Introduction

Individual decision-making about consumption has been the subject of many theories and approaches. In this paper, we are interested to propose some steps to include consumer decision making and behaviour in formal models, trying to do this in a more realistic way than the neoclassical theory.

Agent-based models will become the dominant modelling technique in economics. They have several substantial and formal advantages over neoclassical diagrams "starting with curves", e.g. over demand curve and supply curve.

Instead of the narrow limits of comparative statics between equilibrium points, agent-based models allow to build and manage dynamic environments with both low and high levels of complexity.

In fact, agent-based models allow for high heterogeneity in the micro-agents (consumers, firms, banks....). No representative consumer or representative firm has to carry out the burden of representing different agents of the same class. Consumers aren't requested to share the same preferences or, as in some neoclassical model, the same income. This is a crucial issue for the realism of the model.

Computer simulation as they are, agent-based models are constituted by several building blocks. In particular, the modeller has to specify the inner structure of agents, their decision rules, and the relationships among agents.

Firms and consumers: these are the typical agents in basic economic models. Following the empirical evidence that real people are not as hyper-rational as the neoclassical theory assumes, evolutionary agent-based models consider consumers to be bounded rational, i.e. following easy decision-making rules which use only pieces of available information without requiring too much mathematical calculus.

By adopting this point of view, these models comply with the overwhelming empirical evidence of real agents' behaviours. When you buy a beer, you don't think too much. If you can't drink beer, you simply avoid doing it.

This paper proposes some easy rules for modelling the most common decision of consumers: to buy. This can be particularly useful if you intend to build your own model, but also to better understand this methodology.

We shall do something more than a mere description: we are giving in your hands a model in which these rules have been implemented to let you make experiments, since you can download "Race to market" for free from the Economics Web Institute.

In short, we provide a sketched introduction to a new standpoint in demand theory.

In so doing, we are introducing you to a rich strand of research that exhibits already a good number of agent-based models of consumers [1].

1. To buy or not to buy: this is the question

The basic choice of a consumer is, once he feels a need and he knows that a certain good could satisfy it, to decide whether to buy the good or not.

The easiest decision-making rule in this case is to fix a maximum acceptable price (often called "reserve price"). If the actual price of the good is higher than that, the consumer will not buy it because he can't afford it or he evaluate that it is not worth the expense.

If, instead, the actual price is lower than the reserve price, the consumer buys one unit of it. Why only one?

Let's imagine that you like books and, while searching in a bookshop, you find one that is particularly interesting. Fix your reserve price and give a look on the back cover to the actual price. Sometimes, it is too much. Hopefully, instead, you can afford it. How many copies will you buy in this case? One, of course!

You'll not buy an irrational quantity of the good simply because in this way you exhaust your budget constraint - as the mainstream model of consumer choice would dictate.

This holds in particular for non-grocery goods. As for grocery, see this model in which the consumer can choose different sizes (thus discrete weights and quantities).

That simple rule gives a direct answer to the question. The quantity bought is zero or one. Individual elasticity to price is zero except when the price jumps across the line of the maximum acceptable price.

Market elasticity to price - when we consider all consumers operating on the market - will depend on the distribution of the reserve prices of each one of them.

The overall quantity sold will depend on price since a few consumers change their quantity from zero to one (if the price falls) or from one to zero (if the price increases). Most consumers continue to do the same as before.

In this way, one replicates the standard result of a falling demand at higher price using much less than the many heavy hypotheses of neoclassical models.

The consumer is not requested to be perfectly rational nor to have indifference curve among infinite combinations of two goods.

As far as the aggregated demand curves arising from different distributions of reserve prices are concerned, we'd like now to present you some results and a suggestive interpretation.

In particular we shall link the shape of the demand curve to the distribution of reserve price in the consumers' population. Then we shall refer reserve prices to income, so that we shall derive the shape of the demand curve from income distribution.

