constant increment – 1/10 of the whole. With the screaming argument I’m less sure. As you say the percieved incremental decrease in volume from one less screaming person is negligable at first and the whole cake at the end, to turn a phrase. To properly determine the curvature of this screamer data, you’d need to impute and determine a constant increment (denominator, x value) over which to measure your change in y (utility).

It’s relatively confusing to try and work out how the above analysis effects our comparison of the cake and screamer model, and I think this is further evidence of the simpler point I’m trying to make: the cake and screamer examples are apples and oranges. The experiment is set up incorrectly. If you were to try a constant incremental decrease in decibel volume, I’m quite sure we’d start to see classic marginal decreasing return.

Anyways, I say perceived and that is strictly true, but for the basis of argument percieved means “real”. Psychologically speaking, that is certainly true, and I’m bored by metaphysics. The theory of utililty functions seems to capture and subdue the difference between reality and perception, anyway.

Other thoughts:
A fundamentally confusing factor that gives this experiment extra sparkle is the increasing good in the cake example, and the decreasing bad in the screamer example. Graph these two and your blown away by the result – they are nearly opposite!. Well, of course they are – the cake example is the conceptual inverse reflection of the screamer example over x (increments) and y (utility). Graph the cake example against the screamer example reflected over the line x = y and you will see what I mean.

An economics way to accomplish this reflection might involve the use of Hicksian compensation for how much somebody would accept (dollars) to have an increasing number of people start screaming.

7. Noah Yetter says:

Poverty persists because it is the natural state of man.

• Will says:

says a man on a computer..

• Noni Mausa says:

…which I call the “cell phone and colour TV” argument to dismiss modern-day poverty. It is, of course, incorrect.

Cell phones used to be luxuries, as did colour TVs. Today, colour TVs are given away every day as they flood the market, or they clutter shelves at the Salvation Army.

As for cell phones, there’s many reasons why homeless people have them, and it’s not because they want to flaunt their wealth.

And of course, computers with net access are available free at the local library.

8. brutally frank says:

i have a better one for you…

ceo’s, executives, and the like are so overpaid they have no incentive to come to work.

that’s right.

see when you get paid at such and inflated salary … it’s kind of like overreating… you are stuffed… no incentive to work… hence the unnecessary and often financially suicidal risks they are willing to take.

furthermore these guys are more incentivized to spend more time making money for themselves than they are for their shareholders.

as they become more wealthy their leisure time is more important than even showing up for work and putting in the minimum amount of time.

the crime in all this: they are in control of their companies and organizations; they make the rules or decide to break them; however, they rarely feel the consequences or pay for their actions.

they get to legally steal corporate revenues that should rightfully belong to the shareholder, they take all the icing on the cake.

this is what happens when you over-compensate, over-incentivize, and really reduce the competition for employment.

lower the salaries to below 500K and the real investors will reap the rewards without getting fleeced in the process.

• najdorf says:

brutallyfrank: Rather than theorizing about others incentives and suggesting arbitrary adjustment of them, why don’t you do something about it? Start your own company or become active in agitating for change in an existing company. The joy of capitalism is that you actually have the ability to do something about economic problems, rather than just complaining about them. Every ongoing corporation that “overcompensates” its employees is able to attract enough capital and customers to continue operations. That’s more than I can say for your imaginary corporation of the mind where talented people will do the same amount of job for less money. If you think managerial competence is a plentiful resource then you have a very different view of your fellow man than I.

Are there companies run by idiots? Yes. Nominate some new directors, vote against the compensation package, and take your case to the media. Try to build consensus with other shareholders and attend annual meetings. The corporate system doesn’t exist for the purpose of automatically insuring your welfare, but you’re not without levers to participate.

• brutally frank says:

public corporations should be run by independent boards of directors. the ceo and executives should NOT be voting members of the board but rather there ONLY to report the status and their perspective on the outlook of the company. what we have now is a corrupt and biased group fleecing the shareholders. when the ownership pie is divided up into extremely large numbers of shares owned by extremely large numbers of people — the notion that shareholders can impact any change in policy is ludicrous. it was designed that way to create chaos in order for the CEO and executives to maintain total control and legally steel the profits of the corporation for themselves. large uncontrollable (by the shareholders) are commonplace which begs an answer to this question — who are the real owners of the public corporations? the shareholders or the executives? is buying and selling public stock merely a game of chance without any real notion of making a financial investment?

