School of Economics and Centre for
Competition Policy
University of East Anglia
Norwich NR4 7TJ, United Kingdom
Consumers' surplus for consumers who lack coherent
preferences
Robert Sugden
Paper prepared for conference on Behavioural Industrial Organisation
and Consumer Protection, UCL, 17–18 October 2014
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This paper is work in progress, describing a problem rather than a solution.
It’s a mix of economic theory and history of economic thought.
Theory: it’s part of my attempt to reconcile behavioural and normative
economics.
The general problem is that conventional welfare economics assumes that
individuals have coherent preferences (i.e. stable, context-independent,
‘consistent’), and uses preference-satisfaction as the criterion; but there is
now lots of evidence that individuals don’t act on coherent preferences.
In this paper I focus on consumers’ surplus: can we reconcile this concept
with the findings of behavioural economics?
Consumers’ surplus is a central concept in incremental welfare economics.
In IO, it is used in evaluations of changes in industry concentration, anti-trust
policy, etc. It is standardly defined in terms of individuals’ compensating
variations, i.e. in terms of (assumed) coherent preferences.
If in fact, coherent preferences don’t exist, what should we do?
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A possible answer: in practice, consumers’ surplus is measured by areas
under demand curves, not by discovering individuals’ preference orderings.
In practical applications, demand curves report aggregations over many
consumers, many decision contexts, and extended periods of time.
E.g. an analysis of the alcoholic drinks market, using price of beer and total
consumption per week.
Standard neoclassical theory tells us that the area under the aggregated
demand curve is the sum of the compensating variations for all the
individuals.
But.. the aggregate data don’t tell us whether individual drinkers act on
dynamically consistent preferences on a micro scale (e.g. if they buy a first
drink in evening with intention of buying no more, do they stick to the
plan?).
Even if individuals’ preferences were inconsistent, demand curve for beer
might be quite stable; so standard measurement tools might not affected.
But what is the normative status of the measure?
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This is where the history comes in.
In the light of behavioural economics, it’s interesting to look at
microeconomics before the ‘marginal revolution’. What kind of normative
analysis were economists able to do without assuming utility-maximising
consumers (only rational arbitrage/ profit-seeking behaviour by merchants)?
Particularly interesting: Jules Dupuit, ‘On the measurement of the utility of
public works’ (1844). This is mathematically sophisticated for its time; it is
the founding text of CBA. But Dupuit explicitly denies that he is assuming
rational consumers.
Does this give us any clues about how to use consumers’ surplus without
assuming coherent preferences?
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Dupuit’s analysis
Dupuit’s topic: ‘the conditions which [public] works must fulfil in order to be
really useful’.
‘Public works’ = roads, railways, canals, bridges, water supply systems…
His analysis is addressed to ‘legislators’, i.e. public officials who regulate the
provision and pricing of public works.
In many respects, Dupuit is far ahead of his time. As far as I know, he gives:
-- the first definition of consumer’s surplus;
-- the first analysis of price discrimination;
-- the first recognition of the distinction between pecuniary and
technological externalities;
-- the first recognition of the distinction between transfer payments and real
resource costs.
But: he does not assume that consumers act on consistent preferences – and
is explicit about this…
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Dupuit on (what is now called) the demand function:
[The demand function] ‘is not known for any commodity, and it can even be
said that it will never be known since it depends on the volatile will of
human beings; it is today no longer what it was yesterday. It is thus of no
avail to try to determine this relationship exactly by experience or groping
experiment, but there do exist certain general laws to which the relationship,
in its very volatility, remains constantly subject.’
Significantly, these general laws are observed statistical regularities about
demand curves that sum over many consumers – they are not grounded on
principles of individual choice:
-- a demand curves slopes downwards;
-- the slope becomes more negative as price increases (this is explained as
the result of the ‘pyramid’ structure of social classes).
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Dupuit’s account of consumer choice seems more behavioural than
neoclassical ….
‘The variable, yea mobile, nature of the value of utility is indeed well known
to business men and has long been exploited by them’ [i.e. by price
discrimination].
The same commodity in various guises is often sold in different shops at
quite different prices to the rich, the moderately well-off, and the poor. The
fine, the very fine, the superfine, and the extra fine, although drawn from
the same barrel and although alike in all real respects other than the
superlative on the label, sell at widely different prices.
But price discrimination serves a useful purpose: although the practices of
price discrimination used in business work by setting ‘traps for the buyer’s
vanity and his credulity’, they are often ‘more equitable and fairer than one
might expect at first sight’, and might be good examples to be followed in
setting tariffs for public works.
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What does Dupuit mean by ‘utility’?
‘Hence the saying which we shall often repeat because it is often forgotten:
the only real utility is that which people are willing to pay for.’
