Principle of Subordination of Needs may not Necessarily Lead to the Strictly Lexicographical Order of Choices

This article is aimed to show that there may be a false within Dr. Marc Lavoie's argument about the relationship between principle of subordination of needs and strictly lexicographical order of choices.

Principle of Subordination of Needs 

Principle of subordination of needs is one of seven principles of consumer choices in Post-Keynesian Economics. Basically, this principle argues that each consumer has a pyramid or hierarchy of needs. We can say Maslow's  model of hierarchy of needs is a good example to express this principle.

According to this principle, human's needs are hierarchical. Some needs are relatively more important than others. If consumer has some positive income, this consumer will firstly spend the income on the most important need (for example, food) in order to satisfy this most important need, and then if she still have some residual income, she will spend her residual income on the relatively less important need in order to satisfy it. Actually, this procedure has been discussed in Roy (1943) [1] and Georgescu-Roegen (1954)'s [2] papers already.  In Roy's paper, Roy suggest that actually each consumer has a hierarchy of needs and consumer will arrange her expenditure according to the rank of importance of each need. Georgescu-Roegen also suggest this consumer's behaviour, also, he give a simple example to illustrate the principle of subordination of needs.

Let us take a look at his example. Suppose there are two kinds of goods X, one is margarine (denoted as  ) and another is butter (denoted as  ). And for our consumer, she has two kinds of needs, one is the need to calories (denoted as  ) and the another one is the need to taste (denoted as  ). 

Suppose the relationship between needs and goods are as following:

and suppose the most important need for consumer is the need to calories and second important need for consumer is the need to taste. 

Now let us set a limit level K for the need to calories. Below this level K, consumer will feel that calories is more urgent than taste and therefore will make her choices based on the size of k. Only when two choices have the same value of k, consumer will consider the taste and she will prefer the choice which the value of t is greater. But, over this level K, need to calories will become secondary and need to taste will be the most important one. Consumer will make her choices based on the size of t. Only when two choices have the same value of t, consumer will consider the calories and she will prefer the choice which the value of k is greater. 

Therefore, for needs combination (k, t) and (k', t'), (k, t) is preferred to (k', t') iff:

1. 
2. 
3. 
4. 

We can show this consumer's preference in the following figure:

Here z1 is denoted as the need to calories k and z2 is the denoted as the need to taste t. In this figure, consumer's preference described by Georgescu-Roegen is showed. Actually, the following preference holds: G>F>E>D>C>B>A where ">" means "strictly preferred to".

I highly doubt that Dr. Marc Lavoie argues this principle will lead to a (strictly) lexicographical order of choices by only considering above-mentioned preference type. As a result, due to there is no substitution effect among all consumption bundles and Archimedean axiom is violated in this type of preference, we cannot use a single real number to denote consumer's utility [3], i.e., consumer's satisfaction level or happiness:

With this principle, utility cannot be represented by a unique catch-all utility measure; it can be only by a vector, and there is no longer any continuity.  —— M. Lavoie: Post-Keynesian Economics: A New Foundation, page 100 

But, this argument may not correct.

Principle of Subordination of Needs may not Lead to a Lexicographical Order of Choices

To see why this could happen, first we should define what is a lexicographical order. In mathematical literature, lexicographical order is defined as following:

Given two vectors  and in ,

a>b iff for the minimum i for which .

For example, (1,1)=(1,1), (1,2)>(1,1), (2,1)>(1,2).

According to this definition, the preference type described by Georgescu-Roegen follows lexicographical order. 

However, I do not think the principle of subordination of needs necessarily demand consumer has a lexicographical-order preference. Please take a look at the example showed in figure 2.3 in page 106 of M. Lavoie's book Post-Keynesian Economics: A New Foundation. In this example, consumer will only consider the most important need z1 under the satiation level z1*, therefore, under the satiation level z1* need z2 subordinates to need z1. However, consumer will consider need z2 is the most important and need z1 becomes secondary over the satiation level z1*. Therefore, over the satiation level z1* need z1 subordinates to need z2. Thus, we can see whether the size of z1 is greater than z1*, the principle of subordination of needs always has influence on consumer's choice decision.

But, different from the preference type described by Georgescu-Roegen, in figure 2.3 indifference exists. For example, under the satiation level z1* and given the size of z1, consumer's satisfaction level is indifferent between the various sizes of z2. Therefore, in figure 2.3 point B and point C are indifferent for consumer, which violates the lexicographical order (in the lexicographical order, point C should be strictly preferred to point B). 

Thus, the principle of subordination of needs does not necessarily lead to a lexicographical order of consumer choices. As a result, we can use a single number to denote consumer's utility, just like what Lavoie has done in the pages 106 and 107. Actually, it seems that whether consumer choices follow lexicographical order should depends on the consumer's specific preference type.

Notes and References

[1] Roy, R. (2005) 'The hierarchy of needs and the concept of groups in consumer choice theory (1943)', History of Economics Review, 42 (Summer), 50-6.

[2] Georgescu-Roegen, N. (1954), 'Choice, exceptions and measurability', Quarterly Journal of Economics, 68(4), November, 03-34.

[3] To see why Archimedean axiom is violated and as a result consumer's utility should be denoted as a vector, one may take a look at Fishburn and LaValle's 1998 paper: Subjective expected lexicographic utility: Axioms and assessment. Although the main purpose of this paper is to propose a new theory on expected utility, it still discuss when the Archimedean axiom will be violated in detail.