The pareto rule and welfare economics

Murray N. Rothbard, “Toward a Reconstruction of Utility and Welfare Economics,” in Mary Sennholz, ed.,On Freedom and Free Enterprise: Essays in Honor of Ludwig von Mises (Princeton, N.J.: D. Van Nostrand, 1956), p. 249.

The importance of this article as a contribution to the Austrian literature can be seen in the assessment of Israel M. Kirzner, who said, “[I] can personally attest to the excitement engendered by the lucid manner in which this paper deployed Austrian insights to illuminate fundamental theoretical issues (concerning which contemporary economics was floundering), and by the characteristic erudition which Rothbard poured into that single essay.” See Kirzner, “Welfare Economics: A Modern Austrian Perspective”, inMan, Economy, and Liberty: Essays in Honor of Murray N. Rothband, Walter Block and Llewellyn H. Rockwell, eds. (Auburn, Ala.: Ludwig von Mises Institute, 1988), p. 77.

For the original contribution of Ludwig von Mises on the ordinal nature of utility, see Mises,Theory of Money and Credit (Indianapolis: Liberty Classics [1912], 1980), pp. 51ff. For the blow delivered by Lionel Robbins to Old Welfare economics, see Robbins,An Essay on the Nature and Significance of Economic Science, 3rd ed. (New York: New York University Press, [1932] 1984), pp. 137–41.

In addition to cardinal units for each individual's utility, interpersonal utility comparisons require acommon cardinal unit in which the utility units of different individuals could be expressed. Those familiar with Ludwig von Mises's argument that socialism is impossible because of the inability of central planners to make economic calculations will recognize a parallel between that argument and the impossibility of interpersonal utility comparisons. The impossibility of economic calculation in socialism rests on the absence of a common, cardinal unit in which different types of factors of production can be reckoned. See Mises,Human Action: A Treatise on Economics, 3rd rev. ed. (Chicago: Henry Regnery, [1949] 1966), pp. 206–9.

Pigouvian Welfare Theory is developed in Arthur C. Pigou,The Economics of Welfare (London: Macmillan, 1920). For a discussion of the necessity of having ethical judgments taken from disciplines outside economic theory as the foundation of Old Welfare economics, see Lionel Robbins “Interpersonal Comparisons of Utility: A Comment,”Economic Journal 48 (December 1938): 635–41.

Paul Samuelson,Foundations of Economic Analysis (Cambridge, Mass.: Harvard University Press, 1947), p. 225. He added analytic rigor to this line of argument in idem Paul Samuelson, “Social Indifference Curves,”Quarterly Journal of Economics 70, no. 1 (February 1956): 8–14. He had less sympathy with “the bourgeois penchant for laissez-faire”, which he claimed was “the only case on record where a substantial number of individuals have made idols of partial derivatives, i.e., imputed marginal productivities.” That Samuelson rejected “the belief that the individual should rightfully receive his imputed productivities,” because “[it] is not consistent with a [social welfare] function having properties” which he deems important reflects more on his own ethical biases than on a genuine ethical assessment of laissez faire. See, Samuelson,Foundations, p. 225. Oscar Lange, a New Welfare economist sympathetic to the egalitarian leanings of the Old Welfare school, demonstrated that the Pigouvian analysis can be recast in the New Welfare framework. See idem Samuelson, “The Foundations of Welfare Economics,”Econometrica 10 (1942): 221–23.

Samuelson,Foundations, p. 226.

On ordinal marginal utility, see Mises,Theory of Money and Credit, pp. 59-261. His discussion of the relationship between ordinal utility and cardinal value is inEconomic Calculation in the Socialist Commnnwealth (Auburn, Ala.: Ludwig von Mises Institute, [1920] 1990), pp. 11–13, 23, and 48–49.

On the pricing process, see Mises,Human Action, pp. 327–50.

Ibid., On the pricing process, see Mises,Human Action, pp. 206–9.

The connection between Misesian general economics and Rothbardian welfare economics will be explored below.

This is an excellent illustration of the inferiority of a mathematical methodvis-à-vis a verbal method in economic reasoning. Mathematics is inherently incapable of solving this basic economic problem which is easily handled using literary means. On mathematics and pricing, see Mises,Human Action, pp. 350–57, 701–3, 710–15.

Marshall's discussion of consumer surplus is inPrinciples of Economics (New York: Macmillan, [1890] 1948), pp. 92–101, 124–37, and 831–32.

Ibid., Marshall's discussion of consumer surplus is inPrinciples of Economics (New York: Macmillan, [1890] 1948), pp. 124. Emphasis added.

