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

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At about this same time S. Enke was also grappling with the transportation problem. His model as it evolved was also for a world com- posed of many markets and one commodity. However, he hypothesized that if each region was conceived to have linear product supply and demand functions, and unit transport charges between regions were independent of volume, the (transport cost minimizing and market clearing) flows could be determined by analogy with the electrical network studies of Clerk Maxwell and Kirchhoff. 5 While his multi-market model was a maze of resistors, power sources and current flows, he was able to present a verbal discussion of the economic solution for the three-market case based upon excess supply and demand functions. 6 Thus, while Koopmans and Hitchcock were able to develop the fixed quantities case to a point where a solution was possible, Enke's contribution was to suggest an transport costs. These are actually allocation problems which ignore production and consumption conditions both in the product market and, essentially, in the transportation market. In the multi-mode models it is possible for a modal split to occur. However, it must be of the "all or nothing" variety, that is either all of the traffic between two markets will be carried by one mode, or one mode will carry all it can handle before another will be brought into operation. See, for example: K. B. Haley, "The Multi-Index Problem," Operations Research, Vol. 11 No. 3 (May, June), 1963, 368-379, and . R. W. Lewis, E. F. Rosholdt, and W. L. Wilkinson, "A Multi-Mode Transportation Network Model," Naval Research Logistics Quarterly, Vol. 12, Nos. 3 & 4 (Sept., Dec.), 1965, 261-274. 5. S. Enke, "Equilibrium Among Spatially Separated Markets: Solution by Electric Analogue," Econometrica, Vol. 19 (Jan. 1951), 40-47. 6. For an excellent discussion of this three-market case in geometric form.see: Eugene Silberberg, The Demand for Inland Waterway Transportation, unpublished Ph.D. dissertation, Purdue University, 1964. 9
artificially contrived solution method for the variable export and im- port case. This path was also followed by Samuelson several years later. . In 1962 Samuelson was able to take Enke's electric analogue transportation model and express it in terms of an economic maximization model. 7 He created the concept of "social pay-off" which was defined as the algebraic area under a region's excess-demand curve and showed that the act of maximizing "net social pay-off" over all regions in the model would result in trade equilibrium. By formulating his artificial maximization problem in a programming framework and heuristically sketching its solution, he was able to show that the Koopmans-Hitchcock problem was logically wholly contained within the larger problem. Although the title of Samuelson's article is "Spatial Price Equilib- rium and Linear Programming," the model which he presents is decidedly non-linear, even assuming linear product supply and demand curves. This problem specification issue is formulated very clearly in Vernon Smith's paper of 1963. 8 Smith reformulates Samuelson's problem and shows it as the dual of a general programming problem of rent minimization. We have now seen the transportation problem presented as an electric analogue problem, a social pay-off maximization problem and a rent minimization problem. Smith seems to feel that it is intuitively clearer or purer to think of a competitive market system as one which minimizes the sum of producer and consumer rents, and this is probably true. While Samuelson's "net social pay-off" was novel, the concept of rent has been 7. Samuelson, p. 283. 8. V. L. Smith, "Minimization of Economic Rent in Spatial Price Equilibrium," Review of Economio Studies, Vol. XXX, No. 1 (1963), 24-31. A.
Page 1 and 2: c,q /kao, PROPERTY OF THF H S. GOVE
Page 3 and 4: INSTITUTE FOR WATER RESOURCES In 19
Page 5 and 6: NORTHWESTERN UNIVERSITY AN ECONOMET
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: The first significant generalizatio
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
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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
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in the appendix to that chapter. Th
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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
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. 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
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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
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Initially, the determinants of a fi
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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
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is better than getting P 2 tomorrow
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A, At the kink P . Any_further rais
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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
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or ( 5 1) . 1. Q-14.)4 `("P)EXarg (
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4. 0 -A? 040- Net MR 1 0 so. Ira."
Page 261 and 262:
To determine the demand curve for t
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I • The above equations (1-4) wer
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(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
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• • (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
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products, have different cost funct
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The above data falls short of the q
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lower than air rates. It rises more
Page 289 and 290:
One of the objectives of the study
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a. Regression equation TABLE IV-1 r
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significant. 8 It was, therefore, d
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in large tonnages tend to have a lo
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T .A T ° S Highest value per pound
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. 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
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the river does not have any --, but
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:sLY: x rail 0 truck 0 rail and tru
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'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
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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
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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
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S -, speed of water, in miles per h
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y the above analysis, but for more
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econoinic analysis of the rail linc
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deceleration, Equation (3.8). Moreo
Page 563 and 564:
Then the cargo weight of the ith ca
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(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
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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
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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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Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

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