Experimental Confirmation of Hypotheses Regarding the Value Function for
Consumption, Some Notes and a Request for Feedback
Charles Karelis
How are levels and changes in individuals’ consumption valued? I will argue that
a new approach to experimentation is needed to get to the bottom of this. Ultimately
I would like to find students or faculty at GMU interested in helping to design or
conduct such experiments.
Is this whole matter worth investigating? Some would say no. After all, the
underlying question—how levels and changes in individuals’ consumption are
valued—does not currently play much role in advanced economics. Economics
students encounter the question in introductory microeconomics and rarely
afterwards.
Yet it should be kept in mind that beliefs about how levels and changes in
consumption are valued play a big role in the political and social debates of our day.
For instance, people’s views of this underlying question play a big role in debates
over executive compensation. (“What difference can another million possibly make
to the billionaire CEO?”) They play a big role in arguments about the progressivity of
the income tax. (“The dampening of incentives that will be caused by the Democrats’
proposed income transfers is (or isn’t) outweighed by the much greater value of the
transferred funds to the poor family as compared with the rich.”). They play a big
role in arguments about the motivations of low-income people. (“No wonder they
have a diminished appetite for self-help. They’re getting so much help from the
state.”) They play a role in debates about the proper scope of government
intervention in private conduct. (“Boom-bust consumption hurts us all in the long
run, so soft paternalistic measures to nudge us towards saving are entirely
justified.”) I conclude that investigating the way that levels and changes of
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consumption are valued, and the way experimentation should be used to compare
competing answers, are eminently worth investigating.
In this presentation I am going to focus on one kind of answer: that in general
people act so as to get as much of what they care about as possible. In other words,
my starting point, which I don’t have space here to defend, is that behavioral
economics underestimates the proportion of economic choice that can be
rationalized. For the present, then, my question is limited to, what is the best way to
rationalize economic behavior?
I will consider four approaches. (a) The marginalist theory associated with
Gosssens, Jevons, Edgeworth, and Marshall, and generally taught in introductory
microeconomics courses. (b) The hypothesis centered on the inflected utility
function proposed by Friedman and Savage in their 1948 Journal of Political
Economy article, “A Utility Analysis of Choices Involving Risk.” (c) The Prospect
Theory of Kahneman and Tversky, propounded in many, many articles by them and
recently summarized for general readers in Kahneman’s best-selling 2011 book,
Thinking Fast and Slow. (Note that Prospect Theory understands the value being
maximized by economic decisions in terms of economic losses and gains, rather
than levels of wealth, but with that qualification, Prospect Theory should still be
seen as a way of rationalizing economic decisions.) (d) My own view, put forward in
The Persistence of Poverty (Yale, 2007).
My own theory, which I will explain in a moment, could maybe be described as a
refinement rather than an alternative to the hypothesis put forward by Friedman
and Savage. But the differences are important.

First, while Friedman and Savage offer their inflected utility function as a
way to rationalize common human choices involving risk, I offer my inflected
utility function as a way to rationalize common choices involving not only
risk but also work and consumption smoothing.
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
Second, Friedman and Savage do not pin the inflection point(s) in their
hypothesized function to any particular level of consumption, whereas I
hypothesize that the utility function for a given individual is inflected at the
level where that individual’s consumption is no longer relieving the troubles
caused by deprivation and instead begins to generate positive satisfaction.

Third, while this not strictly part of the hypothesis, I offer a “story” involving
common subjective experience that I think makes hypothesizing a utility
function inflected at an individual’s “poverty line” plausible.

Fourth my hypothesized function has one inflection point, while theirs has
two.
In the interests of getting to the point quickly, let me present the four
rationalizing hypotheses, (a) through (d), in graphic form. Kahneman’s book says
that if Prospect Theory had a flag, the graphic given just below would be drawn on
that flag (282). The same can be said for marginalism, the theory of Friedman and
Savage, and my own hypothesis. Here are the four flags.
.
.
.