A linear demand curve arises from a uniform distribution of reserve prices between two boundaries (min & max), be it a stochastic or deterministic uniform distribution. A diagram showing this case with the demanded quantity on the Y axis and the price on the X axis is the following:

Routinely estimated in empirical research, linear demand curves can thus be generated in this setting very easily. Please note that, by contrast, neoclassical models with standard well-behaved (e.g. Cobb-Douglas) individual preferences aren't able generate a linear demand curve so directly, as you can directly experiment with this software.

Furthermore, in our setting, a concave demand curve arises from a distribution of reserve price with a wide number of consumers having a similar middle reserve price, only few "rich" and few "poor".

By contrast, a convex demand curve arises from a polarised distribution of reserve prices with most consumers having low reserve prices, few are "rich", and only slightly more are in the middle.

Three kinds of society give rise to three shapes of consumers' demand.

Indeed, it is particularly interesting to re-interpret the reserve price as an income indicator, arguing a positive correlation between income and reserve price. Higher reserve prices would thus be indicative of rich people, whereas the poor would express lower reserve prices. This interpretation is plausible and can be demonstrated in two cases.

If existed only one good to buy, the entire income would go there and the higher income would immediately result in higher reserve price.

If people equally shared their budget for different class of goods (say; 20% to food, 25% to home expenditure,...) then higher income would mean higher reserve price on each class.

At the same time, it is a well known stylised fact that, although the rich save more than the poor and the budget shares for consumption goods aren't the same between rich and poor, the rich has indeed an actual expenditure higher than the poor for every category of fulfilled needs (see here for data).

By doing this passage from reserve prices to income, we argue that income distribution is the determinant of demand curve shape.

It's interesting to note that neoclassical demand curves generated by Cobb-Douglas indifference curves of many consumers are convex, corresponding - in our context - to a polarised society with many poor, a weak middle class, and a handful of rich.

By contrast, we expect that where a wide dominant middle class exists, the demand curve will be concave.

Let's now see how the total consumption is distributed in the population. In the neoclassical model with well-behaved properties, all consumers buy at least some quantity of the good. In our approach, given any price chosen by the seller, the consumers that can afford it will buy one unit each. The others will be excluded from consuming a needed good and remain unsatisfied.

The total quantity bought will be equal to the number of consumers satisfied whereas the value of consumption will be the quantity times the price.

In the neoclassical model, an increase in price of a normal good reduces the quantity bought by each normal consumer, whereas here it reduces the number of consumers, each buying exactly the same quantity as before: one unit.

An increase of income for people already buying the good will have no impact on the quantity sold, as instead it would be the case if this increase is concentrated on poorer people: people just below the income that generates a reserve price equal to the actual price, to the extend that the increase in income turns out to be sufficient for overwhelming the threshold.

In another perspective, when considering many markets based on the same principles, the value of macroeconomic consumption will depend on income distribution as well as on the total income.

The strength of the Keynesian multiplier will depend on who receives the increase of income.

How many important consequences arise from such an easy first step!

2. Which one to buy: this is the second question

Product differentiation within a category of goods widens the decisions that a consumer has to take. He has to choose which good to buy - among those he can afford and that could fulfil his needs.

This kind of situation happens in our model "Race to market", as described in the relative paper.

In this model, the good is vertically differentiated according two features: its performance and how easy it is to use [2].

A first rule of choice is to decide a minimum level for each feature to be reached by a good in order to be acceptable. The consumer evaluate the affordable goods for each feature and attribute them a relative "score", in its subjective judgement - based or not on objective characteristics. This subjective judgement could be influenced by advertising and be biased (for instance, because of the country of product origin). Then, he compares the score with minimal thresholds. An "insufficient" good - even in one respect only - is rejected.

If there is only one good which satisfies both the price and quality constraints, that will be chosen.

If there is none, the consumer will buy nothing.

What if there are more than one acceptable goods? We need a further selection rule.

In "Race to market" we chose a palette of three alternative kinds of consumers, applying three alternative rules for purchase decision. Basically, they differ because of the relative role of price and quality.

Rule 1: If - at this stage of the decision-making process - only price is important, the consumer buys the cheapest good that survives to minimal quality requirements.

