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• release COST-BENEFIT ANALYSIS FOR INLAND NAVIGATION IMPROVEMENTS A Report Submitted to the U.S. Army Engineer Institute for Water Resources 206 North Washington Street Alexandria, Virginia 22314 by Econometrics Center Northwestern University Chicago, Illinois Under Contract Number DA49-129-CIVENG-65-11 Edited by Leon N. Mosses & Lester B. Lave Econometrics Center Northwestern University This document has been approved for public and sale; its distribution is unlimited. Copies may be purchased from: CLEARINGHOUSE for Federal Scientific and Technical Information Springfield, Virginia 22141 OCTOBER 1970 (Vol. 2 of 3) 111191#11 IWR Report 70-4
NORTHWESTERN UNIVERSITY AN ECONOMETRIC MODEL OF THE DEMAND FOR TRANSPORTATION A DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL . IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the degree DOCTOR OF PHILOSOPHY Field of Economics By JAMES P. STUCKER Evanston, Illinois August 1969
Page 1 and 2: c,q /kao, PROPERTY OF THF H S. GOVE
Page 3: INSTITUTE FOR WATER RESOURCES In 19
Page 7 and 8: ACKNOWLEDGMENTS LIST OF FIGURES •
Page 9 and 10: Figure FIGURES Page 3.1 Two-Market
Page 11 and 12: Table Page 4.12 Rail Rate Regressio
Page 13 and 14: Table 4.A.5 Rate Regression Rail Qu
Page 15 and 16: This paper presents an economic mod
Page 17 and 18: All transport modes are designed to
Page 19 and 20: CHAPTER II REVIEW OF THE LITERATURE
Page 21 and 22: The first significant generalizatio
Page 23 and 24: artificially contrived solution met
Page 25 and 26: trannportnLion, thin neglect ham cP
Page 27 and 28: to the mode under consideration, cr
Page 29 and 30: that even if the reasoning is 'corr
Page 31 and 32: competition, that is where the qual
Page 33 and 34: His estimating process is divided i
Page 35 and 36: Table 2.1 COMMODITIES CARRIED ON TH
Page 37 and 38: - 15 In a recent volume on the de=a
Page 39 and 40: aggregation over regions for each c
Page 41 and 42: for each of the modes under the ass
Page 43 and 44: ail rates, and here he encountered
Page 45 and 46: had statistical significance; howev
Page 47 and 48: flows with actual shipments. 21 The
Page 49 and 50: CHAPTER III THE TWO-MARKET MULTI-MO
Page 51 and 52: the market price in A it is obvious
Page 53 and 54: P b P o P a T r 0 Fig. 3.4 -- Equil
Page 55 and 56:
for all quantities, we conceive of
Page 57 and 58:
0 (3.6.A) (3.6.B) Q 2 Fig. 3.6 -- T
Page 59 and 60:
• Q2 Qi Q0 Fig. 3.7 -- Two-Mode M
Page 61 and 62:
preference. He pays money today for
Page 63 and 64:
Situation II: Producer Ownership. T
Page 65 and 66:
little consideration will reveal th
Page 67 and 68:
considered these costs in several f
Page 69 and 70:
Then, to calculate the rate of chan
Page 71 and 72:
(T1) (T2) The effect upon Q of an i
Page 73 and 74:
(3.A.7) (3.A.8) APPENDIX A TO CHAPT
Page 75 and 76:
(3.A.17) (3.A.18) ■FQ 5-(43-- -7,
Page 77 and 78:
term more negative and, since it is
Page 79 and 80:
and its inverse (3.B.8) T c • C(Q
Page 81 and 82:
Now, going back to equation (3.3.7)
Page 83 and 84:
APPENDIX C TO CHAPTER THREE The Two
Page 85 and 86:
product to be transported, Q1 units
Page 87 and 88:
(3.C. 3) ,(3.C.6) The monopolist's
Page 89 and 90:
To obtain the greatest profits, the
Page 91 and 92:
.1., OA The sign of — is only sli
Page 93 and 94:
(4.11) (4.12) (4.13) (4.14) 111 Tc
Page 95 and 96:
(4.26) (4.27) (4.28) (4.29) (4.30)
Page 97 and 98:
The tons figure is the total tonnag
Page 99 and 100:
Since the aim of this study is to e
Page 101 and 102:
Distance ' Quantity Rate Eq. (4.33)
Page 103 and 104:
Distance Quantity Rate Eq. (4.33) (