Since my own theory is the only one that will be unfamiliar, let me try to make it
seem plausible with a reminder or two of everyday experience. These reminders
resemble the ones that are used in every introductory economics textbook to
support the law of diminishing marginal utility. I am under no illusion that these
reminders of everyday experience constitute empirical confirmation of my
hypothesis, of course. On the contrary, I offer them only in hopes of showing that the
hypothesis is plausible enough on the surface to deserve a rigorous experimental
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test. (Appended to these notes, for anyone who wants more, are a chapter from my
book and two quick summaries of the book, one by Tyler Cowen and the other by
the author of the Rortybomb blog.)
Much or most consumption of buyable goods is consumption of what I call
reliever-pleasers. These are goods which can be consumed in less-than-sufficient,
sufficient, or above-sufficient amounts. When not enough is consumed, the
deficiency brings troubles or miseries of various kinds, and as the deficits are made
up, these troubles or miseries are more and more relieved, until there is no deficit at
all. Then, as consumption continues to rise above the just-sufficient level, further
consumption produces more and more positive satisfaction.
Examples of reliever-pleasers discussed in my book are transportation, leisure,
living space, and opportunities to participate in community life. Consider
transportation. If you don’t have a ride to and from work, and work is a long way
from home, troubles ensue. For instance, you may get blisters from walking, leave
dishes unwashed in the sink, and get scolded for mistakes you make on the job
because you’re so tired. As you get more and more bus-fare to shorten your walk,
those same troubles diminish till they vanish. On the other side of complete relief,
there is luxurious transportation. If you have a ride all the way to work in a fancy
car, you are likely to take positive pleasure, and the fancier the car, probably the
more pleasure.
For experimental purposes, it may be easier to turn away from reliever-pleasers
to the simpler cases of goods with the inherent power only to do one or the other—
to relieve or please. Examples of pure pleasers would be salve for bee-stings and
water to relieve thirst. Examples of pure pleasers are harder to find, because almost
anything can be used to relieve some misery, but in their usual roles, at least,
desserts and roller-coaster rides are pure pleasers. That said, we must recall that
universally-valued goods are typically hybrid, reliever-pleasers, which relieve or
please depending on our level of consumption of them.
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My core thesis, and my main challenge to conventional marginalism, is that
relievers (and reliever-pleasers at low, relieving levels of consumption) are goods that
have increasing marginal value. Imagine for instance that you’ve been stung by a bee
on your hand, and that I offer to sell you a single dab of salve that will eliminate the
pain of that sting. You’ll pay x dollars for the dab of salve—or exchange y hours of
effort for it. But now suppose that just before you get stung on the hand, you sustain
seven stings elsewhere on your body. Everyone will agree that (leaving aside special
considerations like shock) the extra stings lower x, the amount you’ll pay for the dab
for the sting on your hand. After all, in the case where you have those other seven
stings, relieving this one sting is like quieting a single shout in a riot. Relieving that
sting on your hand when there are seven others will make less perceptible
difference than doing so would have made had that sting on your hand been the
only one you were suffering.
Next, suppose you have sustained all eight stings, and I simply give you seven
dabs of salve for the stings on your body; and then I try to sell you the dab for the
still-uncured sting on your hand. Won’t the gift of the seven dabs raise (not lower)
what you’ll pay for the dab for your hand? After all, because of the gift, relieving this
last sting will be like quieting a shout in an otherwise quiet street. If you agree the
gift of salve raises what you’ll pay for the eighth dab of salve, you are part way to
agreeing that the marginal value of successive dabs of salve is increasing, not
diminishing.
The behavioral corollaries of this also seem to be confirmed by common
observation. For instance, most people seem to agree that if they had eight stings,
they would prefer a 50/50 chance of receiving 8 dabs or zero dabs to receiving 4
dabs for sure. After all, 4 uncured stings hurt almost as much as 8, while having no
uncured stings is much, much better than having 4. Likewise, when it comes to
consumption smoothing, imagine you wake up each day with two stings that will
hurt until night if not treated with salve, and you also get one dab of salve each
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morning. Would you save the salve and consume it in a 2-0-2-0 pattern or would
you consume it in a 1-1-1-1 pattern? From my observation, most people say the first
pattern of consumption would yield great value (in this case, pain relief) in the long
run. This is subject to experimental confirmation of course.