Please note that each consumer is free to set quality requirements, so that this rule is just for choosing inside a selected group of goods. If the consumer sets its requirements quite high, this would produce a purchase of a high-quality good.

Rule 2: If - at this stage - only quality is important, the consumer buys the best good he can afford. Given the reserve price, he will buy the good whose "overall quality" is the highest and each feature has a "sufficient" score.

To apply this rule, one has to build a measure of "overall quality", as we shall see in a moment.

Rule 3: A third group of consumers tries to balance price and quality, then they will choose the best value - for - money product.

Once computed a measure of "overall quality", it can be simply divided by the price, so to order goods in terms of value-for-money.

Let's see a numerical example. Consider a consumer facing two affordable goods that passed all the tests of quality minimal requirements with the following price and overall quality:

If he uses the first rule, he will choose A because it is the cheapest. If the second one, he will choose B, because it has the best quality. If he relies on the third one (value-for-money), he will choose B again, because 30/12(=2.5) is more than 20/10(=2).

Now, it's time to build a measure of "overall quality". A fairly general approach is to use a linear combination of the scores in each feature, weighted according the relative importances for the consumer of the feature itself [3].

Overall quality = score-in-feature1 x importance-of-feature1 + score-in-feature2 x -of-feature2

For instance in the preceding example, the evaluation of the overall quality for good A as 20 could be the result of the following:

Overall quality = 10 x 2 + 6 x 0

In this case, the consumer isn't interested in feature2, to which he gives a weight of zero, whereas an evaluation of 10 in feature1 is weighted by 2.

Apart from these minor details, the three rules for judging "which one to buy" not only bear resemblance to real consumers' criteria but also may give rise to particularly interesting connections with income distribution.

Indeed, we could try to establish a correspondence between income classes and rules of behaviour - at least in probability terms.

The poor are more than proportionally consumer of the first type, looking for the cheapest good.

The rich tend to be of the second type, buying the best good they can afford.

The middle class tends to be of the third type, looking for value-for-money.

It seems plausible and empirically testable. In particular, there is already evidence suggesting that the poor tend to attribute much more weight to price than the rich do (e.g. this paper).

In this way, the simulated population of consumers will be characterised by the income distribution, the rule distribution, and their correlation.

This sets the stage for competing firms with their own products, strategies, and target consumers.

Consumers have differentiated rules and tastes, thus producers will be faced by a quality-dependent demand curve.

Again, since the single consumer is using a rule implying a dis-equation (more than..., less than...), small changes in price or quality will not change anything for most consumers but a critical range of consumers will, instead, pass from zero quantity to quantity one (or the reverse).

A category of goods can thus display a wide permanent price spectrum, with no automatic strength to level down all prices to the lowest.

You can test this statement by playing "Race to market" and reflect on many arising issues. For instance, which kind of society will appreciate quality the most? Where product and process innovation will be most rewarded? Try to find out your own answer.

For an independent empirical market analysis connecting income distribution and a vertical segmentation see this beer study for Vietnam.

3. How many units to buy: this is third question

Economic goods on sale aren't infinitely divisible. If you want a car, you buy one car, not 1.234 cars. They can't be irrational quantities. If your family wants some milk, you'll buy two or three cartons, not the square rood of three. If you go to the butcher to buy a piece of meat, he will weigh it and round any result to the nearest 10 grams: his balance will force him to do it - and his common sense, too.

Neoclassical assumption of infinitely divisible goods and services is rejected by economic life itself.

The choice about the quantity to buy is, then, a discrete choice. One, two, three, four...

Which rules has the consumer for choosing quantities? Many. But an easiest one that we propose, in line with previous developments, is the following: each consumer fixes a maximum acceptable price for each further unit of the good.

The neoclassical assumption of decreasing marginal utility would imply a falling reserve price for each unit. In our setting, the consumer chooses purchases with no explicit link to consumption utility, which might well depend on completely different factors emerging in the moment of consumption (e.g. sunny weather conditions making more enjoyable the good or, instead, a quarrel with the wife leading to the opposite influence).