Page 105 and 106:
Distance Quantity Rate Eq. , Source
Page 107 and 108:
Distance Quantity Rate . Eq. Distan
Page 109 and 110:
where R E average, revenue received
Page 111 and 112:
• Table 4.8 332.42 808.54 478.58
Page 113 and 114:
269.02 931.44 900.75 0.98 0.98 0.97
Page 115 and 116:
Table 4.12 RAIL RATE REGRESSIONS FI
Page 117 and 118:
1. date of the freight bill. 2. ori
Page 119 and 120:
(4.41) Rik ■ 0 30 + 0 31 Mik + 0
Page 121 and 122:
making is usually taken to refer to
Page 123 and 124:
Total 728 79,603 Reduction due to m
Page 125 and 126:
Source of Variance Total Reduction
Page 127 and 128:
there is a wide difference between
Page 129 and 130:
All Commodity Classes. Table 4.20 c
Page 131 and 132:
Source of Variance Total 100 599,25
Page 133 and 134:
Intercept Distance Quantity Density
Page 135 and 136:
Intercept Distance Quantity Density
Page 137 and 138:
stability and density showed very l
Page 139 and 140:
groups into STCC commodity groups,
Page 141 and 142:
The reduced form of this system is
Page 143 and 144:
Exogenous , Changes(X) Transport de
Page 145 and 146:
the quantity of commodity k transpo
Page 147 and 148:
Regression Distance < 200 mi. Rail
Page 149 and 150:
Regression Distance Rail Motor Dist
Page 151 and 152:
increase with distances. This is ra
Page 153 and 154:
Table 4.33 contains the derived rat
Page 155 and 156:
Sample Regression Size Intercept M2
Page 157 and 158:
Mode Int. Mode Sample Size Rate Tab
Page 159 and 160:
Mode Sample Size Table 4.38 STCC 32
Page 161 and 162:
Sample Regression Size Intercept Di
Page 163 and 164:
Table 4.42 STCC 37 - TRANSPORTATION
Page 165 and 166:
the three-mode model. Table 4.43 di
Page 167 and 168:
Summary of the Empirical Results In
Page 169 and 170:
Table 4.45 FREIGHT RATE DATA ANALYS
Page 171 and 172:
Commodity Group II III IV V Total C
Page 173 and 174:
Group Mode . I Truck Rail Water /I
Page 175 and 176:
shipments. After a lengthy analysis
Page 177 and 178:
for Group III is positive, large an
Page 179 and 180:
of the underlying structural parame
Page 181 and 182:
Table 4.49 DEMAND REGRESSIONS FINAL
Page 183 and 184:
• supply The model assumes that t
Page 185 and 186:
Commodity Group Table 4.50 DEMAND A
Page 187 and 188:
APPENDIX A TO CHAPTER FOUR The Effe
Page 189 and 190:
Table 4.A.2 RATE REGRESSION RAIL QU
Page 191 and 192:
Table 4.A.4 RATE REGRESSION RAIL QU
Page 193 and 194:
The overall tendency appears to be
Page 195 and 196:
CHAPTER V SUMMARY AND CONCLUSIONS R
Page 197 and 198:
theoretical basis for their empiric
Page 199 and 200:
competitive industries. Applying th
Page 201 and 202:
in the appendix to that chapter. Th
Page 203 and 204:
BIBLIOGRAPHY Baumol, W. J., "Calcul
Page 205 and 206:
United States Department of Commerc
Page 207 and 208:
NORTHWESTERN UNIVERSITY A MODEL OF
Page 209 and 210:
CHAPTER IV EMPIRICAL RESULTS . Page
Page 211 and 212:
. INTRODUCTION Our goal is to study
Page 213 and 214:
Other studies have been done by the
Page 215 and 216:
. Recently air freight has grown aw
Page 217 and 218:
• For instance, suppose a firm ha
Page 219 and 220:
eceive the same criticisms as above
Page 221 and 222:
Per Cent WA Decrease From Current L
Page 223 and 224:
• Cargo . Brewer's analysis depen
Page 225 and 226:
A different type of approach, is ta
Page 227 and 228:
These substantial estimates of elas
Page 229 and 230:
and the consumption points. These a
Page 231 and 232:
Initially, the determinants of a fi
Page 233 and 234:
axis. Q is the quantity the firm wo
Page 235 and 236:
Arc elasticity of the associated tr
Page 237 and 238:
• same A*es (-p)/-11 Skto 4441.
