an early application of the average total cost concept

American Economic Association

An Early Application of the Average Total Cost ConceptAuthor(s): F. M. SchererSource: Journal of Economic Literature, Vol. 39, No. 3 (Sep., 2001), pp. 897-901Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/2698317 .

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Journal of Economic Literature Vol. XXXIX (September 2001), pp. 897-901

An Early Application of the Average Total Cost Concept

F. M. SCHERER'

E CONOMISTS BEGAN to conceptualize average total cost functions during

the early decades of the twentieth century. But a century before, a German music publishing firm calculated and used in its internal decision making output-dependent average cost estimates for two methods of printing sheet music. This note describes that early experience and juxtaposes against it the relatively late emergence of the ATC curve in the formal literature of economics.

1. The Early Application

In 1796 34-year-old Gottfried Chri- stoph Hartel purchased for 106,000 German Reichsthalers2 (hereafter, Thalers) the Leipzig book and music publishing business of Christoph Gottlob Breitkopf, which under a part- nership contract concluded a year earlier had been renamed Breitkopf & Hartel. University-educated in law, po- litical ;science, and humanities, Hartel and his business manager, Johann Christian Schulze, began to analyze quantitatively virtually every aspect of the firm's operations-sales by type of publication and region, inventories,

physical assets, productivity of the various printing processes, and most impor- tantly for our immediate purposes, the unit costs of alternative printing methods. Most of the firm's original records were destroyed during World War 2, but extracts from those early analyses are reproduced in the first volume of a detailed company history (Hase 1917).

At the time there were two main processes for printing sheet music: engraving, and printing with movable type. With engraving, a skilled engraver scored music staff lines onto a smooth flat copper or (less expensive but less durable) pewter plate and then used punches to indent into the plate the various notes, key signatures, slurs, an- notations, and text. On average, this task required from six to eight hours of careful labor. After the engraved plate (from which two standard-size sheets could typically be printed) was locked onto a flat-bed press, it was inked and wiped with a cloth to remove surface ink and leave only the ink in the engraved recesses. A sheet of paper was pressed upon the plate to receive the remaining ink and then removed, after which the process was repeated to print another sheet. To produce typeset music using a process greatly improved by Johann Gottlob Immanuel Breitkopf in the 1750s, a comnlex matrix of note.

1 Harvard University emeritus; visiting professor, Princeton University.

2 At the time, this sum amounted to the annual wages of approximately 500 journeymen workers.

897



898 Journal of Economic Literature, Vol. XXXIX (September 2001)

24

22

20

18

16

, 14

,)12 r D 0 Engraved| bJO

10 s| -- Typeset |

6

2

0 100 200 300 400 500 600 700 800 900 1000

Quantity printed

Figure 1. Plots of the Data on Average Costs for Engraved and Typeset Sheet Music (Breitkopf & Hartel, circa 1800)

symbol, and line fragments was assem- bled by a skilled compositor. After being locked in a frame, the matrix was installed on a printing press bed and inked, with the music being impressed directly upon the paper from the raised type, omitting the intermediate plate- wiping step required for engraved music. Mainly because the wiping step was unnecessary for typeset music, more sheets could be produced per hour on an 1800-vintage press, so the marginal cost of producing typeset music was lower than for engraved music, although the quality of the engraved products tended to be superior for notationally complex compositions.

Plainly, the printing processes en- tailed fixed setup costs and then the variable costs associated with labor, paper, ink, wiping cloths, and spoilage (which averaged about one-third of the

printed sheets). At some time between 1800 and 1805, Hartel prepared a detailed tabular comparison of the average total costs (excluding general overhead costs, shipping, and composers' honoraria) per printed sheet for the two methods at ten matched output levels.3 His tabular data (Hase, p. 225) are plotted graphically in figure 1, with each solid or open circle corresponding to a reported data point. When the reported average costs are multiplied by the associated quantities (my computation, not Hartel's), the total cost curve for engraved music (assuming pewter plates) is found to be an almost perfect straight line, implying a fixed setup cost of 900

3Hase states unambiguously (p. 225) that the tables were constructed by Hartel "to form the basis for a general accounting of music publishing costs and proceeds" (my translation), not ex post by Hase for his history.



Scherer: An Early Application of the Average Total Cost Concept 899

Pfennigs per sheet (Bogen) and a constant marginal cost of 5 Pfennigs per sheet.4 The fit is so perfect, with a standard error of regression amounting to only 31 Pfennigs, that one is induced to infer that Hartel actually plotted and smoothed the data graphically, although no such graph survives. For typeset music the total cost function is only approximately linear, with a standard error of 88 Pfennigs in a linear regression and a visible indication of declin- ing marginal costs as volume increases. Recognizing nonlinearity, marginal cost for the first 100 to 200 sheets produced using movable type appears to be 4.25 Pfennigs, with an extrapolated setup cost of 750 Pfennigs. In the range of 800 to 1000 sheets, marginal cost falls to 2.50 Pfennigs.