J.R. Hicks attempted to expunge cardinal utility from the surplus approach in a manner consistent with the New Welfare economics. See Hicks, “The Rehabilitation of Consumers' Surplus,”Review of Economic Studies 8, no. 2 (1941): 108–16; idem, Hicks, “Consumers' Surplus and Index Numbers,”Review of Economic Studies 9, no. 2 (1942): 126–37; idem, Hicks, “The Four Consumers' Surpluses,”Review of Economic Studies 11, no. 1 (1943): 31–41; idem, Hicks and “The Generalized Theory of Consumers' Surplus,”Review of Economic Studies 13, no. 2 (1945–46): 68–74.

On this point, see Mises,Human Action, pp. 705–10. Moreover, both bureaucratic cost-benefit calculations and entrepreneurial appraisals require formulating expectations of the future. Bureaucratic expectations are categorically different than entrepreneurial ones because government officials do not place their own wealth at risk on the accuracy of their forecasts. And for those government projects for which there will be no future market, bureaucrats have less basis than entrepreneurs for formulating any type of expectations. On the differences between bureaucratic and entrepreneurial management, see Ludwig von Mises,Bureaucracy (Cedar Falls, Iowa.: Center for Futures Education, [1944] 1983).

What came to be called the Lange-Lerner rule states that central planners can maximize social welfare by solving the perfectly-competitive, general-equilibrium equations to obtain “shadow” prices of all inputs and outputs, then make this list of prices known to the relevant consumers and producers, and finally instruct them to behave as if they were maximizing utility and profit in a perfectly-competitive economy. Enrico Barone, “The Ministry of Production in the Collectivist State,” inCollectivist Economic Planning, F.A. Hayek, ed. (Clifton, N.J., Augustus M. Kelley, [1935] 1975), pp. 245–90; this article was first published in Italian in 1908. Oscar Lange, “Mr. Lerner's Note on Socialist Economics,”Review of Economic Studies 4 (October 1936): 143–44; and idem, Oscar Lange, “The Foundations of Welfare Economics,”Econometrica (1942): 215–28. Abba Lerner, “Economic Theory and Socialist Economy,”Review of Economic Studies 2 (October 1934): 51–61; and idem, Oscar Lange, “Theory and Practice in Socialist Economies,”Review of Economic Studies 6, no. 1 (1938): 71–75. In refuting this approach, Mises specifically identifies Barone as failing to “penetrate to the core of the problem,”Human Action, p. 701.

Abram (Burk) Bergson, “A Reformulation of Certain Aspects of Welfare Economics,”Quarterly Journal of Economics 70, no. 2 (February 1938): 310.

Samuelson,Foundations pp. 214–17.

What is surprising is Samuelson's befuddlement that “Barone satisfies himself with deriving optimalproduction conditions” without bothering to extend his analysis to consumption conditions. He claims that this “oversight resulted from his wish to avoid the use of indifference curves and utility.” Samuelson,Foundations, p. 217, emphasis in original. The absence of consumption optima, however, is no oversight at all for managing acollectivist regime of production. As Mises argued, socialism solves the problem of determining what consumer goods to produce by having the central planners use their own preferences. Mises, “Economic Calculation,” pp. 23–24. Since Barone developed his framework of welfare theory to explain how to manage production in a collectivist state, it is not at all surprising that consumption optima were absent from his set of optimum conditions.

Rothbard, “Toward a Reconstruction,” p. 225. On the early development of the concept of demonstrated preference by Mises, seeTheory of Money and Credit, p. 60; and idem, Rothbard,Human Action, pp. 94–96.

To remain value-free economists, i.e., to abstain from injecting into economic theory ethical propositions, adherents of cardinal utility among the Old and New Welfare economists had to agree with the ordinalists that actions are necessary to demonstrate utility, e.g., consumer surplus is a monetary calculation of utility using a demand curve, which is the result of the actions of buyers in the market. Those cardinal-utility advocates who did not develop value-free theories were not bound by the demonstrated-preference principle, e.g., the Pigouvian prescription, driven by egalitarian ethical notions, of increasing social welfare by equalizing monetary incomes is founded on the undemonstrable principle that each person has a capacity for utility satisfaction identical to that of every other person.