[This concept of utility] ‘is not, in the last analysis, a rigorous measure of the
quality which things have of being able to satisfy men’s needs’… But political
economy, being concerned only with wealth, can take account of the
intensity of a wish only through its monetary expression. Political economy
only bakes bread for those who can buy it...’
Implication: Dupuit thinks that utility, defined as ‘what people are wiling to
pay for’, links with wealth (the subject matter of political economy). Why?
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I suggest the link is the thought: the production and sale of a good is
wealth-creating if and only if consumers’ willingness to pay for it exceeds
the cost of supply. Dupuit’s criterion (for the purposes of political
economy) is wealth-creation in this sense.
Hence Dupuit’s interest in price discrimination. If the cost of supply can be
recovered from consumers by discriminatory prices, we can be sure that
wealth is being created.
Dupuit says that (in later chapters of a never-written book) he will show how
tariffs for public works can be fixed ‘according to rational principles, in order
to produce the greatest possible utility and at the same time a revenue
sufficient to cover the cost of upkeep and interest on capital’.
‘Rational principles’ seems to mean setting a discriminatory tariff such that:
-- total revenue = total cost;
-- no one who is willing to pay marginal cost is deterred from consuming.
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Dupuit uses the area under the demand curve as a measure of the total
‘utility’ of a good to consumers. Implicitly, he also treats it as a measure of
the potential yield of perfectly discriminating prices.
And he claims to be treating the demand curve merely as a statistical
aggregation of observations of consumer behaviour.
Is this approach theoretically valid?
As a first attempt to answer this question, I ask whether (in the absence of
income effects) the area under the demand curve is a measure of total
willingness to pay (= potential yield of perfectly discriminating prices), even if
consumers lack coherent preferences.
The answer is no, but for interesting reasons…
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The corner-shop model
Consider a consumer at three ‘periods’ in a given day (1 = morning, 2 =
afternoon, 3 = evening). At each period, he buys 0 or 1 unit of food, and
consumes 0 or 1 unit. (Consumption is possible only from current or past
purchases.)
‘Experienced utility’ in each period is measured relative to benchmark of
eating and not paying.
Paying always has utility of –p, where p = price (note: this implies zero
income effect, and allows us to use money as a utility unit).
Utility of not eating depends on how many periods have elapsed since
previous eating (or start of day). If no such periods, utility = –1; if one such
period, utility = –2; if two such periods, utility = –3.
Consider demand function for consumption per day, in terms of a nondiscriminatory price that is constant over the day. (Remember that practical
consumers’ surplus measurements aggregate over decision episodes.)
[I assume that ties are broken in favour of eating]
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The rational consumer
(forms optimal plan for day,
maximising sum of experienced
utility)
price consumption exp utility
>4
4
3
2
1
0
(0, 0, 0)
(0, 1, 0)
(0, 1, 0)
(0, 1, 0)
(1, 1, 1)
(1, 1, 1)
–6
–6
–5
–4
–3
0
price
4
daily demand curve for
non-discriminatory
prices
3
2
1
1
2
3
experienced utility gain = U[p = 0] – U[p > 4] = 6
area under demand curve = 6
maximum yield of discriminatory pricing = 6
(e.g. charge price = 4 for first unit bought in day, price = 1 for each
subsequent unit; note that this works only because consumer makes
integrated plan for day).
quantity
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So, for the rational consumer:
area under demand curve = experienced utility gain = maximum yield of
discriminatory prices
(as Dupuit claimed).
But what about a non-rational consumer?
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The myopic consumer
(maximises experienced utility in
current period)
price consumption exp utility
>3
3
2
1
0
(0, 0, 0)
(0, 0, 1)
(0, 1, 0)
(1, 1, 1)
(1, 1, 1)
–6
–6
–4
–3
0
price
daily demand curve for
non-discriminatory
prices
3
2
1
experienced utility gain = U[p = 0] – U[p > 3] = 6
area under demand curve = 5
maximum yield of discriminatory pricing = 3
(consumer is willing to pay up to
either 0 in period 1 + 0 in period 2 + 3 in period 3;
or
0 in period 1 + 2 in period 2 + 1 in period 3;
or
1 in period 1 + 0 in period 2 + 2 in period 3;
or
1 in period 1 + 1 in period 2 + 1 in period 3).
1
2
3
quantity
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If the only real utility is that which people are willing to pay for, I think the
correct measure of utility is the maximum yield of discriminatory pricing.
Because the myopic consumer is never willing to pay for experiences that will
occur in the future, there is no tariff that will induce him to pay more than 3
to buy food over the day. So his ‘real utility’ from food cannot be more than 3.
Implications for further work
I need to create a definition of ‘perfect’ price discrimination which doesn’t
depend on assumptions about coherent preferences, and which allows the
yield of perfect price discrimination to be measured from observable data.
What I know so far: in general, this measurement is not the area under the
demand curve.
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Thank you for listening.
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