These putative facts contrast with what we know about pleaser goods like
portions of dessert after dinner (and reliever-pleasers at high levels of
consumption). A gift of one portion of dessert on a given night will reduce not raise
what you will probably pay for a (another) portion of dessert that night. In addition,
you would probably prefer a single portion for sure to a 50/50 chance of two or
none. In addition, if you receive one portion a day, you will probably consume them
in a 1-1-1-1 pattern, not a 2-0-2-0 pattern over time.
Weakness of empirical support for (a), marginalism
Observation (rather than formal experimentation) offers partial support but also
partial disconfirmation to traditional marginalism. People buy insurance, as
traditional marginalism would lead us to expect, but people also gamble at unfair
odds. Traditional marginalism accommodated such recalcitrant observations by
postulating that people are being irrational when they gamble, a defensive strategy
tellingly criticized tellingly by Friedman and Savage for ad hoc-ism. “It is a testimony
to the strength of the belief in diminishing marginal utility that it has taken so long
for the possibility of interpreting gambling and similar phenomena as a
contradiction of universal diminishing marginal utility, rather than of utility
maximization, to be recognized.” (Stigler and Boulding anthology, 62)
Besides dismissing counterexamples as evidence of irrationality, defenders of
traditional marginalism ignored an enormous volume of counterexamples entirely.
Instead they generalized from familiar cases of risk aversion and consumption
smoothing that involved reliever-pleasers at pleasing levels of consumption. In
other words, they didn’t even ask whether people tended to be risk averse, and to
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smooth consumption, when dealing with reliever-pleasers at relieving levels of
consumption. The reason they didn’t even ask is that they didn’t recognize a
distinction between relieving and pleasing in the first place. These two very
different things had been lumped together by Bentham and Mill in the idea of
“increasing utility.”
Weakness of empirical support for (b), the hypothesis of Friedman and Savage
Friedman and Savage’s failure to win broad support for their hypothesis may
stem partly from the fact that they themselves offered it only as the best explanation
of decisions involving risk; whereas their theory’s main rival at the time,
marginalism, purported also to rationalize work effort at various income levels and
intertemporal allocation of expenditures. In short, they weren’t as ambitious for
their theory as the marginalists had been for theirs. In addition, due to a contextual
shift towards positivistic and behavioral demonstrations in the postwar period,
Friedman and Savage didn’t avail themselves of introspective evidence for
increasing marginal utility, despite the fact that the rival theory had originally been
accepted on precisely that basis. Third, because their hypothesis didn’t tie inflection
points to income levels, there was nothing of that kind for evidence to prove or
disprove. It is difficult to provide empirical support for claims that are inherently
vague.
Weakness of empirical support for (c), Prospect Theory
Kahneman and Tversky contend that the bearer of value for individuals is not
absolute levels of consumption but positive or negative changes from a reference
point that is normally (though not necessarily) identical to the status quo. They
further contend that decision-makers are risk-averse over gains that will take them
above the reference point and risk-loving over losses that will take them below the
reference point. As is well-known, Kahneman and Tversky offer copious
experimental evidence to support these claims.
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Nevertheless, I suspect (and would like to show) that experiments which more
closely reflected real-world economic choices than Kahneman and Tversky’s
experiments do would confirm my theory rather than theirs. Let me try to make this
plausible with an example.
Kahneman describes the following thought experiment in his new book. (280) We
are to imagine that we’ve just been given $1000. Then we are asked to choose
between (i) getting $500 more for sure and (ii) being given a .5 chance of getting
another $1000 and a .5 chance of getting nothing further. The actuarial values of (i)
and (ii) are the same, but Kahneman says that if we are like most people, we prefer
(i). Most people are risk averse in this choice situation.
Then he describes a second thought experiment. This time we are supposed to
imagine that we have just been given $2000. Then we are asked to choose between
(iii) losing $500 for sure and (iv) being given a .5 chance of losing $1000 plus a .5
chance of losing nothing. Again, actuarial equivalency. But here Kahneman reports
that if we are like most people, we will choose (iv). Most people are risk loving in
this choice situation.
But of course, Kahneman points out, the two thought experiments differ only in
that in one the risk being contemplated is a risk of gain, while in the other, the risk
being contemplated is a risk of loss. The absolute sums involved are the same:
everyone is choosing between ending up with $1500 for sure or the equal
possibilities of $1000 or $2000. So, Kahneman concludes, the bearers of value and
the determinants of risk aversion or risk loving for the experimental subjects must
be gains and losses, not absolute levels of wealth.