On this limitation of welfare theory, see David Gordon, “Toward a Deconstruction of Utility and Welfare Economics,”Review of Austrian Economics 6, no. 2 (1993): 103–4. Gordon makes this point in response to a criticism of Professor Rothbard's welfare theory made by Roy Cordato, who argues that, “demonstrated preference ... does not allow for any consideration of harm that is not demonstrated,” which rules out “the welfare effects of envy, trauma, etc.” Thus, voluntary exchanges “may have negative psychic effects on others,” which negates the claim that such activity renders an “unambiguous increase in ‘social utility.’” Cordato,Welfare Economics and Externalities in an Open Ended Universe (Boston: Kluwer Academic Publishers, 1992), pp. 42–43.

Rothbard, “Toward a Reconstruction,” p. 244.

Vilfredo Pareto,Manual of Political Economy (New York: Augustus M. Kelley, [1927] 1971).

Given the strictures of value-free economics, consent can only be inferred from voluntarily-undertaken actions by which preferences are demonstrated.

The socialist proponents of the technique used by New Welfare economists were anxious to show by mathematical proof that central planning could operate a division of labor as efficiently as the market by solving the system of perfectly-competitive, general-equilibrium equations. For Mises's criticism of their attempts, seeHuman Action, pp. 701–3.

Bergson, “A Reformulation of Certain Aspects of Welfare Economics”: 310–34.

Bergson's list of optimum conditions differs from the one presented here. For our purposes, the differences between this list, as developed and synthesized by later authors, and Bergson's is inconsequential. For a presentation of how the perfectly-competitive market achieves the optimum conditions, see Francis Bator, “The Simple Analytics of Welfare Maximization,”American Economic Review 47, no. 1 (March 1957): 22–59.

Samuelson calls Bergson “the first who understands the contributions of all previous contributors, and ... the first to develop explicitly the notion of anordinal social welfare function in terms of which all the various schools of thought can be interpreted” and claims that “there is only one all-inclusive welfare economics, which reaches its most complete formulation in the writings of Bergson.” Samuelson,Foundations, pp. 219 and 249. Emphasis added.

Ibid., Samuelson calls Bergson “the first who understands the contributions of all previous contributors, and ... the first to develop explicity the notion of anordinal social welfare function in terms of which all the various schools of thought can be interpreted” and claims that “there is only one all-inclusive welfare economics, which reaches its most complete formulation in the writings of Bergson.” Samuelson,Foundations, pp. 228–29.

The latter possibility is examined in Samuelson, “Social Indifference Curves”: 14–18.

Samuelson,Foundations, p. 221.

Joseph Schumpeter,History of Economic Analysis (New York: Oxford University Press, 1954), p. 1062.

Samuelson,Foundations, p. 249. Contra Samuelson, Robbins did not think that the impossibility of interpersonal comparisons of ordinal utility ranks prohibited welfare economics. He argued that it prohibited the Old Welfare economics based on the assumption of cardinal utility. This was the major theme offered in Robbins, “Interpersonal Comparisons of Utility.”

Robbins's discussion is in Robbins, “Robertson on Utility and Scope,”Economica (May 1953): 104. Professor Rothbard's comment is in idem Robbins, “Toward a Reconstruction,” p. 235.

It makes utility and welfare theory branches of psychology instead of strictly praxeological disciplines.

On indifference, see Rothbard, “Toward a Reconstruction,” pp. 236–38.

Ibid. On indifference, see Rothbard, “Toward a Reconstruction,” pp. 236–38.

Kenneth Arrow,Social Choice and Individual Values, 2nd ed. (New York: John Wiley and Sons, [1951] 1963).

Tibor Scitovszky, “A Note on Welfare Propositions in Economics,”Review of Economic Studies 9 (1941): 77–88.

Samuelson's thinly-veiled contempt for Arrow's work is illustrated in his comment about how “conventional theory” can be saved on the analogy of “family consensus.” He says, “Perhaps Arrow will produce a proof that such a consensus is impossible.” Samuelson, “Social Indifference Curves”: 9.

Ibid.: Samuelson's thinly-veiled contempt for Arrow's work is illustrated in his comment about how “conventional theory” can be saved on the analogy of “family consensus.” He says, “Perhaps Arrow will produce a proof that such a consensus is impossible.” Samuelson, “Social Indifference Curves”: 10 and 13. The condition of “equal social marginal utilities” cannot be met by a social welfare function of ordinal ranks; only if cardinal numbers are attached to the social indifference curves is such a condition definable, let alone achievable. But assigning cardinal numbers implies cardinal utility whose marginal social values can be made equal. Ordinal ranks cannot make the “social (ordinal) utility of every person's last dollar equal,” as Samuelson claims. Ibid.: Samuelson's thinly-veiled contempt for Arrow's work is illustrated in his comment about how “conventional theory” can be saved on the analogy of “family consensus.” He says, “Perhaps Arrow will produce a proof that such a consensus is impossible.” Samuelson, “Social Indifference Curves”: 15.

