# describing consumption possibility frontiers

## set of feasible consumer market baskets

A market basket is defined to be an assortment of economic goods. This definition does not assume that the goods in question are in a basket, or even that they are located near each other. It is a purely mathematical construct, a subset of the set of all goods. The set M of all market baskets is the set of all subsets of the set of all economic goods. The set F of feasible consumer market baskets is that subset of M that minimally satisfies the feasibility constraints listed below.

### availability constraints

These constraints are imposed by suppliers. They are what we call "package deals." A package deal is a market basket, usually referred to in retail trade as a "bundle," with a single price stated for the bundle. If package dealing were not part of the terms constraining the sale of goods, then each element of the set M of market baskets could be described in simple tabular form, with columns for description, unit price and unit quantity. With package dealing in play, the set M must be constructed by treating individually available goods as "single-item bundles." Each bundle is a set of one or more goods, and the set M of market baskets is the set of all sets than are unions of zero or more bundles.

### budgetary constraints

Let's consider the set B of market baskets which are priced at or below some number b, which we'll take as representing the amount of budgetable money a given consumer is able to spend on goods. We can represent each market basket as a point in n-dimensional space, where each of the n dimensions (each of the n coordinates of the basket's point) represents the quantity of one of n "distinguishable" types of goods. In a hypothetical non-bundled consumer market, this set will be bounded by a "hyperplane," which is a multidimensional extension of the concept of a plane. The hyperplane-bounded region containing the budgetable subset B could be expressed as x1+...+xn<b, where xi represents the quantity of one of the n types of goods, and b represents the size of a consumer's budget.

This is a generalization of the notion of "budget line," a pedagogical instrument sometimes used in textbook examples based on an assumption of a hypothetical economy in which only two goods exist. If there were no package deals, no nonlinear pricing schemes (such as quantity discounts or "per customer" limits on quantity) and no goods without currency-denominated price tags, the affordable set would indeed be neatly be bounded by a hyperplane. The inevitability of such "shell games" makes the boundary of the budget constraint approximately rather than exactly co(hyper)planar.

### formal constraints

These comprise what might be termed "hard normative" constraints. One type of formal constraint would be statutory constraints. For example, a given consumer might be constrained by local ordinance to own at most a certain number of cars, pets, etc. These constraints can be overcome by renting garage space or procuring pet boarding services, but baskets that include quantities of formally limited goods without also containing goods that accommodate these excesses are not included in the formally constraint set of baskets.

### necessary constraints

These are constraints imposed by necessity. Market baskets that fail to meet a consumer's minimal sustenance needs are excluded. Where exactly to draw the boundary between regions of sufficiency and insufficiency is of course debatable, and has been hotly debated for at least as long as the concept of a "safety net" has existed. Market baskets whose "edible component" fail to meet the (say) U.S. RDA of vitamins and minerals, as well as empirically established minimal amino acid spectrum, could arguably be described as insufficient to meet necessities. Since raw necessities include housing and other non-edible goods, the sufficient set for a given consumer would of course be a proper subset of the nutritionally sufficient set.

These preferences are subjective. The efficient subset of the set of market baskets feasible to a given consumer is determined by these preferences. In general, larger quantities are assumed to be preferred over smaller quantities. Additional variables reflecting consumer preferences can be derived algebraically from these quantities. For example, combinations of complementary goods are typically consumed in definable ratios, such as ingredients in a recipe. If quantity Q of an ingredient is possessed, and a recipe calls for quantity R of that ingredient, then Q/R would represent the number of batches that can be prepared. The value of Q/R could then be a maximized variable when charting the efficient frontier of the feasible set.

### consumption preferences

These would be the preferences implied by the "utility function" of microeconomics.

### production preferences

This category of preferences included to account for the stated desire of some consumers to use their consumer spending as an incentive for vendors of consumer goods to conform to some of the consumer's preferences in business practices. The strategy of such consumers usually relies on some combination of boycotts and "buycotts." There are probably no empirical metrics of ethical performance, or of sets of ethical standards. It seems the most reliable way for a company to become a boycott target is by having the largest market share in its industry. For the purpose of this model, we'll generally disregard the production preferences of consumers. Hopefully the future will be more transparent than the present and the public record will contain some tangible information concerning business practices.

### payment preferences

Some consumers would prefer to pay in cash. Most retail vendors seem to prefer annuity-type schemes, or fixed (minimum) periodic payments, with increasing aggressiveness in demanding fixed (minimum) contract durations. This is evident in the number of goods available as "subscriptions," which in many cases used to be also available under other types of terms. It is listed here under preferences (which is to say, consumer-imposed constraints), although it also has properties of a vendor-imposed constraint. Future versions of this document may or may not reclassify it, depending on what trends develop during the next few years. Another type of boilerplate arrangement is becoming increasingly popular with B2C vendors. I generally refer to it as "nonlinear pricing," which is a catch-all term for any type of mathematical definition of price in terms of quantity and other well-defined parameters, using a non-analytical (often referred to as "not well-behaved) function, preferably of more than one variable.