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

elationships in the same manner in which these were performed by
Howe for the incomplete tow process function. Howe found decreasing
..-vturns to scale for his tow process function, i.e., cquiproportionate
incrcnves in the barge and towboat inputs resulted in less than pro-
po .rtionate increases in output. While similar computations are not
made above, there is no reason to believe Howe's result is changed -.' '
In :act, it deems likely that a gleater degree of decreasing returns
to scale would be exhibited by the linehaul process function indlu-
sive of delays, for delay time is in all cases positively related to
the number of barges in the tow. Making and breaking tow require
more time the greater the size of the tow, and a larger towboat would
not likely help very much in reducing that time (although this con-
jecture is 'net investigated in the preceding analysis). Likewise,
locking time will-increase as tow size increases; this is especially
true where -double and triple locking would be required from increases
in tow size. Finally, even miscellaneous delays are likely to be
greater as tow size increases. It was found that miscellaneous de-
lay time is proportionate to running time, but running time is likely
to be greater for large tows than for smaller ones since the former
will travel glore slowly .. This may be thought to be offset to 'some
extent by large towboats but, since Howe found decreasing returns to
scale and diminishing returns to the towboat input, this offset is .
not likely to exist. All in all, it seems reasonable to say.that the
tow process function (including delays) will exhibit decreasing re-
turns to scale. It is also likely, based on the above discussion,
that Howe's conclusion of a flat long-run unit cost curve over a
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