Page 239 and 240:
Suppose that the range of one choic
Page 241 and 242:
is better than getting P 2 tomorrow
Page 243 and 244:
A, At the kink P . Any_further rais
Page 245 and 246:
market price; or inventory costs ma
Page 247 and 248:
The shipper must pay a transport bi
Page 249 and 250:
quantity transported of Z decreases
Page 251 and 252:
The analysis yields a downward slop
Page 253 and 254:
of each market and calculates each
Page 255 and 256:
If more consumption points ,are add
Page 257 and 258:
or ( 5 1) . 1. Q-14.)4 `("P)EXarg (
Page 259 and 260:
4. 0 -A? 040- Net MR 1 0 so. Ira."
Page 261 and 262:
To determine the demand curve for t
Page 263 and 264:
I • The above equations (1-4) wer
Page 265 and 266:
(I). 1■1 (7). Id. (8). •a 0.0.1
Page 267 and 268:
• goods arrive (so that Q A+Q S g
Page 269 and 270:
k The optimal amounts of QA and Q s
Page 271 and 272:
it has been used in economics. Basi
Page 273 and 274:
An analogous relationship exists fo
Page 275 and 276:
• • (11). Now a probability dis
Page 277 and 278:
--_.—..---...........AawmarA D SA
Page 279 and 280:
, (1). APPENDIX TO CHAPTER III SENS
Page 281 and 282:
decreases. Proper choice of P rA (X
Page 283 and 284:
products, have different cost funct
Page 285 and 286:
The above data falls short of the q
Page 287 and 288:
lower than air rates. It rises more
Page 289 and 290:
One of the objectives of the study
Page 291 and 292:
a. Regression equation TABLE IV-1 r
Page 293 and 294:
significant. 8 It was, therefore, d
Page 295 and 296:
in large tonnages tend to have a lo
Page 297 and 298:
T .A T ° S Highest value per pound
Page 299 and 300:
. In addition, only the smallest qu
Page 301 and 302:
Here the deviations are zero. The r
Page 303 and 304:
certain range, the demand estimates
Page 305 and 306:
expected as goods in the discrimina
Page 307 and 308:
• BIBLIOGRAPHY [1] Air Cargo Maga
Page 309 and 310:
[24] 2 Study of the Possibilities f
Page 311 and 312:
[42] Dawson, Michael, "A Technique
Page 313 and 314:
[62] Gorham, G., Sealy, K.R. 1 and
Page 315 and 316:
■•■•■■•••••
Page 317 and 318:
[100] Richards, Anthony, The Role o
Page 319 and 320:
[120] Traffic World Marketing Study
Page 321 and 322:
! i \ NORTHWESTERN UNIVERSITY FREIG
Page 323 and 324:
While working on this dissertation
Page 325 and 326:
BIBLIOGRAPHY Anderson, T.W. "An Int
Page 327 and 328:
VITA MICHEL VINCENT BEUTHE Born in
Page 329 and 330:
of cost iv iazroduced at once along
Page 331 and 332:
In the present theoretical formulat
Page 333 and 334:
It is possible to generalize this m
Page 335 and 336:
however, because of their nature, t
Page 337 and 338:
ij xo ij ,Diagram 3, . 0 X ij of th
Page 339 and 340:
equal to+ where E is the median of
Page 341 and 342:
CHAPTER II Discrimination With One
Page 343 and 344:
which is,.in this case, the only q
Page 345 and 346:
Notc that the first subscript of a.