• Denise says:

You don’t really mean all that, right…?

The income effect doesn’t mean that people stop coming to work. It just means people work less. That still doesn’t give them license to break rules and subvert the stockholders — quite the opposite, actually. If they become corrupt and the media gets wind of it, what’s the first thing that happens? Right, the stockholders pull their investments, the company loses its financial backing, and it’s at the mercy of the Fed’s next big bailout.

It’s easy and popular to generalize about evil corporations these days thanks to Michael Moore et al’s age of one-sided documentaries, but by and large there’s an increasing expectation of social responsibility. Pharmaceutical companies for example give an astounding number of free doses of Hepatitis C vaccines to Africa every year for all the condemnation they get for holding patents.

But let’s say some CEOs do spend all their money on themselves. Am I the only one who doesn’t see the harm in that? Instead of hoarding money, they re-inject it back into the economy.

What does any of this have to do with poverty traps though?

• brutally frank says:

sure i do. IMHO if the CEO, and the top couple of tiers of the largest corporations in the world never came to work. the corporations would never miss them. never. these companies run on inertia. the inertia created by the people at the bottom of the corporation up to the middle layers where all the tactical decisions are made. if no strategic decisions are made the corporation will continue to exist in its current state to infinity and beyond. executives, the MT heads, add little or no value to the corporation except to redirect the corporations profits into their own pockets. if the House and Senate were really smart. They would start eliminating or minimizing certain “expenses” that corporations are allowed to deduct on their taxes. My recommendation is that they limit and cap the “total compensation” expense (tax deduction) corporations are allowed for operating expenses, i.e. wage/salaries, bonuses, stock options, etc. The cap should be set at the 95th percentile of household income in the usa, PER individual employee. Meaning corporations and businesses can only deduct the total compensation for each employee up to the 95th percentile of household income in the USA. Corporations are free to pay and compensate their employees however they wish, but they must pay taxes over and above that 95th percentile value. This would end what is essentially a tax subsidy or benefit that working class people pay toward incomes and salaries over and above their own. This is a very difficult concept to understand, but if you are pretty intelligent and zen in on it for a while you will understand the “fairness” that this proposal has. I call it part of my 95% solution. Where lawmakers should analyze policies and vote in favor of the financial interests of at least 95% of all Americans. When 95% of all households earn less than \$100,000 per year (approx). This kind of approach is extremely important. Economic policy should attempt to push wealth down the socio-economic ladder to enable those at the bottom to rise to the top. Not the other way around. This concept is also counterintuitive. When the incomes of those at the bottom rise, they are able to enrich those at the top not the other way around. Again these concepts are counterintuitive, but look at our current economic situation and you will understand that these ideas will move us up and out.

9. Damien R S says:

“screaming” makes me think of “broken windows”. If you have a clean neighborhood and then suddenly there’s a bunch of broken glass (windows, beer bottles), that’s bad! Clean it up. But if there’s a lot of glass and trash, just cleaning up some doesn’t seem worth much, it’s still a neighborhood with loose trash and broken glass. Heck, that maps a fair bit to domestic cleaning too.

A cruder argument would be that you’re not buying utility or marginal relief, but a change in binary state, from screaming to quiet or messy to clean, and buying an ‘improvement’ that doesn’t actually change state is worth very little.

I’m not sure how this actually maps to poverty. Possible state changes: hungry to not, no electricity or water or heat to having them, in debt to not.

10. Pingback: Michael Alan Miller » A cake fan

11. Noni Mausa says:

Two points:

First, keeping in mind that wealth is created by people, one necessary part of the poverty equation is that “poor people always create wealth if they are living even a little above the level of imminent death.” They just produce it in tiny amounts.

“Poverty persists because it is convenient to have around.” is true, but it also arises as a result of trying to skim the largest possible wealth from the largest number of people. Greed in the financial elites reduces the overall wealth of a nation, and produces many other nasty side effects, but it doesn’t kill the cow — it just makes it a sick cow.

However, this counterproductive greed also satisfies peoples’ desire to dominate if they can. And it’s a positive feedback loop. The increased skimming leads to the need for more brutal skimming, more intrusive spying, more paranoid defenses for the upper class, and more tight controls on emigration — because as people get poorer they resist the skimming by hiding their meager wealth, lying, crime, or simple escape. The form of a totalitarian state is necessarily the result of such greed.