From his analyses Hartel is reported to have drawn three main action impli- cations. For one, assuming on grounds that are unclear a net selling price of 15 to 18 Pfennigs per sheet after deducting agents' margins, shipping costs, and un- sold inventory losses,5 he determined that in order to defray general overhead costs and make a profit on works with no early assurance of sales exceeding 300 units, he could at most pay composers a fixed honorarium of less than 3 to 4 Thalers per sheet, or (at sales of exactly 300) 2.88 to 3.84 Pfennigs per printed copy. These calculations evi- dently underlay his well-documented6 bargaining with Ludwig van Beethoven,

causing Hartel to lose out to other pub- lishers for early Beethoven works (for which sales volumes were particularly uncertain), to gain Beethoven's favor in publishing many of his middle works (including the 5th and 6th (Pastoral) symphonies), and then to lose out again when Beethoven escalated his honorarium demands after inflation eroded the real value of the annual pension he was receiving from three Viennese nobles.

Second, Hartel concluded that in order to achieve his profit goals, he would have to reduce the number of de- fective copies printed-i.e., increasing X-efficiency. Whether he succeeded is not documented; the best evidence is his firm's survival over more than two centuries.

Third, during the 1790s a new means of printing music, lithography, was in- vented. Hartel communicated exten- sively with agents of the inventor between 1799 and 1802, and in 1806 began, following his own experiments, to use the new process commercially. Comparative volume-dependent calculations carried out in 1814 revealed both setup and marginal costs with the new lithographic process to be substan- tially lower than with pewter engraving. From that year on lithography displaced engraving to an increasing degree at Breitkopf & Hartel, and in 1822 it was decided that any further engraved works, especially those requiring complex notation, would be produced using either already engraved or melted-down pewter; no new pewter would be purchased. Lithography would be favored over movable type for all inexpensive and quickly sold works.

Knowledge of how printing costs var- ied with volume was also useful in another kind of decision outside the scope of Hartel's business-choosing whether to reproduce a musical manuscript me- chanically or to have copies made by

4 At the time, there were 12 Pfennigs in a Groschen and 24 Groschen to a Thaler, or 288 Pfennigs per Thaler. During the late 18th century a Thaler exchanged for approximately 0.25 English pound sterling, although exchange rates fluctuated widely during the early years of the Napoleonic wars.

5 My conjecture from other evidence is that a much higher price, given the absence of copyright, would have induced rampant piracy.

6 For letters from Hartel, see Hase, pp. 161-78; from Beethoven, see Kalischer (1909), vol. I, various.



900 Journal of Economic Literature, Vol. XXXIX (September 2001)

hand, at nearly constant but (compared to printing at substantial volumes) high average cost, by a professional copyist. However, from the records of Giovanni Ricordi, principal publisher of Giuseppi Verdi's operas, we have evidence of so- phisticated choices that recognized the comparative advantage of these alternative processes. After a copyright law was adopted for much of Italy in 1840, Ricordi actively pursued a business of renting or selling opera scores to pro- vincial Italian theaters. For the string section and chorus parts, on which numerous copies were required, he engraved and printed the sheet music, but for the wind and soloist parts, on which the low quantities would entail high printing costs, the music was copied by hand (Jensen 1989, pp. 34 and 90).

2. The State of Economic Thought

Hartel's economic analyses antici- pated by two-thirds of a century the frontiers of economic analysis. The clas- sical economists such as Adam Smith, David Ricardo, Robert Turgot, and John Stuart Mill were not inclined to reason in functional terms, let alone in terms of specific volume-dependent cost functions. Augustin Cournot (1838) demonstrated a deep understanding of total cost and its derivatives, but did not consider average total costs as a decision-making tool. His U.S. contem- porary Charles Ellet Jr. (1839) esti- mated average costs per ton-mile as back- ground for a theory of railroad and canal profit maximization under monop- oly, duopoly, and vertically stacked mo- nopoly, but treated his cost parameters as constants and not as volume-dependent.

The first known volume-dependent average cost function mentioned in the formal. literature of economics was: by another railroad engineer, Austrian Wil-

helm von Nordling (1886).7 Combining time series and cross-section data, he plotted total costs as a function of railroad volume and drew theoretically sound inferences about fixed, average, and marginal cost relationships.