Page 347 and 348:
I .' 1) (22) P 1 (X) = (25) Therefo
Page 349 and 350:
(34) P 2 (X) (36) 1 = 1 a b c ' and
Page 351 and 352:
CHAPTER III An Application - Corn T
Page 353 and 354:
time the draft is honored by the co
Page 355 and 356:
2. Critique of the Data. We must no
Page 357 and 358:
made through questionnaires to coun
Page 359 and 360:
we can still hope to obtain satisfa
Page 361 and 362:
common and contract carriers are co
Page 363 and 364:
Table II. Rail Time Regressions: Ti
Page 365 and 366:
3. The Statistical Results. After t
Page 367 and 368:
Table IV gives the discriminant fun
Page 369 and 370:
February non-weighed July weighed T
Page 371 and 372:
the binary problems, when the choic
Page 373 and 374:
Table VII Probabilities that an obs
Page 375 and 376:
Table VIII, Probability of Correct
Page 377 and 378:
significantly different from the 'n
Page 379 and 380:
-X _21 5.15 L4.45 TRUCK RAIL lalm
Page 381 and 382:
CHAPTER IV. A Predictive Model of R
Page 383 and 384:
C ab /C a is smaller than one, the
Page 385 and 386:
II. Rail-Water Competition: One Por
Page 387 and 388:
Until now, no attention has been pa
Page 389 and 390:
9 ) (Z a - kZ b ) = C w /C r Zab +
Page 391 and 392:
shipper. In the reality of competit
Page 393 and 394:
DIAGRAM 5 For the most interesting
Page 395 and 396:
DIAGRAM 7 waterway may be numerous.
Page 397 and 398:
Note the restriction of Y to its ab
Page 399 and 400:
the road-water route. In (24) C t (
Page 401 and 402:
Squaring both sides, one obtains an
Page 403 and 404:
interesting expressions. However, t
Page 405 and 406:
CHAPTER V. This chapter attempts to
Page 407 and 408:
TOTAL . COST D = -(L r - L t ) 2 Th
Page 409 and 410:
2. Two Markets Model. subject --co
Page 411 and 412:
X 0, X 2 - 0. It can readily be see
Page 413 and 414:
the river does not have any --, but
Page 415 and 416:
:sLY: x rail 0 truck 0 rail and tru
Page 417 and 418:
'NLY: K rail 0 truck 0 rail and tru
Page 419 and 420:
Table XI. Rail Rates Regressions: C
Page 421 and 422:
mileages. The reason why this ratio
Page 423 and 424:
Table XIII. Boundary Equations. Wat
Page 425 and 426:
DIAGRAM 21 Figure T shows the actua
Page 427 and 428:
truck sample is small ( 148 origins
Page 429 and 430:
In this application of the spatial
Page 431 and 432:
NORTHWESTERN UNIVERSITY LIBRARY Man
Page 433 and 434:
in the dissertation. In addition, h
Page 435 and 436:
Analysis of Tow in Motion 66 Introd
Page 437 and 438:
Table • TABLES Statistical Result
Page 439 and 440:
deepening or widening the channel,
Page 441 and 442:
lines and isoquants. This locus is
Page 443 and 444:
limited to the cost and production
Page 445 and 446:
problem because engineers also atte
Page 447 and 448:
are ignored. Making sure that the r
Page 449 and 450:
variables, the form of the basic re
Page 451 and 452:
family of cost curves obtained in t
Page 453 and 454:
economies of scale exist in ihe tra
Page 455 and 456:
in which R = resistance, in taw-rop
Page 457 and 458:
(2)marginal productivity of the boa
Page 459 and 460:
conditions are not always met in pr
Page 461 and 462:
production relationship, e.g., a ma
Page 463 and 464:
Howe's production and planning mode
Page 465 and 466:
of the barge coefficient seemed to
Page 467 and 468:
1962 counterparts. However, only (1
Page 469 and 470:
A 10 peicont increase in all inputs
Page 471 and 472:
proportion of constant costs. Typic
Page 473 and 474:
In short, cost was estimated as a f
Page 475 and 476:
o f cars, etc.). Each is then multi
Page 477 and 478:
haul. The variable (Z/X) was used i
Page 479 and 480:
In the switching process--which con
Page 481 and 482:
defined to be the percentage change
Page 483 and 484:
other production analysis of rail i
Page 485 and 486:
of transportation, the inputs contr
Page 487 and 488:
It will be convenient to define T f
Page 489 and 490:
vchicles, is considered to be a poi
Page 491 and 492:
F t (v) = B/v. 6 Therefore, the equ
Page 493 and 494:
The graphical expression of Equatio
Page 495 and 496:
And the distance traveled, D c , du
Page 497 and 498:
CHAPTER IV LINEHAUL PROCESS FUNCTIO
Page 499 and 500:
Form of Process Function The proces
Page 501 and 502:
particular . trip', that tonnage ma
Page 503 and 504:
ostimated from a capacity cable for
Page 505 and 506:
The function was originaliy fit by
Page 507 and 508:
were greater than 11 miles per hour
Page 509 and 510:
effective-push functions will be ex
Page 511 and 512:
ilotilla. These assumptions will no
Page 513 and 514:
Upon testing the hypotheses indicat
Page 515 and 516:
for in the first case tows were sem
Page 517 and 518:
a 0 / V I HP 3000 - 12 - 225 • H
Page 519 and 520:
3.5 3.0 1.5 5.. 2.0 7, 4.0 ■•
Page 521 and 522:
A final note concerning the effect
Page 523 and 524:
predict the time required for trave
Page 525 and 526:
Given the tonnage, 0, to be carried
Page 527 and 528:
existence. For example, the locks o
Page 529 and 530:
If all locks on the waterway arc tr
Page 531 and 532:
loaded ones in 1950; therefore p is
Page 533 and 534:
T L -2; Single Double Locking Locki
Page 535 and 536:
u T L 1 Table 4.7 INDIVIDUAL AND SY
Page 537 and 538:
it would leave the system. Alternat
Page 539 and 540:
The government should incur the cos
Page 541 and 542:
I si,:e was 3.1 bares. The small av
Page 543 and 544:
To simplify the analysis all delay-
Page 545 and 546:
characteristics and delays. Therefo
Page 547 and 548:
Equation (4.37) divides the total :
Page 549 and 550:
Xore confidence may be attached to
Page 551 and 552:
Recapitulation of Tow Linehaul Proc
Page 553 and 554:
function. The difference beiween th
Page 555 and 556:
S -, speed of water, in miles per h
Page 557 and 558:
y the above analysis, but for more
Page 559 and 560:
econoinic analysis of the rail linc
Page 561 and 562:
deceleration, Equation (3.8). Moreo
Page 563 and 564:
Then the cargo weight of the ith ca
Page 565 and 566:
(4, 6, or 8), the weight of the loc
Page 567 and 568:
Analysis of Train in Motion Introdu
Page 569 and 570:
and F(v) = 1.3w c + 29a 0.045w c v
Page 571 and 572:
Adiustment for Grade and Curvature.