Second — another response to living in the screaming room would be to use some of your credits to buy earplugs. In the real world, that would show up as ignoring the letters and phone calls of debt collectors, ignoring health problems, not fixing up the house, and doing without services we would consider essentials — like running water, or heat, or electrical power.

I knew a disabled fellow on welfare who went for several years without hot water and for a year or so without running water, because his landlord wouldn’t replace the HW tank or, later, fix the plumbing. The one-time cost of my friend complaining about his water would have been to be forced to move his household and probably end up in a tiny apartment or even a shelter, rather than the battered rental house he’d been in for 15 years. He compensated by getting a subsidized YMCA membership and showering there, and carrying water bottles with him and filling them in public washrooms whenever he went out.

Noni

12. Fred Beloit says:

Economics eh. May I ask Economics a polite question? If there are so many millions out here without jobs, how can it be that there are no shortages of products and services that I may need or just want? In fact there are more products and services than ever.

• Noni Mausa says:

I suspect this is a transient situation. The warehouses are still full, (which situation itself pushes unemployment) and as for services, people are scrambling to provide services because they, too, need an income.

If nothing is done in such a situation, we can expect to see a downward spiral of less manufacturing (because fewer can afford the stuff) and more unemployment, plus fewer services (because fewer can afford them) leading to more unemployment. The endpoint of that spiral is, of course, a Depression.

13. Fred Beloit says:

Thanks, Noni. The warehouses and stores may be stocked, but has the production of, and introduction of new, products and services actually slackened?

14. crayz says:

There’s increasing utility in each additional screamer you convince (pay) to be quiet. Four paragraphs that boil down to picking graph axes and showing a line going down isn’t a rebuttal

• Nate says:

“…paragraphs that boil down to picking graph axes … isn’t a rebuttal” is exactly the argument I’m trying to make about demonstrating instances where marginal decreasing utility doesn’t work.

RortyBomb even goes so far as to say, in her/his OP, that “The more quiet it got, the more a marginal difference in how quiet it is would be worth to you.” Right, quiet. Not really people screaming. Were wrapping “humans screaming” around u = f(dB) so we can tell a story (sparkle!).

The story about 11 humans in a room, 10 of them screaming and one of them paying, can be explored several ways. A lot of people right now seem to love to pick the axes that tell us something “counterintuitive”, and pass it off as the result. It’s disingenuous given how easy it is, like you say, to completely reverse their result by “merely” switching graph axes.

So incidently, here is another story: There are 10 people in a room with you. One of them turns to you and says “hey I really feel like screaming – what’ll it take money-wise for you to let me”. You say 100 dollars. Then, another person turns to you and asks you the same question. Do you ask for more or less than 100 dollars? Now again, until all 10 people are screaming.

Just like I was saying earlier, it’s the screamers story in reverse. By reverse I mean “were time to simply run backwards”. Back to our graph axes – Where is the time axis? Not there – in fact I don’t think we’ve even discussed time as a parameter in the utility function. But that’s just an aside.

• Marginal Futility says:

I think you are ignoring that the y-axis (from utility to disutility) is also changing here: what you’ve described is decreasing marginal disutility.
I think that actually validates the way that Mike / Karelis use the cake example, or at the very least, speaks to a need to consider utility and disutility differently. Similarly, it is meaningful to consider gains and losses differently.
I’m as wary of faux-economic contrarianism as the next guy, but this is actually a pretty well-established concept. As someone above noted, it’s an S-shaped utility function that goes through the origin – pretty much the essence of Kahneman and Tversky’s Prospect Theory: http://en.wikipedia.org/wiki/Prospect_theory

Trying to switch up the axes all the time so that we can use our familiar from-the-origin, first quadrant frame short-changes how people perceive, experience, and evaluate the world around them. And why bother, when you can fit the familiar phenomenon and the so-called contrarian one into the same picture?

• Nate says:

I like that! Thanks for linking to Prospect Theory, it was an interesting read. You’ve convinced me – I’m almost certainly wrong in my zealous defense of marginal decreasing utility.

15. dcpi says:

@ Reason

Would a citizen’s income work? The common wisdom is that many or most lottery winners return to poverty or their prewinning financial state fairly soon after their payout. What are the implications of that, if it is indeed true?

