Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

Since the function (7) is discontinuous in the barge inputs, it
was necessary to evaluate the function over a set of specified values
of all inputs. According to Howe, "these values cover farily well the
range of operating conditions found on the Ohio, Upper Mississippi,
Missouri, Illinois Waterway, and the Gulf Intracoastal Canal." (p. 30).
The set of derived relationships exhibits reasonable properties.
In particular it was discovered that, (1) both the tow boat and barge
inputs showed diminishing productivity (2) the tow shows "decreasing
returns to scale" which can be attributed to the waterway inputs, and
(3) "U-shaped" average cost curves, costs rising beyond some point
. . because speed reductions more than offset the effects of addi-
tional carrying capacity." (p. 36).
Howe recognized that his process function was not adequate for
describing the activities of a barge firm in organizing its traffic
into tows and in scheduling the movement of those tows across the
waterway. As was demonstrated by the process function, the point-to-
point operation of a tow was subject to decreasing returns to scale
due.to the limitations of the waterway. However, the firm " . . . may
experience constant returns because Of its ability to duplicate
individual operating units as total output grows." 7
Howe then turns to developing production functions for the barge
firm. Of particular interest is his discussion of how the capital
inputs should enter the production function. Howe argues that the
entire capital stock in barge transportation is not alwas used at any
one time. Observed current output is thus related to the portion of
the capital stock actually used. It is not related to the capital
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