Natural Images in Economic Thought: Markets Read in Tooth and Claw.

The book collects twenty papers from a conference on "Natural Images in Economics" held at the University of Notre Dame in September 1991. Mirowski opens part one with a typology of ways to understand the relation of "the Natural" and "the Social," and classifies some of the papers within it. Klamer and Leonard then explicate the concept of "metaphor" that subsequent papers employ.

Part two studies mathematical formalism and physics metaphors. Cohen argues that, before nineteenth century energy physics, attempts to construct economics with the Newtonian mechanics paradigm failed. Grattan-Guinness wonders why linear and nonlinear programming and locational equilibrium formulations in 1820s French mechanics took 120 years to emerge as full blown research areas. Bausor asks why recent use of mathematical methods of qualitative dynamics succeeded in fluid mechanics but failed in economics. Porter interprets the evolution of nineteenth century economics as a triumph of an ideal of formal mathematical rigor over one of practical engineering quantification.

Alborn opens part three by exploring problematic mechanical and biological images of circulation in the Victorian money market, and relates them to difficulties in that period's economic history. White examines how Jevons incorporated questionable notions, from a mechanics-influenced physiological psychology, into his economics. Kingsland argues that Lotka's mathematical models in biology had little impact there, but influenced Simon's construction of an influential economic theory.

Part four considers biological metaphors. Christensen studies natural science metaphors in Quesnay's economics. Hutter traces an organism metaphor for society through German economic thinkers. Schabas doubts that Darwin influenced Marshall, Mill, and later economists much, but Limoges and Menard think that his reading of Darwin helped Marshall shape his notion of the division of labor. Niman claims that biological analogies could transform the theory of the firm in a positive way, while Rosenberg argues that Darwin's biology can't help economics much. Hodgson maintains that, though he sought to draw on evolutionary biology, Hayek's thought is difficult to reconcile with Darwin's theory.

Part five focuses on how economists construct "the Natural" historically. Mirowski looks at examples of reconstruction of "the Natural" at moments of crisis. Henderson sketches how economics gained a place in the hierarchy of the sciences in the nineteenth century. Murphy uses concepts of nature, custom, and stipulation to explore the division of labor. Moore considers alternative approaches to feminist accounting theory that would construct "the Natural" in different ways.

In his first Natural Images essay, Mirowski suggests that critics of More Heat Than Light [2] thought that "[t]he putative author of this problematic text could not seem to make up his mind whether or not economics ought to imitate physics" [p. 10]. In fact, his earlier article [1] had the good historical insight that physics helped to shape microeconomics, and the later book [2] elaborated that insight. However, isn't their use of a bad analogy to conclude that "[n]eoclassical economic theory was appropriated wholesale from mid-nineteenth century physics; utility was redefined so as to be identical with energy" [1, 366], what made them both problematic texts?

How did Mirowski portray nineteenth century physics to begin his analogy?

Consider a point-mass displaced a distance q(= AB) in a two-dimensional plane . . . by a force vector F. The force vector can be decomposed into its perpendicular components, F = i[F.sub.x] + j[F.sub.y] . . . Similarly, the vector of displacement can also be decomposed into its components, dq = idx + jdy. The work done . . . is defined as . . .:

[Mathematical Expression Omitted].

Energetics redefined the change in [mv.sup.2] . . . to be the change in kinetic energy. The vector characterisation could then be translated into a single-valued scalar function, T. . . . Suppose that the above expression in the parentheses were an exact differential; in other words, there existed a function U such that:

[F.sub.x] = [Delta]U/[Delta]x; [F.sub.y] = -[Delta]U/[Delta]y; U = U(x, y).

This uniquely identified scalar function U was interpreted as the unobserved potential energy of the particle. Then it is the total energy of the particle, T + U, which is conserved through any motion of the particle. [1, 366-67]

So he conflated kinetic energy (1/2m[[absolute value of v.sup.2]], usually labelled T) with change in kinetic energy ([Mathematical Expression Omitted], usually labelled [Delta]T). He also confused the definition, work done [equivalent to] [integral of] ([F.sub.x]dx + [F.sub.y]dy) between limits B and A, with the nondefinitional relation, work done = [Delta]T. Thus Mirowski began by garbling nineteenth century physics.

How did he compare nineteenth century microeconomics to physics?