16. Mike says:

Lots of great comments everyone. Some people here and elsewhere are converging of a critique of this model that it isn’t accounting for ‘lumpy’ goods. So if I have a car with no tires, i have increasing marginal utility in tires – i can sort of drive it with 2 tires, drive it better with 3 tires, and drive it normally with 4 tires. However what I want is a functioning car. The book goes into detail on that critique, so you are going to have to read it for a response!

Another analogy used often is bee stings – if you have 10 bee stings, getting rid of the first one is worth less than getting rid of the last one. I actually wasn’t getting it from that example, and it was easier for me to think through this example, but that’s another good one if this isn’t clicking.

A comment from Wilbur at Yglesias’ comments that I want to make sure gets reprinted here:

==
Yes, Karelis’ ideas are vitally important and have simply not gotten enough attention (because our neo-classical model really doesn’t work to take ideas of individual despair into account). This is almost exactly what we have found in working with homeless. Using the bee sting analogy, which I believe is by far the easiest to understand – if you get one bee sting you want to take care of it immediately, but if you get a hundred bee stings it really doesn’t make any difference to treat a single bee sting, you are stil in the same amount of difficulty. Now think about a homeles individual. He does not have a place to live, but because he doesn’t have a place to live he probably also doesn’t have a job, has very poor nutrition, has no health care, has emotional problems – as well as issues with dignity and a willingness to show yourself in public. If you find this person a job he still has all of the other problems, so while he will start off happy with the job it will slowly dissolve because of the othere issues, so job counseling or even providing a job really doesn’t do that much good. The deficit model of poverty that has dominated poverty research has been very, very destructive. But poverty research, just like health care, is an industry where people are not willing to give up perquisites even though it has not lead to any greater understanding of poverty.
==

• Nate says:

Composite goods are so tricky! By the way, how about a car with 5 tires. Or 6 tires? Or 20 tires? Couldn’t we just normalize the data by assumption “A car starts with four tires”, and then move on? With the assumption “A car starts with four tires”, I’d bet we have marginal decreasing utility across all possible number of tires.

Again, how much could I pay you to let me puncture the first tire. The second tire. The third tire, etc.

Stories are great but they really are just argument by analogy.

Just as an aside, I think there are strict conditions on when you can and cannot “assume” marginal decreasing utility. I would agree with you that the issues the homeless face needs to NOT be treated as some kind of marginal decreasing utility issue. Marginal decreasing utility is a mathematical concept that primarily just makes academic economists lives easier and only applies in “how many of one type of widget” situations. Homelessness is definitely a composite, necessary conditions thing.

17. Marco says:

Rortybomb and all,

For some reason, my previous attempt at posting this failed. So let’s try the “installments approach”

Here goes Part 1 of 3:

———————-

I’m always pleasantly surprised by the high level of some contributions in this blog.

It’s a bit risky (and potentially unfair) to dismiss a work out of hand, without having read it (as I haven’t read Karelis’ book). Furthermore, as RortyBomb (who in my experience reading his blog, is usually quite informed) seems enthusiastic about it, it is even riskier.

But, as some previous posters, I am sceptical. Maybe the “screaming room” example was unfortunate, but it seems to me this is neither new, nor particularly useful.

Imagine we are going to manually represent the situation, with a graph. One draws two coordinated axes: for simplicity’s sake, the horizontal one measures the number of “screamers”; the vertical one measures our “satisfaction” or “utility” with the noise.

So, let’s represent the situation when 10 people scream: starting from (0, 0), which is the origin of coordinates, we move ten units horizontally, towards the right. Upon reaching the point representing 10 “screamers” (that is, (10, 0)), we move vertically a distance numerically equivalent to our “satisfaction”. This vertical distance is arbitrary, of course, and we call it u(10). That (10, u(10)) point belongs to our ordinal utility function.

Let’s do this now for 9 “screamers”. Again, we begin at (0, 0) and move to a position immediately to the left of the (10, 0) point that we reached in the previous example. Upon reaching this new position (i.e. (9, 0)), we move vertically a distance equivalent to our “satisfaction”.

———————- (end of Part 1)

18. Marco says:

And now goes Part 2.

