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by Valentino Piana (2012)



1. Introduction
2. Examples of cumulative bundles
3. What's a cumulative bundle?
4. Why is cumulative bundle important for consumer theory?
5. Consumer decision-taking rules based on cumulative bundle
6. Difference of "cumulative bundle" to other similar concepts
7. Why "cumulative bundle" is relevant to the evolutionary theory of consumer

8. Drills and questions for you

Appendix I - The paradox of cumulative bundle



1. Introduction

What's you have in your fridge, in your wardrobe or more in general in your house is a structured set of goods purchased over time. It reflects your personality, your purchasing environment, your income and tastes, your decision-making style.

For instance, if your house exhibits many exotic souvenirs of yours, you probably made many holiday trips in far away countries.

Simple as it is, the concept of "cumulative bundle" is new in the theory of consumption and it is fundamental for a number of important issues. This paper introduces the main ideas while leaving to this other essay a first use of the concept in a comparison of the cumulative bundles of a poor and a rich, backed by this formal model.

2. Examples of cumulative bundles

In a house, cumulative bundles are the books on the bookshelves, stoves in the cupboard, food in the kitchen, garments in wardrobe, the files in the computer hard-disk.

In trips, it's the content of the suitcase (when you go and you come back, with all modifications inbetween). For small children, it's the set of toys and other goods they grasped and licked over the first months of life, building up the first experiences of desire and preferences.

At the exit of supermarkets, it's the basket of goods purchased, testified by the expenditure bill receipt they give to the consumer.On the supply side, the goods on the supermarket shelves are a cumulative bundle (see this paper for a consumer choosing from such a bundle). Competition across POS (point of sales) is based on the properties of their cumulative bundles (in addition to location, image, etc.).

Many manifacturing firms usually store their production and sell from the cumulative bundle in their warehouses - while deciding next production lots based on inventory levels (for a model of a firm taking such decision see here).

3. What's a cumulative bundle?

It's a collection of durable goods and stored non-durable goods, which a person or a household has been purchasing over time, reflecting past choices and suggesting new purchases. Usually located in one place, it is at the disposal for use, when the owner(s) choose(s) which piece of the cumulative bundle to put in action immediately.

By extension, it is a collection of goods at commercial and industrial premises ready for sales (or any other use). In a urban context, a city can be seen as a cumulative bundle of buildings and open organised spaces planned and built over time (possibly by urban regeneration).

The composition of a cumulative bundle is the results of new purchases and the decumulation (e.g. consumption / exhaustion of physical and economic life) of the bundle inherited from the past period.

4. Why is cumulative bundle important for consumer theory?

The composition, width and age of the cumulative bundle exerts an important influence on consumers' purchases and the satisfaction of his needs. They help understand, model and forecast consumer activities.

Many consumer decision-taking rules use his comulative bundle as a relevant input element, while the full range of effects of those decisions need the cumulative bundle to be grasped.

Consumer theory tries to explain the choice of consumer by keeping into account its income and tastes. But, for instance, a consumer can refuse to buy a good that he likes and can afford, because... he already owns a replica of it at home! If you ignore his cumulative bundle, you'll make the wrong prediction about his purchases.

In many real shopping experiences, the consumer buy many things during the same purchase trip, with his budget constraint being related to the total of purchases (a cumulative bundle) and not on the single item.

The overall degree of satisfaction of his needs will depend on the aggregate properties of the bundle more than one specific good purchased, especially because certain items might need the presence and activation of others in order to provide satisfaction. The use of each item can be different (multiple use for multiple goals and needs) depending on which other item is present and activated (for example, think to television sets, DVD players and DVD disks, which can be used for educational or entertainement purposes).

However, as a simple firs step, one could enlist a number of needs (including both "basic need" and other needs) and know "how much" a certain good contribute to the fulfillment of each. Ignoring or keeping into account synergies and reciprocal relations, one could estimate whether the consumer needs are satisfied (or not). Reflections on how the needs of the poor and the rich are satisfied by their cumulative bundles are presented here.

Neoclassical theory of consumption does not distinguish several "needs" but rather work on an aggregate measure ("utility"), thus is prevented to understand a number of real situation in which purchases are directed to fulfill specific needs, not presently covered by the consumer's cumulative bundle. For a wider comparison between standard textbook neoclassical theory of consumer and our opposite alternative see this paper.

Many models of consumer decision-making focus his choice on one specific market (see this) but his decisions depends not only from his preferences and decision rules but on the cumulative bundle he already owns.

