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Economists 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. Plainly, the printing processes entailed fixed setup costs and then the variable costs associated with labor, paper, ink, wiping cloths and spoilage. The first known volume-dependent average cost function mentioned in the formal literature of economics was by another railroad engineer. In the important theoretical developments emerging toward the end of the 19th century, marginal cost functions continued to be emphasized, and average, costs neglected, by neo-classicists. 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. His example from the field of music publishing turns the practical application clock back by eight decades.

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