Page 573 and 574:
Curve resistance, like grade resist
Page 575 and 576:
F . 0 VI Fd(v) F (v) t Fig. 5.1 --
Page 577 and 578:
and (5.26), and 2-miles-per-hour sp
Page 579 and 580:
per trip into several components, e
Page 581 and 582:
N t = number of trains on a given r
Page 583 and 584:
Table 5.1 STATISTICAL ANALYSIS OF T
Page 585 and 586:
Each of the terms V f and C represe
Page 587 and 588:
nowever, in the case of the rail li
Page 589 and 590:
-, 1 9, D 0 ,- ._ 200 ! i 175 '—
Page 591 and 592:
Horsepowe r ( in t hou sa n ds ) 3
Page 593 and 594:
exceeded 6,000 horsepower, for at p
Page 595 and 596:
Curvatures of greater than 5 degree
Page 597 and 598:
hohavior of rail costs. First, the
Page 599 and 600:
eing charged at the higher rate. Th
Page 601 and 602:
2. If train speed is greater than o
Page 603 and 604:
maximula attainable horsepower of t
Page 605 and 606:
price for each locomotive unit from
Page 607 and 608:
I L' is given by (0.5)($94HP L - $4
Page 609 and 610:
Figure 5.4 displays a set of short-
Page 611 and 612:
Economics of scale, in fact, seem t
Page 613 and 614:
Tab1e 5.8 LONG-RUN MARGINAL COST OF
Page 615 and 616:
obtained this way may then be added
Page 617 and 618:
The estimating methods for each of
Page 619 and 620:
Cos t per ton -mi le (m ;1 1s ) 7.2
Page 621 and 622:
CHAPTER VI SUMMARY AND CONCLUSIONS
Page 623 and 624:
eached for acceleration, which take
Page 625 and 626:
wide range of output would have to
Page 627 and 628:
Isoquants between car and locomotiv
Page 629 and 630:
eported in the dissertation will in
Page 631 and 632:
10. M. Bronfenbrenner and P. H. Dou
Page 633 and 634:
13. A. V.ctor Cabot and Arthur P. H
Page 635 and 636:
7. There are in fact three differen
Page 637 and 638:
26. Eric Bottoms, "Practical Tonnag
Page 639 and 640:
19. Hay, An Introduction to Transpo
Page 641 and 642:
BIBLIOGRAPHY American Railway Engin
Page 643 and 644:
Howe, Charles M... "Methods for Equ
Page 645 and 646:
Soberman, Richard. "A Railway Perfo
Page 647 and 648:
NORTHWESTERN UNIVERSITY ESTIMATION
Page 649 and 650:
TABLE OF COIMETS Page Chapter I. In
Page 651 and 652:
CHAPTER I INTRODUCTION AND REVIEW O
Page 653 and 654:
On the other hand, the statistical
Page 655 and 656:
and capital Outlays are also treate
Page 657 and 658:
TABLE 1 SUMMARY ESTIMATES OF RAILRO
Page 659 and 660:
C (X) FIGURE • ■ 9
Page 661 and 662:
The effects of two types of classif
Page 663 and 664:
egression equations will produce bi
Page 665 and 666:
S = speed in miles per hour W = wid
Page 667 and 668:
(6) S = h(HP, L, B, H, D, W) The ac
Page 669 and 670:
stock which remains idle. Under the
Page 671 and 672:
The planning function also exhibite
Page 673 and 674:
Of the production functions, (13, 1
Page 675 and 676:
sources of data. Despite the use of
Page 677 and 678:
The reader should note several them
Page 679 and 680:
from variations in rates based on v
Page 681 and 682:
service the firm would want to set
Page 683 and 684:
oat output, or effort, is not propo
Page 685 and 686:
this level of disaggregation are ex
Page 687 and 688:
CHAPTER III A STATISTICAL PRODUCTIO
Page 689 and 690:
A second way of generating data inv
Page 691 and 692:
variables, even if it is not accura
Page 693 and 694:
Three major inland waterway firms p
Page 695 and 696:
from changing depth or stream flow.