In particular, we underline that across the components of the cumulative bundle (and new purchases), there is a wider number of relationships than just substitution or complementarity, which have been studied at length in neoclassical theory, e.g.:

1. style coherence (e.g. in furniture or apparel);

2. colour complementarity (e.g. you purchase some shirt "to match" the colour of a skirt you have in the wardrobe);

3. propedeutics, with a good being necessarily in the cumulative bundle before another can work and provide some need satisfaction (e.g. you need a DVD player before you purchase music DVD, you need a connection to an energy source - e.g. through an electric grid - before you can use any electricity-powered device, etc.) - this can be seen as an asymmetric complementarity, because the reverse is not true (you don't need a specific music DVD to use a player with another DVD, you don't need a device before you have an energy connection).

4. container and contents, where e.g. the choice of the former impacts on the total quantity of the latter.

In another vein, the location where choice is taken is not only the "point of sale" but can be the house (or, more in general, the location of the cumulative bundle), where the consumer reflects on what is lacking, should be renewed, added, replaced, etc. Based on that, the itinerary of purchase trip, with a sequence of POS may be established. Once in the POS the selection of what to buy or not from what's on offer will be based (in part) on what decided earlier and on the perspective next POS.

If the consumer takes into account the presence of a good in the cumulative bundle and avoids repurchasing, it would be possible to demonstrate an asymmetric reaction to price falls and price increases leading to the same price level. In the neoclassical theory, the demand curve assumes that there is one level of demanded quantity for each level of price, irrespective of past dynamics (i.e. whether the price has been reached after a discount or after an increase). In empirical settings, you can easily imagine that the demand depends on past prices, with a temporary discount leading to very different effects on purchased quantity than a temporary increase in price.

In another vein, one could point at the fact that the single choice of consumer has an irriducible degree of freedom, which has to be modeled as random extractions; by observing cumulative bundles one can make forecast of modifications of them over time.

In surveys, in addition to self-reporting and self-declaration, questions on (and appraisal of) the composition of the cumulative bundle provide independent indications about consumer decisionmaking rules, income and lifestyles. By looking at "vintages" of purchase, one can sometimes track the past dynamics of those elements (e.g. a recent income large increase resulting in a wide difference in age between elements of the cumulative bundle).

The composition of the cumulative bundle can lead to purchase of maintenance services, while income could come from certain items of the cumulative items (or their synergies); thus income, savings and disposable income, and consumption levels are all influenced by the cumulative bundle. It reflects householde investment decisions in durable goods; especially in family-run small firms, these choices are intertwined with business investment as well.

5. Consumer decision-taking rules based on cumulative bundle

Purchase decisions can reflect the substitution of previous elements of the bundle with identical or better elements.

1. A broken or exhausted component of the cumulative bundle is a reason for repurchasing, if the consumer does not want to remain without it (he dislikes the inventory break).

If the consumer likes variety, the next purchase will be a different variant from the exhausted one. If by contrast he exhibits strong "attachment" to the variant (e.g. because of brand loyalty), the purchase will perfectly replicate it.

2. In markets where over time new "edition" appear (e.g. periodical journals), the presence of a collection of such goods in the cumulative bundle can lead to further purchases of the "series". The chosen good is a new edition of the same "title". Similarly, having seen many films of a certain kind with a certain actor can be taken as a hint for next choices at the boxoffice.

3. In the allocation of budget for next purchases, a consumer can follow an "equalization" rule, choosing goods that engender an equal satisfaction for different needs from the resulting cumulative bundle.

Need satisfaction of the rich and the poor with the equalization rule of budget allocation

The chosen good is what is "lacking" from the previous cumulative bundle - a good that is not in the house and fills a gap in a need that was not satisfacted.

4. By contrast with 2, a consumer can follow a "specialization" rule, for which he chooses goods that provide a particularly high satisfaction of one need.

Specialization rule for budget allocation and the resulting need satisfaction

The chosen good adds up to the previous cumulative bundle the satisfaction of "priority" need of the consumer.

5. An important feature that a consumer could take into consideration is the life duration of the goods he purchases. A longer time life of the goods allows for wider cumulative bundle (while keeping the same income and expenditure levels), as you can verify with this model.

6. Maintenance and Operations of the components in the cumulative bundle give rise to a flow of "derived" purchases. For instance, electricity is needed to keep in motion a number of devices, so the demand for electricity "derives" from decisions that don't explicitly target it (nobody says: "let's go shopping and buy some energy") - this is an explanation of the low price elasticity of electricity, which in turn is one out of many reasons calling for "innovative economic policies for climate change mitigation", not just energy price increases.