————– (beginning of Part 2 of 3)

How much we move, now? We can’t move a distance less than u(10), which is the vertical distance we moved in the previous step: if we moved less, it would mean we are definitely less satisfied with 9 “screamers” than with 10. So, we must move at least as much as we did previously: u(9) >= u(10). [1]

Now, let’s note this: a diminution of noise (a leftwards movement along the horizontal axis, from 10 to 9), leads to an evaluation at least as good as before. That is, we have a utility function with non-positive slope (i.e. du/dx <=0).

Although this is not the common assumption of most ordinal utility maximization problems, it's far from unique. Another instance is the time allocation problem, where the decision-maker has to allocate 24 hours between work (which produces disutility: the utility function has negative slope along the work-hours axis; but which produces fiat-money income, in the form of an hourly-wage rate) and leisure (which produces utility per se: the utility function has positive slope along the leisure-hours axis).

Although I am not sure about his interpretation, Karl Smith is right in mentioning the S-shaped utility curves. The earliest example of such a function – that I know of – is from a 1948 paper by Friedman and Savage. [2]

Not only is this not new, but there are many problems with the notion of utility maximization.

Firstly, it has been empirically shown that people do not behave that way.

And there are good reasons for that, too: we don't seem to be capable of the incredible feats of information processing required by utility maximization. Let's pause a moment, and imagine we change the example from time allocation, to our weekly shopping. Just go into any supermarket and have a look at the sheer volume of choices: prices, sizes, brands, colours, flavours, ingredients. And (in the most literal interpretation of the microeconomic assumptions) you are supposed to know all that, not only for that supermarket, but for all supermarkets; all investment options, all jobs and employers, all residential choices, all possible partners, all mobile phone/internet/cable TV providers, all routes to the supermarket, all insurance companies and policies, all parties and candidates.

————– (end of Part 2 of 3)

19. Marco says:

And, finally – fingers crossed – Part 3 of 3!

————– (beginning of Part 3 of 3)

Clearly, one could consider a relaxation of these substantial requirements, but then we fall into suboptimality (i.e. markets are not “efficient”, whatever that means).

Furthermore, I believe Dismal is in the right track when he/she pointed that there are many causes of poverty that escape one’s control. He/she mentioned many, and did very well at that, so I don’t need to repeat them here.

And, to be honest, Dismal’s observations seem to me of a rather more fundamental nature than my own.

Sorry I did not comment on other posters (many of which made also excellent points).

Cheers

Marco

NOTES:

[1] As Rortybomb mentioned the “just noticeable difference”, it’s conceivable that we would move exactly the same distance we moved for 10 “screamers”: u(9) = u(10). This could lead to strange and uncomfortable situations: either “thick” utility curves (i.e. not functions) or discontinuous functions. So, let’s try to avoid it: even though we don’t perceive any difference, we may intellectually acknowledge that 9 “screamers” instead of 10 is a step (albeit a small one) in the right direction and give it a u(9) which is just slightly larger than u(10): u(9) > u(10).

[2] Friedman, M.; L.J. Savage. “The Utility Analysis of Choices Involving Risk”. Journal of Political Economy, 1948. Vol. 56, pages 279-304.

————– (end of Part 3 of 3)

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21. Gulzar says:

Explaining the persistence of poverty has been one of the most enduring of socio-economic debates. Despite all this, there have been no satisfactory enough single explanation that captures all the reasons behind poverty and its persistence. And I am inclined towards the belief that complex challenges like poverty cannot be explained in a grand and all-encompassing narrative.

Conservatives and free-marketeers advocate the importance of getting incentives right in addressing the problem of poverty. They claim that once the required framework that provides everyone with equality of opportunities is put in place it becomes easy to eradicate poverty. These microeconomic foundations have been used to favor policies that emphasize good governance, institutions, rule of law, access to basic health care and education, and so on. They have also been invoked to oppose direct welfare measures that go beyond the most minimum of social safety nets and even multi-lateral aid. It is claimed that such support measures fail to achieve their poverty alleviation objectives and only end up distoring incentives by discouraging effort and promoting inefficiency and corruption.

Such simplifying narratives of a complex issue like poverty is audacious at best and plain ignorant at worst. Such explanations fail to appreciate the true complexity of poverty and deprivation and fails to acknowledge the importance of specific contextual factors (local community instiutions, weather, geography, politics etc) that keep people poor. Its underpinning rational economic man also ignores the bounded rationality of human beings that behavioural economists have exposed under a number of different circumstances with poor people. It is from this framework that I find Charles Karelis’s work interesting and a welcome addition to the growing literature that helps us better understand the context in which poverty flourishes and the reasons why it is so impervious to change.