Page 697 and 698:
made for each. (In the log-linear r
Page 699 and 700:
•Ps Variable Name Riven Districts
Page 701 and 702:
Variable Name River Districts Port
Page 703 and 704:
La Variable Name River Districts TA
Page 705 and 706:
Variable Name River Districts TABLE
Page 707 and 708:
t..n .....1 TABLE 6 . . VARIABLE ME
Page 709 and 710:
A. Linear Regression (Arithi.etic M
Page 711 and 712:
are roughly comparable across all c
Page 713 and 714:
termed "labor embodied technologica
Page 715 and 716:
TABLE 8 COMPANY ONE LINEAR REGRESSI
Page 717 and 718:
the other monthly coefficients indi
Page 719 and 720:
CHAPTER IV AN ANALYSIS OF DIRECT TO
Page 721 and 722:
with the use of dummy variables. To
Page 723 and 724:
A more direct method, and the one e
Page 725 and 726:
. cost In using; for example, , cro
Page 727 and 728:
• ,,, • .. -Excluded Variables
Page 729 and 730:
200,000 EBM per year) comes to abou
Page 731 and 732:
Form C weights have limited accurac
Page 733 and 734:
study as to the level of output to
Page 735 and 736:
The firm in the sample operates a l
Page 737 and 738:
would tend to be slightly higher co
Page 739 and 740:
3. other bulk 4. petroleum products
Page 741 and 742:
In addition, river districts with s
Page 743 and 744:
where: Cost = annual total direct b
Page 745 and 746:
1964 1965 Variable Name Barge Type
Page 747 and 748:
TABLE 13 F-TESTS FOR BARGE COST REG
Page 749 and 750:
tend to rise with increases in barg
Page 751 and 752:
ing is quite consistent with a prio
Page 753 and 754:
TABLE 16 PERCENT COMMODITY REGRESSI
Page 755 and 756:
arge was to ship one more commodity
Page 757 and 758:
1 are the costs of operating and ma
Page 759 and 760:
preparation of barges is necessary
Page 761 and 762:
estimated was the same for all thre
Page 763 and 764:
TABLE 17 DIRECT BARGE EXPENSE r 2 =
Page 765 and 766:
Variable Name TABLE 19 TERMINAL EXP
Page 767 and 768:
considerable growth in the past twe
Page 769 and 770:
also be used in conjunction with di
Page 771 and 772:
to an already scheduled tow). Two k
Page 773 and 774:
The terminal results are quite tent
Page 775 and 776:
The five firms in the sample repres
Page 777 and 778:
sure the extent of this activity, a
Page 779 and 780:
1 linear form of- the functions hav
Page 781 and 782:
C. Net Tons of Barge Capacity TABLE
Page 783 and 784:
Indirect cost is the same for towbo
Page 785 and 786:
A. Total Horsepower TABLE 22 CROSS
Page 787 and 788:
1 .‘ A. Total Horsepower TABLE 23
Page 789 and 790:
to scheduling. In addition, we obse
Page 791 and 792:
:CHAPTER VII SUMMARY AND CONCLUSION
Page 793 and 794:
the coefficients of the dummy varia
Page 795 and 796:
. The coefficients of the dummy var
Page 797 and 798:
Supporting results for neutral tech
Page 799 and 800:
port agencies. A considerable amoun
Page 801 and 802:
I to inland waterway operators, sin
Page 803 and 804:
Footnotes--Continued 7 Howe, Jan.,
Page 805 and 806:
Footnotes--Continued This is also w
Page 807 and 808:
Bibliography--Continued Interstate
Page 809 and 810:
UNCLASSIFIED Security Classificatio
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