Maurice Allais' well-deserved Nobel Prize fortuitously brought to our attention an injustice inadvertently done him, to which we were unknowing accessories. For years the literature has ascribed to us the parentage of the transactions-cost model of optimal cash balances, with its notorious square-rootformula derivedfrom inventory theory.' Recently, we found that its essence is contained in Allais' 1947 Economie et Interet (pp. 238-41). As Jacob Viner used to say, no matter to what source the origin of an economic proposition is ascribed, someone is sure to come up with an earlier one. In any event, here is a translation of the pertinent passages. Allais describes the model in footnotes (11) and (12) to the following text (pp. 238-41):

In the literature, comparisons between absolute levels of productivity in different industries occur frequently. This paper explores the meaning and possible significance of such measures. Prices must be used to permit the required comparison of the outputs of different industries. It is shown that base-year weights produce a valid measure of productivity growth but not of absolute productivity level. Current price weights do yield a valid index of absolute productivity but one that tends to be equal for all industries because of the general equilibrium mechanism that reallocates resources from low-productivity to high-productivity industries.

[Energy-production subsidies are, paradoxically, shown to be likely to increase U.S. dependence on imported oil. Standard studies of net energy yields are shown to be seriously biased upward for two reasons. First, many omit indirect energy inputs, which, our input-output calculation shows, probably causes large errors. Second, those studies all omit the energy opportunity costs of nonenergy inputs (e.g., the fuel substituted elsewhere for the labor used to produce energy). We prove that, absent externalities, any fuel-output subsidy which causes an otherwise unprofitable expansion must yield an incremental fuel output smaller than the increment in energy input plus the energy opportunity costs of other inputs.]

An empirical study applying the theory of scale economies and inter-product complementarity. Several recently formulated concepts of the theory of scale economies are examined with the aid of estimates of cost functions, using data for publishers of scientific journals. In one case the observations are shown to fall near the outer limits of the range of declining costs, implying that neither amalgamation nor breakup of firms will reduce total cost. In another case the observations fall well within the subadditive range, implying that amalgamation can provide savings. The study confirms the applicability of the new theory of scale economies.

An empirical study applying the theory of scale economies and inter-product complementarity. Several recently formulated concepts of the theory of scale economies are examined with the aid of estimates of cost functions, using data for publishers of scientific journals. In one case the observations are shown to fall near the outer limits of the range of declining costs, implying that neither amalgamation nor breakup of firms will reduce total cost. In another case the observations fall well within the subadditive range, implying that amalgamation can provide savings. The study confirms the applicability of the new theory of scale economies.

I. The problem, 547. — II. Cost of capital: whose opportunity cost? 548. — III. A few formal relationships, 549. — IV. A diagrammatic approach to cost of capital, 552. — V. Transactions costs and taxes in practice, 555. — VI. A few comments on the opportunity loci, 559. — VII. Characteristics of an optimal financial structure, 561. — VIII. The real marginal cost of debt and equity, 564. — IX. A measure of the cost of capital, 567. — X. Capital as a weighted average, 569. — XI. Conclusion, 571. — Appendix A, 571. — Appendix B, 575.