6. Difference of "cumulative bundle" to other similar concepts

"Wealth" is the part of a cumulative bundle which provides interests, revenues and other material advantages, which has a sale market where (part of, all or more than) the original price paid can be recovered. In the cumulative bundle there are items that cannot be sold because their use is private and influences very specific acts of consumption.

The difference with "capital" is even wider - because capital is the set of durable goods that concurr to production processes, only some of which are carried out by households.

The extremely fruitful concept of "consumption system" (Boyd and Levy 1963) covers a bundle of products that cohere around, and facilitate, an activity (e.g. eating) for the goal of fulfilling one need (e.g. nutrition). The similarities with the "cumulative bundle" are several, including the internal articulation and the many complementarities among the goods. But a cumulative bundle can satify many needs (partially or totally).

7. Why "cumulative bundle" is relevant to the evolutionary theory of consumer

Cumulative bundle confirms, in consumption theory, a major tenet of evolutionary economics: "history matters" - choices are a sequence, largely following a "path dependency" in which later steps heavily depend on previous ones. The choice of your place of living influences the POS you find convenient to shop at, which in turn determines the supply conditions you are exposed at and, as your flows of choice accumulate, you fill your place of living with a certain cumulative bundle.

The "explanation" of the reason why things are such as they are is - in the evolutionary approach - is the consideration of the process of change of a previous - structured - set of conditions and routines.

The concept of "cumulative bundle" allows for and object-to-object analysis (with one cumulative bundle to have internal tension to evolve to another one) leaving decision-making as an intermediate step.

For a wider presentation of the evolutionary theory of consumption see this paper.

Moreover, an unexpected use of cumulative bundle items and their relations can lead to significan innovation both in consumption and production processes.

More than one person could rely on the same cumulative bundle (as it happens with furniture in a house where several people live). This provides a material basis for their solidarity networks, over which the communication and social networks - a typical issue for evolutionary economics - might be extended.

8. Drills and questions for you

Analise a cumulative bundle you can observe. Take a room of your house and count how many items it contains and where there is a prevalence of high price, low prices or intermediate price items. Compare with the corrisponding room in a house of person you know is significantly richer or poorer than you. Where are the main differences you can identify? Do these differences involve the presence of certain (top or bottom - quality) item or their level of duplication?

If you or a person you know mainly shops at premises giving a receipt bill with the readable list of purchased item, cumulate the bills over one week or one month and analyse the cumulative bundle of item purchased. Can you single out specific need fulfillment they contribute to? Each item is for one need only or for several? Can you make a list of (broad and narrow) needs fulfilled with the cumulative bundle? Comment it with the buyer. Which purchases were linked to his / her previous cumulative bundle and how?

If the empirical cumulative bundle can be described as a list of strings or numbers, try this testbed for introducing and comparing alternative artificial routines that may be able to generate structurally similar cumulative bundles.

Appendix I - The paradox of cumulative bundle

Cumulative bundle might be expected to reflect the preferences of the purchaser. However, if the purchasing routine is different from actual use, cumulative bundle might end up to be filled in with undesired items for the consumer.

Let's take the example of shirts - with they being either white or coloured. For simplicity's sake, let's assume that the initial cumulative bundle contains half and half. If during a certain season, the owner / user prefers the coloured, the cumulative bundle will tend to have a larger proportion of white, because of the following process: each day the owner chooses one shirt. At the end of the day, he puts it in a buffer, to be washed, dried, ironed and put back in the cumulative bundle. If the time for these operation is long, the cumulative bundle will exhibit a larger proportion of white. If this time lasts more days that than the absolute number of coloured shirts, there will be a moment in which the cumulative bundle will be made only of undesired things.

In another class of cases, when focusing on how the cumulative bundle is reduced by the consumption of non-durable goods, if there is a discrepancy between the reasons and the temporal dynamics of purchases and consumption (i.e. here the exhaustion of a non-durable), preferred goods will be consumed frequently whereas goods that are in the cumulative bundle but that are less liked and appropriate for current consumption will remain in the bundle. This leads to smaller and smaller shares of "liked" goods, with "non-liked" getting the prevalence. If the time to repurchase is long enough, it might even happen that the cumulative bundle does not contain the liked goods any more.

Give a look to your fridge after a long period you do not go shopping: it may be full of food you do not really like, with all your preferred items having being consumed away.




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