The Review of Austrian Economics

, Volume 24, Issue 3, pp 311–318

Rothbardian demand: A critique

Authors

Article

DOI: 10.1007/s11138-011-0147-3

Cite this article as:
Hudík, M. Rev Austrian Econ (2011) 24: 311. doi:10.1007/s11138-011-0147-3

Abstract

This paper refutes Rothbard’s claim that the law of diminishing marginal utility implies a non-increasing demand curve. It is argued that the law under Rothbard’s interpretation is, in fact, irrelevant for demand theory. An example of increasing demand is provided.

Keywords

DemandGiffen behaviourMarginal utilityConsumer theory

JEL Classification

B53D01

This paper refutes Murray Rothbard’s claim that the law of diminishing marginal utility (LDMU) implies a non-increasing demand curve.1 This claim can be divided into two parts: (1) the demand curve is always non-increasing and (2) this property is ensured by the LDMU. As for the first part, it is true only as long as the income effect is neglected, while the second part is false because LDMU, as interpreted by Rothbard, has no implication for demand theory, since, in order to ensure its universal validity, Rothbard formulates LDMU in terms of subjective units relevant to the agent. This, however, is precisely the reason why the law becomes irrelevant for demand theory because the demand function represents an objective relationship between an amount of commodity and its price. To prove this irrelevance, an example of Giffen behaviour2 can be constructed without violating subjectively interpreted LDMU.

The paper proceeds as follows: part I reviews the relevant literature, in part II, the meaning of the law of marginal utility is discussed and part III criticises Rothbard’s derivation of demand from the LDMU and provides an example of increasing demand. Part IV discusses possible objections against the example, while part V concludes.

1 Literature

Since there is little published criticism of Rothbard’s claim, I take his view as widely accepted among Austrians. One of the few critics, however, is Caplan (1999), who points out inconsistencies in Rothbard’s price theory, such as his admitting the possibility of a backward-bending individual supply curve of labour and his reference to substitution and income effects. Allowing for the income effect opens the door to Giffen behaviour in consumer theory in the same way that this effect makes the backward-bending labour supply curve possible. In response to this kind of criticism, there seem to be two positions among Austrians. The first is represented by Hülsmann (1999), who implicitly rejects Rothbard’s approach and prefers to follow Mises in not being concerned with the shape of demand curves. What role then the LDMU plays in the theory, if not influencing the shape of the demand curve, is unclear. The second position takes the existence of Giffen behaviour for granted (Garrison 1985; Block 1999). In his response to Caplan, Block (1999) maintains that demand is always non-increasing ceteris paribus, i.e. when the income effect is neglected.3 According to him, Rothbard had in mind from the very beginning the compensated demand; indeed, Rothbard (2009, p. 239n) explicitly uses the Marshallian assumption of the constant marginal utility of money, which is, of course, equivalent to saying that the income effect is negligible. However, Rothbard is wrong in saying that relaxing this assumption only reinforces the law of demand, as this is the case only under the assumption that a single good is consumed—only then is the income effect always positive. By introducing more goods, the possibility of a negative income effect (and Giffen behaviour) emerges. The acceptance of this line of reasoning in terms of substitution and income effects immediately raises the question about the difference between Austrian and mainstream demand theories. One obvious difference is that the Austrian analysis professes to make use of the LDMU; nonetheless, to my knowledge, nowhere in the literature is the relevance of LDMU for the shape of the demand curve discussed. In the next section, Rothbard’s interpretation of this law is examined, and it is argued that it cannot possibly have any consequences for demand theory.

2 The law of diminishing marginal utility

The LDMU is formulated as follows: whenever the supply of a good increases by one additional unit, provided each unit is regarded as of equal serviceability by a person, the value attached to this unit must decrease. For this additional unit can only be employed as a means for the attainment of a goal that is considered less valuable than the least valued goal satisfied by a unit of such good if the supply were one unit shorter.4

Let us examine in more detail what this law says. First, we focus on the meaning of the term ‘unit’. Rothbard (2009, p. 74) makes clear that what is meant is not any physical unit, but a relevant unit—as viewed by the consumer himself. For example, consider a consumer who ranks three different types of salads (X, Y, Z), each of which requires four tomatoes as follows:
  1. 1.

    A salad X, which can be produced only with four tomatoes.

     
  2. 2.

    A salad Y, which can be produced only with four tomatoes.

     
  3. 3.

    A salad Z, which can be produced only with four tomatoes.

     
The relevant unit is now four tomatoes; accordingly, the third LDMU unit will be valued less than the second and the second less than the first:
  1. 1.

    The first four tomatoes.

     
  2. 2.

    The second four tomatoes.

     
  3. 3.

    The third four tomatoes.