We do not need to impose any particular relationship among the reserve price of the first unit and the reserve price of the others.

Indeed, if the second unit has a higher reserve price than the first, an actual price between the two will result in no units bought, not in a "second unit" purchased with a "first" unaffordable.

In a dynamic setting, the quantity would depend on the expected length of time that will elapse before next purchase occasion and the expected consumption in that period.

A special offer with a discount price would probably imply a larger number of purchased units if the product can be piled up in inventories at home.

To see how an entire basket of goods is purchased in a retail grocery supermarket, and which kind of rules can be applied by bounded-rational consumers, see our paper on "Size, price, and consumer rules".

4. How often to buy: this is the fourth question

In real life, purchase occasions depend on life micro-pattern. For many working people, Saturday is the day in which the largest shopping takes place, with minor occasions during the week, largely structured along house/work paths and timing.

Housewives are freer to schedule shopping activities, but they tend to follow routines, too.

These occasions usually concentrate in time and space the purchase of several goods in order to reduce transport time and costs through multipurpose purchase trips.

For an individual, the consumer buying behaviour pattern described by the number of (re)purchase acts of a category will depend on two main elements:

1. the typical average of the category (that in turn belongs to macro-categories as non-durables or durables, with all their nuances);
2. the type of consumer (heavy consumer, light consumer and all the intermediate positions).

Heavy consumers repeat very often their purchases. In so doing, they cumulate category-specific knowledge and skills.

Certain empirical researches show that heavy consumers are often early adopters of innovative goods in the category, since they are more conscious of the unsatisfactory features of the old good. Here there is much room for debate. What is your opinion?

How often to buy a specific good in a category will depend on the brand loyalty of the consumer. If he buys always the same brand, the frequency for the good will be equal to his frequency for category. If he alternates few brands (loyalty to a shortlist), his purchase of one will be a share of the total. If he chooses many brands following irregular patterns, the frequency for the good will be erratic.

A perfect brand loyalty can be due to many different reasons:
1. independent purchases ending always in the same way because of unchanged properties (quality, price) of the goods and of the consumer (income, decision-making rules, weight of quality features,…);
2. independent purchases ending always in the same way because of rising dominance of the chosen brand;
3. a positive value for continuity in itself;
4. a positive feedback loop of choice, satisfactory experience, re-purchase;
5. inertia and minimization of choice costs aimed to avoid the repetition of an extended search and evaluation process;
6. high switching costs;
7. a perceived high risk of dissatisfaction attached to a new choice;
8. monopolistic position of the brand for the specific need of the consumer.

Instead, loyalty to a shortlist of brands combines (i) a bundle of goods that satisfy the consumer with (ii) a preference for variety. When you go out to dinner and choose always something you like but not in a row exactly the same dish, you are in this situation.

Please note that much of the discussion of these issues in marketing science has been oriented to assess the impact of advertising and to check a possible un-elasticity to price of brand loyal consumers.

In "Race to market", the present version of the model is purposefully simplified: the good is a durable and a consumer having bought doesn't need to repeat his purchase. This makes the exhaustion of the potential market as the tail of the typical story.

If you like to see what happens with a more complete model, please participate to our experimental sessions, signalling your intention by e-mail.

5. Agent-based consumers and marketing science

This essay is a first attempt to provide a consumer decision model useful for marketing strategies and tactics.

Indeed, the tree-shaped choice pattern we devised and described in this paper has a good matching with the description of aggregate market variables in marketing science.

The overall result of the individual choice of "buying or not" gives market penetration, i.e. the percentage of potential consumers who become actual customers.

The overall distribution of results of the individual choice about "which brand to buy" turns out to be the market shares of the different brands.

The overall distribution of results of the individual choice about the number of units to buy distinguishes heavy users from light user, to the extent that a big purchase is followed by a personal intensive consumption concentrated in time. For instance, if the good is alcohol-based, this variable singles out the (possible) drunkers.

Keeping into account all the abovementioned dimensions of choice, one can better interpret the amount of sales over a certain span of time.