Arrow,Social Choice, pp. 96–103.

On the concession of defeat, see Abram Bergson, “On the Concept of Social Welfare,”Quarterly Journal of Economics (May 1954): 249; and Paul Samuelson, “Welfare Economics: Comment,” inA Survey of Contemporary Economics, B.F. Haley, ed., vol. 2 (Homewood, Ill.: Irwin, 1952), p. 37.

On the theory of market failure, see Francis Bator, “The Anatomy of Market Failure,”Quarterly Journal of Economics 72 (1958):351–79.

Not the least of these assumptions is perfect information. After listing the standard set of assumptions, F. A. Hayek comments on the meaning of perfect information. “I shall here,” he says, “not go into the familian paradox of the paralyzing effect really perfect knowledge and foresight would have on all action.” See Hayek, “The Meaning of Competition,” inIndividualism and Economic Order (Chicago: University of Chicago Press, 1948), p. 95.

F. A. Hayek says, “It is difficult to defend economists against the charge that for some 40 to 50 years they have been discussing competition on assumptions that,if they were true of the real world, would make it wholly uninteresting and useless.” See Hayek, “Competition as a Discovery Procedure,” inNew Studies in Philosophy, Politics, Economics and the History of Ideas (Chicago: University of Chicago Press, 1978), p. 179. Ernphasis in original.

Rothbard, “Toward a Reconstruction,” p. 255.

Ibid.,Rothbard, “Toward a Reconstruction,” p. 255.

Nicholas Kaldor, “Welfare Propositions of Economics and Interpersonal Comparisons of Utility,”Economic Journal 49, no. 195 (1939): 550. Emphasis original.

Rothbard, “Toward a Reconstruction,” pp. 246–47.

Some neoclassical economists recognized this defect of the general equilibrium approach in their development of the theory of second best. They demonstrated that if a market system is not in general equilibrium, then one cannot discern the correct government policy toward a market failure in any one market using the general equilibrium framework. The seminal article on the theory of second best is Kelvin Lancaster and Richard Lipsey, “The General Theory of Second Best,”Review of Economic Studies 24 (1956): 11–32.

On the compensation principle as a defense of the status quo, see Murray N. Rothbard,The Ethics of Liberty (Atlantic Highlands, N.J.: Humanities Press, 1982), pp. 203–5.

Robbins, “Interpersonal Comparisons of Utility”: 638. Quoted in Kaldor, “Welfare Propositions”: 549–50. Kaldor rightly criticizes Robbins, saying, “It can be demonstrated ... that in the classical argument for free trade no such arbitrary element is involved at all.” Ibid.: Robbins, “Interpersonal Comparisons of Utility”: 550. It is not on the basis of the compensation principle, however, that such an argument can be sustained; but on the principle of mutual benefit in voluntary exchange, as Professor Rothbard demonstrates.

As Professor Rothbard puts it, “It is not possible ... for an observer scientifically to compare the social utilities of results on the free market from one period of time to the next.” Rothbard, “Toward a Reconstruction,” p. 255.

J.R. Hicks, “The Foundations of Welfare Economics,”Economic Journal 49, no. 196 (December 1939): 696–712.

To illustrate conditions under which the free market would not maximize social welfare (specifically, imperfect competition), Hicks uses the example of a firm dosing down. He says, “The loss involved in its cessation is measured by the compensation which would have to be given to consumers to make up for their loss of the opportunity to consume the missing product, plus the compensation which would have to be given to producers to make up for the excess of their earnings in this use over that they could earn in other uses.” Ibid.:: 709–10. Clearly, this “economic reform” involves no government intervention, but is a purely private affair of voluntary “reorganization” of factor usage.

Ibid.:To illustrate conditions under which the free market would not maximize social welfare (specifically, imperfect competition), Hicks uses the example of a firm closing down. He says, “The loss involved in its cessation is measured by the compensation which would have to be given to consumers to make up for their loss of the opportunity to consume the missing product, plus the compensation which would have to be given to producers to make up for the excess of their earnings in this use over what they could earn in other uses.” Ibid.:: 706.

Ibid.:To illustrate conditions under which the free market would not maximize social welfare (specifically, imperfect competition), Hicks uses the example of a firm closing down. He says, “The loss involved in its cessation is measured by the compensation which would have to be given to consumers to make up for their loss of the opportunity to consume the missing product, plus the compensation which would have to be given to producers to make up for the excess of their earnings in this use over what they could earn in other uses.” Ibid.:: 712.