     
Now, let us see what ‘unit of equal serviceability’ means. Consider the following example of a consumer ranking:
  1. 1.

    Cake A, which can be produced only with two eggs.

     
  2. 2.

    Cake B, which can be produced only with three eggs.5

     
  3. 3.

    Cake C, which can be produced only with one egg.

     
Let us take one egg as a unit; the first egg can be used only for satisfying the least important end, i.e. to bake cake C. The second egg enables us to produce cake A, which is valued the most. Therefore, the second egg is valued higher and LDMU seemingly does not hold. To rewrite the previous scale in terms of means (eggs) rather than ends (cakes):
  1. 1.

    The second egg

     
  2. 2.

    The third egg

     
  3. 3.

    The first egg

     
However, the first egg and the second egg are not capable of satisfying the same range of ends as they are not of equal serviceability. For that matter, LDMU is not violated—to apply it here, we only have to appropriately define a relevant unit, which in this case is three eggs. It is straightforward to see that the first three eggs are of equal serviceability as the second three eggs (they can gratify either the second or the first and the third ends):
  1. 1.

    The first three eggs (cakes A and C)

     
  2. 2.

    The second three eggs (cake B)

     

In general, in cases where various ends require different amounts of goods, we take the end that requires the maximum amount of a good, which we define as the ‘relevant unit’.

It is precisely the fact that LDMU holds only for subjectively defined units of equal serviceability that makes the law irrelevant for the demand because the consumer has ends which differ in the size of the relevant unit, and hence purchases units of different serviceability. A concrete example is given in the next section.

3 LDMU and demand

First, we examine how Rothbard derives demand from LDMU. Consider his value scale example (Rothbard 2009, p. 239):
  1. 1.

    Seven grains of gold

     
  2. 2.

    The first pound of butter

     
  3. 3.

    Six grains of gold

     
  4. 4.

    Five grains of gold

     
  5. 5.

    The second pound of butter

     
  6. 6.

    Four grains of gold

     
  7. 7.

    Three grains of gold

     
  8. 8.

    The third pound of butter

     
  9. 9.

    Two grains of gold

     
This value scale, involving comparisons between absolute amounts of gold and additional units of butter, is at first sight rather bizarre—it is not clear what the consumer’s endowment at each situation is6—one would rather expect a value scale comparing various combinations of gold and butter, as is the case in standard microeconomics, or changes of these combinations, as we find in the approach of Bernardelli (1938, 1952). Nevertheless, Rothbard makes clear that what he has in mind is that the amounts of gold are various prices; hence, what he asserts to be a value scale is already a demand schedule (Table 17). Now, what makes sure that the demand for butter is non-increasing? As Rothbard (2009, p. 239) puts it:
Table 1

Rothbard’s Demand Schedule

Price (grains of gold)

Quantity (pounds of butter)

p = 8

0

p = 7

0

p = 6

1

p = 5

1

p = 4

2

p = 3

2

p = 2

3

p = 1

3

His [the buyer’s] maximum buying price for a second pound of butter will be considerably lower. This result is always true, and stems from the law of utility; as he adds pounds of butter to his ownership, the marginal utility of each pound declines. On the other hand, as he dispenses with grains of gold, the marginal utility to him of each remaining grain increases.

As we have seen in the previous section, this statement is correct only if a pound of butter is a relevant unit—only then LDMU applies. Otherwise, there is no guarantee that the first pound of butter is valued higher than the second pound. Hence, Rothbard does not derive downward-sloping demand from the value scale, as his value scale is already a demand schedule and he already assumes it to be downward-sloping. It is easy to show that demand can be increasing (without violating LDMU), as shown in the following example. In order to avoid possible methodological objections, the example does not use mathematical formalisation and is as close to Rothbard’s own treatment as possible. In addition, it is unique in the sense that it derives Giffen behaviour from the preference ordering defined on the set of ends rather than bundles of goods.8

Assume that a consumer is endowed with six tomatoes and zero eggs and has the following ranking of ends:
  1. 1.

    Cake A, which can be produced only with two eggs.

     
  2. 2.

    Salad X, which can be produced only with four tomatoes.

     
  3. 3.

    Cake B, which can be produced only with three eggs.

     
  4. 4.

    Salad Y, which can be produced only with four tomatoes.

     
  5. 5.

    Cake C, which can be produced only with one egg.

     
  6. 6.

    Salad Z, which can be produced only with four tomatoes.

     

I now argue that at the price of one tomato for one egg (p = 1), the consumer will demand two eggs, whereas at the price of two tomatoes for one egg (p = 2), he will demand three eggs.