Yet I suspect that the “reference-point relativity” that Kahneman and Tversky
found to determine whether risk or certainty is preferred in these two thought
experiments is artificial. That is, I suspect the finding of the importance of reference8
point relativity stems from the fact that the choices were presented to the subjects
in a manner that did not invite them to imagine what the various outcomes would
mean to them in real life. The numbers were presented without context, in other
words. In a real world situation, for a real individual, the goods that are purchased
with $1000 or any other non-trivial sum have a notable inherent capacity to bring
relief or positive pleasure, quite apart from whether they are being gained or lost;
and this inherent capacity will play a big role, perhaps the biggest role, in the
individual’s attraction to or aversion to risk.
For example, suppose what is being bought is salve. Also suppose the price of
dabs of salve is $250 each. Finally, suppose that you have eight uncured bee-stings.
Sticking with the structure of Kahneman’s “gain” thought experiment, where
subjects were risk-averse, suppose you start by getting $1000, and that this enables
you to relieve 4 of the stings. Next you are offered a choice. You can opt to receive
another $500 for sure—which relieves 2 more and leaves 2 uncured; or you can opt
to get a 50% chance at another $1000, which could bring you to complete relief of
all eight stings.
Now that we know the money is going towards relievers, I bet that not only I but
most people would be risk-loving, not risk-averse. I would take the bet because
winning the bet and getting dabs 7 and 8 is so valuable, while losing the bet and
ending up with four uncured stings instead of two uncured stings isn’t a big loss
relatively speaking. This is testable, but I have a high degree of confidence that most
people would reason the same way. In short, I think people will be risk-loving, not
risk-averse over gains in this kind of case, so that Prospect Theory is incorrect.
In saying this I don’t mean to deny that the inherent capacity of goods in
particular contexts to please or relieve distress has to be set alongside the fact that if
I gain any goods or the money to buy them I may be pleased by that gaining itself,
while if I lose any goods I may be disappointed by that losing. In other words, I don’t
deny that both the inherent hedonic impact of goods and the impact of gains and
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losses are factors in decision making. Rather what I am saying is that the pleasure of
the gaining and the pain of the losing will automatically appear to dominate in
people’s decision making whenever we strip out or subtract, by our presentation of
choices, the inherent capacity of the funds or the goods to please or relieve. And this
is what seems to have happened in Kahneman’s example, due to its abstractness.
The same problem would afflict experiments in which the items gained and lost are
inherently trivial to the subjects, such as pens or coffee cups; only the gaining or
losing would then remain to affect choice.
It follows that if experiments designed to reveal people’s attitudes towards risk
(or work, or consumption-smoothing) are going to mirror real-world economic
decision-making, the goods in question, or the quantities of the goods in question,
need to be inherently and notably relieving or positively pleasing. Moreover if the
experiments are going to be thought experiments, the alternatives need to be
presented vividly rather than abstractly, so that subjects imagine whether the goods
in question would be functioning for them as relievers or pleasers.
That condition on experiments having been met, it would be extremely
illuminating to learn whether subjects were generally risk-averse over the prospect
of gains in reliever goods perceived as such. Further it would illuminating to learn
whether subjects were risk-averse over the prospect of losses in pleaser goods
perceived as such. If those two things turned out to be the case, that would tend to
support my hypothesis. On the other hand, subjects’ being risk-loving over losses in
positive pleasers or their being risk-averse over gains in relievers would tend to
support Prospect Theory. Subjects’ being risk-averse over gains in pleasers or riskloving over losses in relievers would not be illuminating, however, since both
Prospect Theory and my hypothesis predict that. Finally, one can imagine result that
would call for a so-far uninvented hybrid of the two theories, such as subject’s being
risk-loving over gains in powerful relievers but risk-averse over gains in mild
relievers.
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Accompanying these notes please find an undergraduate paper from a behavioral
economics class at Williams College taught by Robert Gazzale, in which the authors,
Atkins and Romero, record and discuss an experiment aimed at confirming my
hypothesis.
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