22. Scott says:

So the poor more often find themselves facing situations of increasing marginal utility, and the cost of initially improving their situation is too high. That just begs the question, why do the poor more often find themselves in those situations? Why should the poor happen to find themselves more often in room #2 than in room #1?

I don’t see this argument as explaining the persistence of poverty at all. You need the additional assumption that at low levels of utility, the marginal cost of working is higher than the marginal benefit of silencing the first few screamers. Yet you could just as easily make that assumption in the cake room as well, where the marginal cost of working that first hour is higher than the marginal benefit of your first piece of cake. It doesn’t matter whether marginal benefit rises or falls afterwards, you’re not going to work in either case.

It’s an interesting idea since we normally assume diminishing marginal utility. But unless I’m missing something, the assumption on marginal utility isn’t driving the result.

23. Noni Mausa says:

Scott asked: “That just begs the question, why do the poor more often find themselves in those situations?”

Because of the definition of “poor” that Karelis uses in his book. These are people whose income falls short of meeting all their needs, or so close to that number that any small, unexpected event can push them into poverty.

So then they are in a position of “quieting the screamers” — paying various bills, but not receiving relief from doing so. If you’re faced with 8 bills but only 4 bills worth of money, how do you choose which to pay? Especially when next month, and next year, you won’t be earning any more than you are now?

In a chronic situation of insufficiency, Karelis presumes that a new set of choices takes the place of the sober sensible choices of people who have a small, but sufficient income. (The hardworking bootstrap people so beloved in the stories of the right wing.)

The timeline shortens, choices become immediate rather than long-term, many consequences lose their sting, crime and defaulting on debts become useful options rather than the losing propositions they usually are, and scrounging and reapplication of one resource to do the work of another, or doing without, become common. Life becomes more expensive, not less.

Because of the constant “screaming,” alcohol and drugs become more attractive, to dull the noise and its consequent stress.

Noni

• Nate says:

Wow, succinct AND eloquent post Noni.

• Mike says:

Agreed. Slam dunk Noni.

24. Pacer says:

So what if the poor person decided to forego cake today, instead lending their token to another poor person in exchange for two tokens tomorrow? And so on every day for a month, at which point their income could easily be paying for a scream-free room and a piece of cake each day, all paid for by the interest on their various token loans.

I’m sure there’s a lot that science can tell us about the causes of poverty, but none have proven to me that there’s any substitute for delayed gratification, saving, investing, and otherwise pushing consumption into the future in exchange for greater total consumption. Then there is the situation with investing in children so that they might have a head start in the token game…

25. Noni Mausa says:

Still unclear on the concept, I see. A few questions:

If the poor lender lends to the poor borrower, and neither of them ever has enough, where exactly does the interest come from?

If the poor lender lends his cake for today, what does he eat so as not to starve? In this argument “cake” doesn’t mean an extra. It is his food. We don’t last long without it.

More importantly, the poor borrower is strongly motivated to take the lender’s cake and not repay it.

Noni

26. Pingback: Savings Lottery « Rortybomb

27. Danny says:

I’m really excited about the book. I am initially won over by the screaming argument as it may relate to the lack of resources, hope, opportunity, etc. of the very poor. The cake argument, though, i assume to be the incentive to make more for the middle and upper class. It would seem to me that the incentive to grow unbound amounts of wealth, or more cake, doesn’t diminish so easily. Greed begets more greed. Or am i leaping to false inferences?

Can’t wait to read this book, it’s due back at my library this week.

28. Nick Gogerty says:

This is a great post and definitely begs the question of why more assessment of structural dynamics aren’t brought into play when assessing systemic or chronic problems such as poverty.

typical solutions are point based (single NGO, action) or crisis response, but fail to address systemic structural issues that lead to vulnerability.

Endemic persistant Disease such as malaria or water borne illnesses in the developing world are great structural issue type problems, leading to structural weaknesses further down the development chain.

thanks for the post and highlighting the book. The more people can have a dialog using shared frameworks of thought such as “tragedy of the commons, diminishing returns, extra marginal returns etc.” the more thoughtful and hopefully effective proposed solutions may be.