In the important theoretical develop- ments emerging toward the end of the 19th century, marginal cost functions continued to be emphasized, and average costs neglected, by neo-classicists such as Leon Walras, Vilfredo Pareto, Francis X. Edgeworth, and (in his Principles of Economics, 1890) Alfred Marshall.

However, in the third edition of his Economics of Industry (1899, p. 231), Marshall presented a three-output table of hypothesized average total costs and observed that it illustrates the starting point of many interesting problems, but failed to follow through with a geomet- ric average total cost function. Irving Fisher's principles textbook (1912) sup- plemented diagrammed marginal cost and supply curves with a correct verbal discussion (p. 327) of the short-run relationships between average cost and volume when fixed costs are incurred. The first edition of Richard T. Ely's Outlines of Economics (1893) contained no cost curves, but the (coauthored) third: (1920) edition had diagrams (p. 176) showing average costs falling with volume up to thresholds at which addi- tional fixed costs must be sunk. A simi- lar but smoothed diagrammatic version appeared in a 1921 article by Frank Knight.

From these scattered and primitive beginnings, and with the "empty boxes" colloquy of the 1920s as a focusing mechanism, the average total cost function and its relationship to marginal and fixed costs emerged fully developed in articles published between 1928 and

7 Its priority is asserted in Hans Staehle (1942).



Scherer: An Early Application of the Average Total Cost Concept 901

1931. Although the concept is absent from his famous 1924 treatise, A. C. Pigou presented a well-articulated short-run ATC curve in a 1928 article. Definitive refinements followed in articles by Roy Harrod (1930, 1931) and Jacob Viner (1931). Viner claimed priority by "presenting charts such as those contained in this article" to his students "for a long period antedating the writings" of competing contempo- raries. However one judges the priority contest, from that time on average cost 'functions commanded a prominent position alongside marginal cost curves in theories of the' firm.

Afterword

Art imitates nature. The concept of volume-dependent average costs began to enter the mainstream of economic theory only as the twentieth century dawned; it was fully integrated three decades later. The received economic literature traces the first real-world application of the concept to the 1880s. My example from the field of music publishing turns the practical application clock back by eight decades. Gottfried Hairtel did not try to extend his cost calculations into a systematic theory, but he used them to choose among technical alternatives and to estimate the rents out of which he could pay honoraria. Earlier examples of applications may exist. Challenges are invited.

REFERENCES

Cournot, Antoine Augustin. 1838, 1971. Recher- ches sur les principes mathe4matiques de la the'orie des richesses. Reprint of 1927 ed., trans. Nathaniel T. Bacon. NY: Kelley.

Ellet, Charles Jr. 1839. An Essay on the Laws of Trade in Reference to the Works of Internal Im- provement in the United States. 1966 reprint, NY: Kelley.

Ely, RichardT. 1893. Outlines of Economics. NY: Macmillan.

Ely, Richard T.; Thomas S. Adams, Max 0. Lorenz and Allyn A. Young. 1920. Outlines of Econom- ics, 3rd rev. ed. NY: Macmillan.

Fisher, Irving. 1911. Elementary Principles of Eco- nomics, 3rd ed. NY: Macmillan.

Harrod, Roy F. 1930. "Notes on Supply," Econ. J. 40:158, pp. 232-41.

. 1931. "The Law of Decreasing Costs," Econ. J. 41:164, pp. 566-76.

Hase, Oskar von. 1917. Breitkopf & Hdrtel, vol. I. 1968 reprint, Wiesbaden: Breitkopf & Hartel.

Jensen, Luke. 1989. Giuseppe Verdi and Giovanni Ricordi with Notes on Francesco Lucca. NY: Garland.

Kalischer, Alf C. 1909. Beethoven's Letters: A Critical Edition with Explanatory Notes. Trans. J. S. Shedlock. Freeport: Books for Libraries Press.

Knight, Frank. 1921. "Cost of Production over Long and Short Periods," J. Polit. Econ. 29:4, pp. 304-35.

Marshall, Alfred. 1899. Economics of Industry, 3rd ed. London: Macmillan.

Nordling, Wilhelm von. 1886, "Le Prix de Revient des Transports par Chemin de Fer," Annales des Ponts et Chause'es, 6th Serie, Tome XI, pp. 292-303.

Pigou, Arthur Cecil. 1924. Economics of Welfare. London: Macmillan.

. 1928. "An Analysis of Supply," Econ. J. 38:149, pp. 238-57.

Staehle, Hans. 1942. "The Measurement of Statis- tical Cost Functions: An Appraisal of Some Recent Contributions," Amer. Econ. Rev. 32, pp. 321-33.

Viner, Jacob. 1931. "Cost Curves and Supply Curves," Zeitschrift far Nationalokonomie 3:1, pp. 23-46.



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