We are not here dealing with the right of self-ownership but with the fact of self-ownership. While moral ownership cannot be established merely by the fact of ownership, economic ownership can. For a natural-law argument for the right to self-ownership, see Murray N. Rothbard,For a New Liberty, rev ed. (New York: Macmillan, [1973] 1978), pp. 26–37; and idem Murray N.,Ethics of Liberty, pp. 29–34. For an axiomatic argument for the right to self-ownership, see Hans-Hermann Hoppe,The Economics and Ethics of Private Property (Boston: Kluwer Academic, 1993), pp. 195–201.

See Ludwig von Mises,The Ultimate Foundation of Economic Science, 2nd ed., (Kansas City: Sheed Andrews and McMeel, [1962] 1978), pp. 1–9.

On this process, see Hans-Hermann Hoppe, “Book Review ofMan, Economy, and Liberty,”Review of Austrian Economics 4 (1990): 257–58.

Hoppe,The Economics and Ethics of Private Property, pp. 232–33.

Cordato,Welfare Economics, p. 44.

That these circumstances of action at any point in time depend on past action is clear; but this fact does not result in an infinite regress or indeterminacy since the starting point of the free market is self-ownership.

Cordato's charge, that “Rothbard's conclusions [about the welfare properties of the free market] would only hold in an error-free world of perfect knowledge, where expectations necessarily coincide with results,” is entirely unfounded. Cordato,Welfare Economics, p. 43. This charge is more suitably made against the New Welfare economics.

Ibid.,Cordato's charge, that “Rothbard's conclusions [about the welfare properties of the free market] would only hold in an error-free world of perfect knowledge, where expectations necessarily coincide with results,” is entirely unfounded. Cordato,Welfare Economics, p. 44. Professor Rothbard's discussion of entrepreneurship is inMan, Economy, and State (Auburn, Ala.: Ludwig von Mises Institute, [1962] 1994), pp. 5–6, 55–56, and 463–69.

Cordato,Welfare Economics, p. 43.

Cordato himself criticizes the New Welfare economics for requiring both interpersonal and inter-temporal utility comparisons to implement Pareto Optimality. Cordato,Welfare Economics, pp. 6–7. Also, discussing his own concept of demonstrated preference, he says, “prefereces that are revealed at one point in time cannot be assumed to remain constant over time.” Ibid., Cordato himself criticizes the New Welfare economics for requiring both interpersonal and inter-temporal utility comparisons to implement Pareto Optimality. Cordato,Welfare Economics, p. 59. While it is impossible to say anything on demonstrated preference grounds about theex post, subjective profit or loss of a sequence of actions, it is possible to calculate the monetary profit or loss of the specialized entrepreneurex post, as shown above. Even in the case where a specialized entrepreneur earns profit (loss) from a sequence of actions, however, it is not possible to say that hisex post utility is greater (less) than thatex ante. Cordato makes this error in his example of an individual who expends resources in a free market pursuing a goal, yet fails to reach it, when he concludes, “clearly he would have experienced a loss in utility.” Ibid.,Cordato,Welfare Economics, p. 43. Such a statement presupposes the ability to make inter-temporal utility comparisons.

Ibid.:Cordato,Welfare Economics, 43. On this criticism of Cordato, see Gordon, “Toward a Deconstruction,” p. 105.

Murray Rothbard,Power and Market (Kansas City: Sheed Andrews and McMeel, 1970), pp. 18–20. David Gordon also makes this point in “Toward a Deconstruction,” p. 105.

Cordato,Welfare Economics, p. 43.

Consider the analogy of government taxing a person's income. At the time the tax is paid, under duress, the person is made worse off than otherwise. After the tax is paid, he will adjust his action to the new circumstances, including this aggression, in the way he finds most preferable. That he does so is no refutation of the Pareto-Inferior nature of the interaction between the tax-man and himself.

This is analogous to the distinction Professor Rothbard makes when discussing the difference between individual utility and total utility, as the aggregation of the marginal utilities of units of a stock, and the marginal utility of different-sized units. Total utility is an illegitimate, cardinal concept which must be rejected. As he points out, what is marginal, in cardinal terms, is the unit of the stock, not the utility obtained by its possession. See Rothbard, “Toward a Reconstruction,” pp. 234–35. Perhaps this definition of social welfare will satisfy those who have asked explicitly for one. See, Gary North, “Why Rothbard Will Never Win the Nobel Prize,” inMan, Economy, and Liberty, Block and Rockwell, eds., p. 105.