At p = 1, there are seven feasible bundles (the first figure in the ordered pair denotes the number of eggs, the second one denotes the number of tomatoes), as shown in the first column of the Table 2. The numbers in the second column represent the ranking of the ends, which will be satisfied with the respective bundle.
Table 2

Bundles Feasible at p = 1

Bundles of goods (eggs, tomatoes)

Ends satisfied

(0, 6)

2nd (X)

(1, 5)

2nd, 5th (X, C)

(2, 4) (K)

1st,2nd (A, X)

(3, 3)

1st, 5th (A, C)

(4, 2)

1st, 5th (A, C)

(5, 1)

1st, 3rd (A, B)

(6, 0)

1st, 3rd, 5th (A, B, C)

The chosen bundle is in bold

Bundles (2, 4) and (6, 0) suggest themselves to be chosen; since the consumer’s ranking does not give us the answer, whether satisfying the second end is more important than simultaneously satisfying of the third and fifth ends, it is possible that the consumer will choose bundle (2, 4).

At p = 2, there are four feasible bundles (Table 3). In this case, bundle (3, 0) is chosen. The two optima are depicted in Fig. 1. Table 4 and Fig. 2 represent demand for eggs.
https://static-content.springer.com/image/art%3A10.1007%2Fs11138-011-0147-3/MediaObjects/11138_2011_147_Fig1_HTML.gif
Fig. 1

Diagram of the Bundles.

https://static-content.springer.com/image/art%3A10.1007%2Fs11138-011-0147-3/MediaObjects/11138_2011_147_Fig2_HTML.gif
Fig. 2

Diagram Showing the Demand for Eggs.

Table 3

Bundles Feasible at p = 2

Bundles of goods (eggs, tomatoes)

Ends satisfied

(0, 6)

2nd (X)

(1, 4)

2nd, 5th (X, C)

(2, 2)

1st (A)

(3, 0) (L)

1st, 5th (A, C)

The chosen bundle is in bold

Table 4

Demand for Eggs

Price (tomatoes/1 egg)

Quantity (eggs)

p = 6

0

p = 5

0

p = 4

0

p = 3

2

p = 2

3

p = 1

1

4 Discussion

One possible objection to the above presented example is that nothing prevents us from deriving the demand curve for the relevant unit, i.e. in this case a “three-egg”. This, however, is not going to help unless we also forbid the divisibility of the relevant unit. Practically, it means that we allow the consumer to purchase only “three-eggs” because, say, eggs only come in packages of three. In this instance, the demand for this particular consumer would really be non-increasing, but how plausible is it that goods will be sold only in relevant units? This “solution” becomes next to absurd once we consider market demand, so what is required is that the “three-egg” is the relevant unit for all consumers; otherwise, there can always be a consumer who exhibits Giffen behaviour.

5 Conclusion

I have argued that LDMU is irrelevant for demand theory and, in particular, I have provided an example that it does not (contrary to Rothbard’s claim) imply non-increasing demand. If the argument is correct, then it must be concluded that Rothbard failed to construct a viable alternative to mainstream demand theory. If there is to be a specific Austrian approach to demand, it probably must proceed along different lines than those sketched by Rothbard.

Footnotes
1

… because of the law of utility, an individual demand curve must be either “vertical”, as the hypothetical price declines, or rightward-sloping (i.e. the quantity demanded, as the money price falls, must be either the same or greater), not leftward-sloping (not a lower quantity demanded)” (Rothbard 2009, p. 240). He writes further that “this is the necessary configuration of every buyer’s demand schedule (Rothbard 2009, p. 240).

 
2

I accept the arguments of Jensen and Miller (2008, p. 1552) and prefer to talk about Giffen “behaviour” rather than Giffen “good”. See also Battalio et al. (1991, p. 969).

 
3

However, cf. Block (2003, p. 67), who states that demand curves are downward-sloping, without mentioning the ceteris paribus clause and proclaims the law of demand as a priori true.

 
4

This particular formulation is Hoppe’s (2007, p. 14). For alternative formulations and discussion, cf. e.g. Mises (1996, p. 199ff.) or Rothbard (2009, p. 21ff.).

 
5

This ranking does not imply that two eggs are preferable to three eggs, i.e. that less is preferred to more!

 
6

For instance, when buying the second pound of butter, had the consumer already bought the first one? If so, at what price?

 
7

Reproduced from Rothbard (2009, p. 240).

 
8

In this respect the example is close to the approach of Lipsey and Rosenbluth (1971), who analyse the Giffen case within a Lancasterian framework.

 

Acknowledgements

I would like to thank Jeffrey Herbener, David Lipka, Joseph Salerno, Dan Šťastný and an anonymous referee for their valuable comments on earlier drafts of this paper.

Copyright information

© Springer Science+Business Media, LLC 2011