¹ North, Douglass, “International Capital Flows and the Development of the American West,” Journal of Economic History, 16 (Dec. 1956), 493CrossRefGoogle Scholar; see also, North, Douglass, The Economic Growth of the United States, 1790–1860 (New York, 1966).Google Scholar

² Haites, Erik, Mak, James, and Walton, Gary, Western River Transportation (Baltimore, 1975), ch. i.Google Scholar

³ Mak, James and Walton, Gary, “Steamboats and the Great Productivity Surge in River Transportation,” Journal of Economic History, 32 (Sept. 1972), 623CrossRefGoogle Scholar; see also, Haites, Mak, and Walton, Western River Transportation, ch. v.

⁴ Haites, Mak, and Walton, Western River Transportation, ch. iv; see also, Hunter, Louis C., Steamboats on the Western Rivers (Cambridge, 1949), pp. 377, 659.Google Scholar

⁵ Hunter, Steamboats on the Western Rivers, 377.

⁶ Walters, A. A., “Production and Cost Functions: An Econometric Survey,” Econometrica, 31 (Jan.-Apr. 1963), 52.CrossRefGoogle Scholar

⁷ The data were uncovered by Jeremy Atack, Fred Bateman, James Foust, and Thomas Weiss in the course of their research in nineteenth century U.S. manufacturing. The sample represents 7 percent in number and 10 percent in tonnage of all steamboats in operation on the western rivers in 1850.

⁸ One vessel, the Uncle Sam (741 tons), was built to carry only freight and was described as the “pioneer” freight boat. In general, steamboats carried both passengers and freight. As Hunter noted, “Once established, the practice of carrying passengers and freight together was continued because conditions proved unfavorable to specialization.” Hunter, Steamboats on the Western Rivers, 344–45.

⁹ Lytle, William M., Merchant Steam Vessels of the United States, 1807–1868, publication no. 6 (Mystic, Conn.: The Steamship Historical Society of America, 1952)Google Scholar; and Supplements no. 2 and no. 3 (1954 and 1958).

¹⁰ Mak, Haites, and Walton, , Western River Transportation, Table 13 and The Louisville Daily Journal, 20 (1850).Google Scholar

¹¹ Lave, Judith R. and Lave, Lester B., “Hospital Cost Functions,” American Economic Review, 60 (1970), 379–95.Google Scholar

¹² To the extent that the observed average cost of operating a particular steamboat may also reflect “mistakes in judgment” of the individual operator, an error term “e” has been added.

¹³ This is equivalent to converting passenger output to equivalent ton-miles of freight output. Steamboats generally carried both deck and cabin passengers. The recorded passenger revenue is not divided between these categories. And we do not have deck and cabin passenger fares for most routes. Hence, there is no alternative means of calculating output.

¹⁴ The Louisville Daily Journal, 20 (1850) gives a weekly summary of steamboat freight rates between Louisville and various destinations on the western river system. Because rates varied widely, and in inverse relationship to the stage of the river during the navigation season (see also, Haites, Mak, and Walton, Western River Transportation, ch. vi), average freight rates (in cents/ton mile) were calculated for the New Orleans (.324), St. Louis (.447), Cincinnati (1.343), and Tennessee River routes (1.733) by averaging weekly rates for “pound freight” during the peak shipping season—i.e., April 8 to June 4, 1850. The freight rate for the Wabash River route (1.357) was calculated from Hunter, Steamboats on the Western Rivers, p. 659. The calculated freight rates confirm Hunter's observation that rates were higher on the short and on the tributary routes compared to those on the distance trunk routes.

¹⁵ Haites, and Mak, , “Steamboating on the Mississippi: A Study of a Purely Competitive Industry,” Business History Review, 45 (Spring 1971), Table A2, 72–73Google Scholar. Operating months varied from 7 to 12 months.

¹⁶ Fogel, R. W. and Engerman, S. L., Time on the Cross (Boston, 1974), Vol. I, p. 170Google Scholar, report that “on average, slaveowners earned about 10 percent on the market price of their bondsmen. Rates of return were … approximately the same across regions … and over the period from 1820 through 1860, there was no secular trend in the level of profits away from the average.” They also indicate that this rate of return was equal to, or greater than, that obtained in a variety of non-agricultural enterprises during the antebellum period.

¹⁷ The annual payment is calculated from the expression i(1 + i)ⁿ/[(1 + i)ⁿ − 1] where i is the interest rate (10%) expressed as a decimal and n is the period of the investment. The average lifespan (n) was 6.36 years for vessels on the New Orleans route, 6.50 years for vessels on the St. Louis and Cincinnati routes, 5.20 years on the Tennessee route and 3.33 years on the Wabash River route. The corresponding annual payments per dollar invested are .22000; .21656; .25588; and .36774.

¹⁸ The 9 percent figure is based on estimates for the Louisville-New Orleans trade and thus overstates the working capital requirements on the shorter routes.

¹⁹ See Haites, Mak and Walton, Western River Transportation, pp. 157–158.

²⁰ For comparison, we also estimated these cost relations linearly. Since the results are similar, we display only the log-linear results.

²¹ This statement is true only over the range of vessel sizes observed. At any time, the optimum size distribution of steamboats was both a function of the market(s) and the state of technology. Given these constraints, it is conceivable that vessels could be built and assigned to routes that were either too large or too small for optimum efficiency; and that at the margin, some entrepreneurs would actually make the mistake of building such vessels. One such mistake might well have been the John Simpson, the largest vessel on the Tennessee River route. At 228 tons it was two standard deviations above the mean tributary (i.e., over the entire manuscript sample) vessel size of 149 tons.

²² Whether a “trade” is long-distance or short-distance is somewhat arbitrary. The vessels on the short-distance Cincinnati route may well have been exceptions to the rule. The two vessels were 375 and 473 tons respectively. Three other vessels reported in the 1850 manuscript census which operated on short-distance trunk routes were below 300 tons each. The average size of the 14 tributary river steamboats was 149 tons, while the average for the St. Louis and New Orleans trade was 397 tons.

²³ Assuming all operators would have been equally adept at operating vessels of the optimum size.

²⁴ See also, Friedman, Milton, “Comment,” in Business Concentration and Price Policy (Princeton, 1955), pp. 230–38.Google Scholar

²⁵ Mak and Walton, “Steamboats and the Great Productivity Surge in River Transportation.”

²⁶ The “quotes” are from Hunter; see the introduction and n. 5 (above).

²⁷ The absence of economies of scale provides support for the validity of the estimates of steamboat costs presented on Haites, Mak, and Walton, Western River Transportation (Appendix C) and our earlier work. Some of those cost estimates were made by pro-rating observed cost data for the same time period by vessel size, hence implicitly assuming no economies or diseconomies of scale.