One of the most interesting concepts in behavioural economics is utility functions. They are interesting because they allow us to predict future actions based on gross and marginal utility of a good in conjunction with principles such as Engels curves that determine the propensity to spend based on income bracket.
Utility functions are defined on the set of possible alternative goods that could be purchased- preferably equivalent and within the customer’s price range. They reflect the consumer’s behaviour of maximisation of perceived utility of a good rather than minimising its opportunity cost.
They are normalised to span the range [0,1], which is allowed since linear-affine transformations are allowed as shown by von-Neumann (though this is interesting, I have been waiting for an excuse to use the word affine since linear algebra in first year).
The basis for revealed preference is that a customer maximises the utility over minimising the price of a purchase, and that the functions follow an axiom of revealed preference. The axioms for RP are; weak, strong and general. The exact definitions can be found here <1>.
The strong axioms regard indirect RP, whereby the set of considered goods expands or changes over a larger set and if in the first considered set A>B, and in the second B>C, then the strong axiom implies A>C in any choice set containing A and C.
The main outcome of experiments meant to determine how rational the utility functions of the population as an aggregate in the literature is that under a dictator-game style setup, people’s utility functions deviate for the majority of the time from being ‘rational actors’ who maximise their own welfare. In the study by Andreoni and Miller (2002) <2>, there were three groups of people that became apparent- the selfish, the perfect substitutes, and the Leontief.
The results from a group of undergraduate economics students that were then used to generate data on randomly generated synthetic subjects found that most of the population’s utility functions violated GARP in some way. Moreover, in specific situations they also violated SARP for a large majority of the time. However, their utility function is at least rationalisable.
These anonymous tests uncover how far charity stretches to the individual. But they also do not allow for additional features such as reputation.
If these studies had randomised pairs with pseudo-anonymised data, some players might gain a reputation for their style and so be discriminated against.
Within realistic models aiming to measure the habits of individuals with regard to giving and good will, the act will either be in a state of imperfect information where the direct benefit is unknown and the act of giving involved is down to the marketing skills of those involved, or in a system such as a discount model with known beneficiaries and known benefit.
In other studies, in particular <3>, there was a non-trivial expression of a ‘warm-glow’ effect, where the actor gave away more money than made sense in classical models.
This is an effect that deserves more attention than it gets, whereby individuals gain a warm glow feeling from making moral choices. EDIT: as <6> states, there has been an 800% increase in the number of papers on this topic released in the past decade- it gets exactly the attention I believe it deserves.
However, in all of the classic set-ups under laboratory conditions, the experiments used require your opponent to be a directly visible person that benefits from the social contribution in a directly measurable way.
Even if the randomisation of payouts does not depend on the partner, this might imply a games-manship that is not generally exhibited in consumer choice. This is reinforced by the same study where there was an observed effect that might represent spite expressed towards opponents, where the less-favourable strategy for both is followed.
I am interested by special conditions under which the Strong Axiom of Revealed Preference (SARP) is broken. However, I think that by placing people in an adversarial situation (even by implication), noise in the form of interpersonal animosity is introduced.
Anecdotally, when I took part in a similar study at my university my strategy was not very realistic. I began a prisoner’s dilemma set of games with the mindset of perfect substitution but quickly progressed to selfish behaviour due to the strategy the others in the group were taking.
Within a market-choice type scenario, I would argue that the products are not humanised in the same way as has been used in experiments. Not that I am claiming that previous experiments are wrong in their scope or reasoning, within a closed market with a large number of buyers and sellers these experiments are reasonable and realistic. However I do not think they cover the scenario of an open market with imperfect information with interaction strictly between utility maximising and price maximising economic agents. I think that in particular it would be interesting to see what effect external qualities have on revealed preference.
One such example (of indirectly revealed preference) is free range and battery farmed eggs. If given the choice between two packets of eggs – A, free range at £1.50, and B, battery farmed at £1, which pack shall they choose?
The decision process is reliant primarily on their income, hence the need to control for Engels curves to measure the ‘affordability of morality’.
A third packet is entered into the race- C, also free range, this time at £1.20. What is the order of preference now, and has it changed considering that the customer has now seen an alternative moral choice for a markedly lower price-gap?
One method of revealing such an effect within a study is by restricting choice to choosing two options from a limited basket (in this case A, B and C) that only contains one of each.
I think that one part of the population, regardless of income level, will choose the cheapest monetarily. Another segment will choose to maximise their morality, and buy only free range (with an upper ceiling on the price that we need not worry about since heuristically I presuppose that the market will have set a price that maximises profit which shall fall some way under this ceiling).
I think that a third group would seek to average the moral benefit, by first choosing A over B, then by buying either A or C, and then B, representing either fixed or variable factor perfect-substitutes in previous studies.