Simply redefine the variables of the earlier equations: let F be the vector of prices of a set of traded goods, and let q be the vector of the quantities of those goods purchased. The integral [integral of] F [center dot] dq = T is then defined as the total expenditure on these goods. If the expression to be integrated is an exact differential, then it is possible to define a scalar function of the goods x and y of the form U = U(x, y), which can then be interpreted as the 'utilities' of those goods. In exact parallel to the original concept of potential energy . . . Relative prices are equal to the ratios of the marginal utilities of the goods by construction . . . The mathematics . . . are the same in both instances [1, 368].

That is, let (q, T) be (particle position, kinetic energy) in physics and (consumer good quantities, total expenditure) in economics, and ([F.sub.x], [F.sub.y]) be ([p.sub.x], [p.sub.y]). Then the definition of total expenditure in economics, [integral of] ([p.sub.x]dx + [p.sub.y]dy) = T, is like the garbled physics relation: [integral of] ([F.sub.x]dx + [F.sub.y]dy) between limits B and A = T. Also, if [exists] a utility function U(x, y) s.t. [p.sub.x] = [Delta]U/[Delta]x and [p.sub.y] = [Delta]U/[Delta]y then [[p.sub.x]/[p.sub.y]] = [[Delta]U/[Delta]x]/[[Delta]U/[Delta]y] follows and the mathematics of physics and economics seem similar. So Mirowski garbled nineteenth century microeconomics into something resembling his garbled nineteenth century physics.

In fact, physicists assumed that particle position is a function of time t and that for some forces [exists] a potential energy function U(x(t), y(t)) s.t. [F.sub.x] = -[Delta]U/[Delta]x and [F.sub.y] = -[Delta]U/[Delta]y. For such forces they assumed that nature minimizes [integral of] [T(dx(t)/dt, dy(t)/dt) between limits [t.sub.2] and [t.sub.1] - U(x(t), y(t))]dt, from which (work done = [Delta]T) follows. In contrast, economists assumed that consumption occurs in a given time period with given prices but never that [exists] a utility function U(x, y) s.t. [p.sub.x] = [Delta]U/[Delta]x and [p.sub.y] = [Delta]U/[Delta]y. Instead, the physicists' potential energy function (differentiable with respect to particle position components) suggested to economists that they should make Bentham's utility a differentiable function of consumer good quantities. Then economists assumed that markets allow a consumer to maximize U(x, y) (in keeping with Bentham's "greatest good for the greatest number") subject to a budget constraint, from which [[p.sub.x]/[p.sub.y]] = [[Delta]U/[Delta]x]/[[Delta]U/[Delta]y] follows.

So the mathematics of the two theories differ. One theory uses an exact differential while the other does not. Both theories involve optimization but their optimands differ, and one optimization is constrained while the other is not. One theory entails minimization and the other maximization. The relation (work done = [Delta]T) plays a different role in physics than does the total expenditure definition in economics. Total expenditure is certainly not similar to kinetic energy, and utility is identical to neither potential energy nor total energy. Mirowski misconstructs an analogy.

In his second Natural Images essay, Mirowski insightfully argues that when sociobiologists developed a potential rival to microeconomics in the 1970s, economists responded with animal experiments. One version of consumer theory holds that budget constrained consumers maximize utility functions even if they are not conscious of doing so. Animal experimenters sought to bolster this claim by establishing that budget constrained rats (presumably lacking self consciousness) choose consumption quantities so as to maximize utility functions. They offered rats two commodities - Tom Collins mix and stale root beer - and let the animals choose quantities by pressing different buttons. The researchers took income (I) as "a limited number of level presses" and price as "the size of the cup of liquid" [p. 464].

From Mirowski's fuzzy account it appears that what the animal experimenters took for quantities, prices, and income did not satisfy a budget constraint of the form [p.sub.x]x + [p.sub.y]y = (or [less than or equal to])I. If that is so, were their experiments even germane to consumer theory? If rat quantity choices were not really budget constrained, how could the experiments establish that budget constrained rat quantity choices maximize utility functions? Mirowski does not ask these questions. Instead he plays on the double meaning of "trial" to liken the animal experimental trials to some medieval European legal proceedings in which animals were put on trial for harming people. Isn't this analogy an interpretive reach?

His Natural Images coauthors do not imitate Mirowski's proclivity to mar good historical insights with bad analogies. Many of their essays exemplify how history can help to understand the foundations of economics. The book is a good reference for teachers of the history of economic thought or philosophy of economics. Weak editing does mar two pieces that resemble notes for, rather than finished, essays.

Leland G. Neuberg New York University 

References

1. Mirowski, Philip, "Physics and the 'Marginalist Revolution'." Cambridge Journal of Economics 1984, 8, 361-79. 2.

2. -----. More Heat Than Light. New York: Cambridge University Press, 1989.