More in general, we think that marketing science has much to teach to economics. Agent-based evolutionary economics is ready to learn.

6. The golden rule

In this paper, we proposed a few rules of choice and behaviour to be used in agent-based models comprehending consumers. Other rules have been already employed and many more could be imagined.

In the open debate about which rules should be selected, one modeller's "golden rule" might be proposed.

It should be always possible to convert the formal rule - used in the simulation model - into a question for real consumers in a questionnaire.

Real-world market research over consumers makes large use of questionnaires, to be submitted to housewives and purchasers by phone, face-to-face interviewing, panel software, Internet, and so on.

Our rules should be convertible into simple questions that a normal consumer can answer.

This "golden rule" has two advantages:
1. it avoids too strange and difficult rules to be used in formal models;
2. it allows for empirical feedback to the model.

It is not irrelevant that this simple first criterion cannot be satisfied by neoclassical theory of indifference curves. You cannot build reasonable questions about "Are you a Cobb-Douglas type?"

Instead, from "Race to market" we could obtain questions - and this is already an important result.

In this moment, you can even personally answer to them from this dynamic page.

7. Conclusion

Neoclassical theory of consumer is being challenged with the new strand of evolutionary agent-based theory and models. This paper provides many hints about the rules that could be given to consumers in agent-based simulations.

It proposes four major problems the consumer faces. In order to solve each of them, one or more consumer decision rules are proposed, straightway leading to important consequences on macro level.

In particular, demand patterns are traced back to income distribution. Income and prices are as important here as in the neoclassical model, but easy rules allow bounded rational consumers to take decisions, by limiting the requirements of information and computation capability that make the neoclassical model so unrealistic.

A "golden rule" for the modeller is offered to the open debate about which rule to employ in agent-based models.

By micro-founding demand, the agent-based models can offer important suggestions to marketing strategies and to policies focused on consumer welfare.

NOTES

[1] See in particular the following:

A consumer memory-based model of new product diffusion within a social network by J. Kottonau, J. Burse, C. Pahl-Wostl

Agent-based Explorations into Consumer Choice Modeling by C. Stumpo

Agent-based modelling of customer behaviour in the telecoms and media markets by P. Twomey and R Cadman

An Agent-based model for the study of publicity/consumer dynamics" by J.J. Merelo, A. Prieto

An integrated approach to simulating behavioural processes: A case study of the lock-in of consumption patterns by M. Janssen, W. Jager (1999) in Journal of Artificial Societies and Social Simulation

Artificial Life simulations: Consumer behavior modeling for marketing strategy by B. G. Tedesco

Consumer Behaviour and Technological Complexity in the Evolution of Markets by M. Valente

Consumer Decision Making and Beyond by L. Schiffman, L. Kanuk

Demand Dynamics With Socially Evolving Preferences by R. Aversi, G. Dosi, G. Fagiolo, M. Meacci, C. Olivetti

Engel Curves Specification in an Artificial Model of Consumption Dynamics with Socially Evolving Preferences by G. Fagiolo

Integrated Multi-agent-based Supply Chain Management by D. Frey, T. Stockheim, P. Woelk, R. Zimmermann

Modelling consumer behaviour by W. Jager

Modelling Demand for Innovative Products by M. Valente

Multi-Agent Based Simulation of Consumer Behaviour: Towards a New Marketing Approach" by L. Ben Saida, A. Drogoulb and T. Bouron

Networks of agents with advertising by F. Alkemade

Simulation Methodology: an Example in Modelling Demand by M. Valente

Waves in Consumption with Interdependence among Consumers by R. Cowan, W. Cowan, G.M. P. Swann.

[2] See Note 1 for agent-based models that propose other ways to cope with product differentiation, in particular the works by Marco Valente.

[3] Needless to say, this arithmetic, however simple, isn't directly used by real consumers! But this formula allows the artificial consumer to reach a punctual decision corresponding to the informal way of judging quality. Indeed, it is feasible to ask real consumers to rate the importance of different features, e.g. on a Likert scale.