This differs from price minimisation due to the order in which the preferences are revealed. Moreover, it differs from perfect substitution because it implies that the utility function of that segment seeks to minimise price while cancelling a perceived moral debt.
It is interesting to ask what size of the population see a moral cause as a bonus, and which as a debt to be paid off once they aware aware of its presence.
This implies that if a portion of the population views it as either a bonus or debt, a discounted utility model with directly-revealed-preference as a foundation as in <5> is applicable and worth studying.
One issue is that the moral aspect of a good with private and public benefit cannot fit within a traditional discount model. Currently the only appreciable way of comparing charity is by an incomplete picture- fitting the questions presented in <5> to purchases of private goods with public good attached would be a nightmare. The study mentioned offers one of the few long term versions of charitable action and requires no opportunity cost to the user.
It is not possible to compare long-term truly altruistic investments in other’s welfare to short term unclear benefits given such as in the scenario above.
The egg experiment would be interesting to see if the moral cause is interpreted either as a benefit or a debt. If a benefit, then a portion of the population will seek to maximise morality at cost to themselves. If a debt, then the moral payout will be an outlier with all subsequent choices made to minimise the spend.
A long term gift-aid question would then also be able to see what portion of the population act as perfect substitutes, Leontief, or selfish within a truly anonymous setup with known benefit to your actions, assuming that this type of behaviour fits within a constant-elasticity of substitution (CES) function as defined in <4> and has been found in previous examinations of discount models and RP.
I now propose a situation that would test if the moral aspect of a private good could fit within a discounted utility model.*
(Though this differs from previous DU studies because it tracks preferences in real time instead of previous studies that forecast the discounted utility, whereby we might see a modified time-discount function.)
A shopper is asked to buy a bundle of eggs of specified size per week. Taking from both free range and battery farmed eggs, a new pack is made from both. The fraction of free ranged, F and battery, G is such that F+G=1. By being informed of how many (but not which ones) are free range and battery, the shopper chooses from the selection over the course of several months. The prices of the bundles are worked out from the unit price of FR and BF eggs.
A time series analysis would prove whether being kept aware of the moral aspect changes the long term decisions of the customer. A control group of those unaware could be generated either from access to the participant’s loyalty card information to glean data from, or from a random selection of subjects in concurrence with the proposed study.
Another important control to take into account is public opinion regarding the moral question being asked, though the noise caused by this can be put down to imperfect knowledge.
This type of study would uncover reasonable results for what portion of the population is truly altruistic in the purest sense, which are the most selfish and which seek to average their morality-scores.
Additionally, it is interesting to ask in which domains of price, quantity and necessity the discounted utility model reflects either a hyperbolic model as in the previously mentioned study, a parabolic one such as in <6>, or a differently shaped curve as I would expect. Moreover, for products that allow similar-to-ethical choices, what is the effect of their branding, and what is the optimal period for such branding moves to gain or retain market share? If a moral choice is presented to the buyer in both supermarket and raw-material goods supplier situations, the way in which the consumer reacts would indicate intelligent marketing strategies for anyone seeking to either proffer a unique moral aspect of a product or compete with others on the market.
For example, if it is shown that a majority of purchasers of eggs chose to be perfect substitutes for the chickens then adding a new aspect (similarly ‘this is the cow that made your milk’ on milk-cartons) would give the company a competitive edge.
If however they were shown to be mixed-substitute, they could offer a mix of battery and free range eggs to offer the ideal returns for the consumer in terms of morality and price.
*Another example of how to see which rational the population operates with in such a model is to examine data on 5p, 10p, 50p, etc carrier bags due to the implicit direct link between price and durability and the implied knock-on environmental effects.
<1>https://econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/VarianRevealed.pdf
<2>Andreoni, James, and John Miller. “Giving According to GARP: An Experimental Test of the Consistency of Preferences for Altruism.” Econometrica, vol. 70, no. 2, 2002, pp. 737–753. JSTOR, JSTOR, http://www.jstor.org/stable/2692289.
<3>Palfrey, Thomas R., and Jeffrey E. Prisbrey. “Anomalous Behavior in Public Goods Experiments: How Much and Why?” The American Economic Review, vol. 87, no. 5, 1997, pp. 829–846. JSTOR, JSTOR, http://www.jstor.org/stable/2951327.
<4>http://econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/elasticity%20of%20substitutionrevised.tex.pdf
<5>Lazaro, Angelina & Barberán, Ramón & Rubio, Encarnación. (2002). The discounted utility model and social preferences. Journal of Economic Psychology – J ECON PSYCH. 23. 317-337. 10.1016/S0167-4870(02)00079-X.
<6>https://mpra.ub.uni-muenchen.de/16416/1/MPRA_paper_16416.pdf
Alastair's Assorted Assumptions 