G. L. S. Shackle on Linear Programming and the Theory of the Firm (1961)

G. L. S. Shackle’s review of Kenneth E. Boulding and W. Allen Spivey’s Linear Programming and the Theory of the Firm combines admiration for mathematical exposition with resistance to the idea that economic decision can be reduced to calculation. Its principal distinction is between mathematics as a lucid, practically valuable discipline and mathematical technique elevated into a comprehensive philosophy of rational behaviour. Shackle praises the book’s strongest contributions while questioning its packaging, editorial coherence, and claims to methodological novelty. The review moves from Spivey’s mathematical pedagogy through Boulding’s reflections on uncertainty to the relationship between marginal analysis and mathematical programming, before placing these techniques within a longer history of mathematical economics.

Spivey’s chapter on basic mathematical concepts supplies the review’s initial standard of excellence. Shackle suggests that readers might value it independently of its application to linear programming: its achievement lies in making mathematics intelligible without sacrificing precision or elegance.

It is beautifully done, with that detached, unassuming completeness and economy of statement which marks the writing of the real mathematician.

“Style” here means more than attractive prose. Completeness and economy are intellectual virtues: an exposition should provide what understanding requires without unnecessary machinery. This praise also establishes the basis of Shackle’s dissatisfaction with the book’s construction. The outstanding mathematical chapter might have supported a tidier and cheaper work devoted simply to explaining linear programming and its prerequisites. His opening conceit of Spivey’s “jewel” wrapped in softer material makes the reservations inseparable from admiration for the strongest contribution.

Boulding’s introduction matters for a different reason. Shackle places it alongside The Image and A Reconstruction of Economics, portraying Boulding as an imaginative nonconformist whose departures from conventional economics have not received their due. He values the former’s expansive vision of human affairs and the latter’s attempt to reconstruct economic theory through stocks rather than flows, while distinguishing the excitement of that idea from its less striking execution. This background prepares the reader for Boulding’s challenge to a single criterion of rational conduct under uncertainty.

Shackle takes that challenge as an attack on the assumption that rules can infallibly prescribe action despite incomplete information. The existence of several systematic patterns of behaviour does not eliminate decision: choosing among those patterns itself requires another decision.

Can it be that Professor BOULDING is here using the word decision to mean something other than the doing of sums and reading off the answer?

The irony identifies the review’s conceptual centre. Calculation can yield an answer within a framework, but selecting the framework need not itself be another calculation. Shackle likewise welcomes Boulding’s acknowledgment that theories of behaviour encounter questions of free will and determinism. His mock alarm at economics becoming entangled with metaphysics exposes the narrowness of treating the discipline as an exclusively arithmetical means of achieving given objectives. The review does not develop a separate theory of uncertainty; it singles out Boulding’s remarks as unusually penetrating limits on methodological confidence.

Returning to Spivey, Shackle makes several precise criticisms. An interrupted explanation of counting, a misleadingly divided equation, and a mistaken mathematical symbol blemish an otherwise exemplary exposition. These are consequential because the chapter’s prevailing clarity creates unusually high expectations. His larger regret is that Spivey does not make fuller use of matrix algebra. A modest extension could, he argues, have produced an excellent independent treatment of vectors, matrices, and determinants, freed from an exclusively linear-programming orientation. He nevertheless finds Spivey’s subsequent account of programming lucid and patient, especially in its use of three-dimensional diagrams to engage visual understanding.

The discussion of Yuan-Li Wu and Ching-Wen Kwang’s comparison of marginal analysis and mathematical programming brings practical usefulness into sharper focus. Shackle praises their economical prose and their explanation of perfect competition, although he notes that an elementary programming example takes several pages to reach an immediately apparent result. Their concluding qualification earns his strongest approval:

'Our analysis has therefore demonstrated that, in all these cases, the familiar concepts of the marginal analysis can be applied to indicate the logical properties of the optimum solution. On the other hand, the traditional tools of marginal analysis may fail to provide a convenient method of arriving at the optimum solution. The availability of techniques for the numerical solution of economic and business problems is indeed the basis of the importance of mathematical programming'.

The distinction is between characterizing an optimum and conveniently finding it. Mathematical programming can supply important numerical procedures without displacing the familiar concepts that explain an optimum’s logical properties. Shackle commends this as professional modesty and honesty: practical computational achievement needs no inflated claim of conceptual revolution.

The closing historical perspective extends the same argument. Invoking mathematical economists from De Ceva through von Thünen, Cournot, and Edgeworth, Shackle presents numerical and geometrical methods as the cumulative work of a longstanding discipline.

But to label a very various collection of methods with a high sounding name, and to suggest that it then constitutes a radical novelty, is less desirable.

He explicitly accepts “linear programming” as a justified term; his objection concerns exaggerated novelty elsewhere in econometric vocabulary. The review thus defends mathematics while resisting its conversion into intellectual branding or an exhaustive account of choice. Its final demand that an editor should edit returns to the book’s uneven organization: brilliant contributions deserve equally careful presentation.