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

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(3.C.18) - IZ A + q 2 Z2 - 1 2 + 0 1.--- 3(12 "2 A 42 3a ,2 e a)'o 42 - Ad, A,A act Equations (3.C.17) and (3.C.18) are linear in the two unknowns 3(12 ax and may be solved for and -5-c; • It can be shown that the first bracketed expression in (3.C.17) is equivalent to B ll ; the second bracketed expression in (3.C.17) and the first bracketed expression in (3.C.18) are equivalent to B 12 E B 21 ; and the second bracketed expression in (3.C.18) is equivalent to B 22 . Hence, we may rewrite these two equations As (3.C.19) (3.C.20) Solution by Cramer's Rule yields (3.C.21) (3.C.22) 3(12 SA B + B C 11 3a 12 aa a 2 q 2 ,a Bq 2 ax B + B — 0. 21 aa 22 3a B 22 ICa +Q 2 C q2'a 3q2 Sa IBI B 21 ICa +Q 2 C q2'a ax aa 1BI The expression 1C a + q2 c is analogous to the expression I Fa + q2 Fn '0 1 found in (3.C.9). Here we are shifting only the "C" '2 curve, whereas before the "C - Z 2 ■ F" curve was shifted. This expression will again directly determine the sign of iv-, IBI c 0. 3(12 as B22 0 and 77
.1., OA The sign of — is only slightly more difficult to determine. aa 2 2 The sign of B 21 E B 12 -IZ + Q 2 ZQ2,A + Q ,A I may be either positive or negative. The first two terms of this expression represent the marginal increment to profits which could be brought about by in- creasing the quality of service. The final term represents the marginal cost of this prospective increase. (Assuming for the moment that IC a + Q 2 CQ2,aI is positive) if MR > MC, A will be increased; whereas if MR < MC, A will be decreased. 78
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
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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
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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
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CHAPTER II REVIEW OF THE LITERATURE
Page 21 and 22:
The first significant generalizatio
Page 23 and 24:
artificially contrived solution met
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trannportnLion, thin neglect ham cP
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to the mode under consideration, cr
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that even if the reasoning is 'corr
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competition, that is where the qual
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His estimating process is divided i
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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: To obtain the greatest profits, the
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
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Exogenous , Changes(X) Transport de
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the quantity of commodity k transpo
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Regression Distance < 200 mi. Rail
Page 149 and 150:
Regression Distance Rail Motor Dist
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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
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Mode Int. Mode Sample Size Rate Tab
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Mode Sample Size Table 4.38 STCC 32
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Sample Regression Size Intercept Di
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Table 4.42 STCC 37 - TRANSPORTATION
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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
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shipments. After a lengthy analysis
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for Group III is positive, large an
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of the underlying structural parame
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Table 4.49 DEMAND REGRESSIONS FINAL
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• 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
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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
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. INTRODUCTION Our goal is to study
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Other studies have been done by the
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. Recently air freight has grown aw
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• For instance, suppose a firm ha
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eceive the same criticisms as above
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Per Cent WA Decrease From Current L
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• Cargo . Brewer's analysis depen
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A different type of approach, is ta
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These substantial estimates of elas
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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
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Arc elasticity of the associated tr
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• same A*es (-p)/-11 Skto 4441.
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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
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The shipper must pay a transport bi
Page 249 and 250:
quantity transported of Z decreases
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The analysis yields a downward slop
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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
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• goods arrive (so that Q A+Q S g
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k The optimal amounts of QA and Q s
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it has been used in economics. Basi
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An analogous relationship exists fo
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• • (11). Now a probability dis
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--_.—..---...........AawmarA D SA
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, (1). APPENDIX TO CHAPTER III SENS
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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
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Here the deviations are zero. The r
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certain range, the demand estimates
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expected as goods in the discrimina
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• BIBLIOGRAPHY [1] Air Cargo Maga
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[24] 2 Study of the Possibilities f
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[42] Dawson, Michael, "A Technique
Page 313 and 314:
[62] Gorham, G., Sealy, K.R. 1 and
Page 315 and 316:
■•■•■■•••••
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[100] Richards, Anthony, The Role o
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[120] Traffic World Marketing Study
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! 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
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of cost iv iazroduced at once along
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In the present theoretical formulat
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It is possible to generalize this m
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however, because of their nature, t
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ij xo ij ,Diagram 3, . 0 X ij of th
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equal to+ where E is the median of
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CHAPTER II Discrimination With One
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which is,.in this case, the only q
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Notc that the first subscript of a.
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I .' 1) (22) P 1 (X) = (25) Therefo
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(34) P 2 (X) (36) 1 = 1 a b c ' and
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CHAPTER III An Application - Corn T
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time the draft is honored by the co
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2. Critique of the Data. We must no
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made through questionnaires to coun
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we can still hope to obtain satisfa
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common and contract carriers are co
Page 363 and 364:
Table II. Rail Time Regressions: Ti
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3. The Statistical Results. After t
Page 367 and 368:
Table IV gives the discriminant fun
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February non-weighed July weighed T
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the binary problems, when the choic
Page 373 and 374:
Table VII Probabilities that an obs
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Table VIII, Probability of Correct
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significantly different from the 'n
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-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 +
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shipper. In the reality of competit
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DIAGRAM 5 For the most interesting
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DIAGRAM 7 waterway may be numerous.
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Note the restriction of Y to its ab
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the road-water route. In (24) C t (
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Squaring both sides, one obtains an
Page 403 and 404:
interesting expressions. However, t
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CHAPTER V. This chapter attempts to
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TOTAL . COST D = -(L r - L t ) 2 Th
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2. Two Markets Model. subject --co
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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
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Table XI. Rail Rates Regressions: C
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mileages. The reason why this ratio
Page 423 and 424:
Table XIII. Boundary Equations. Wat
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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,
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lines and isoquants. This locus is
Page 443 and 444:
limited to the cost and production
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problem because engineers also atte
Page 447 and 448:
are ignored. Making sure that the r
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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
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in which R = resistance, in taw-rop
Page 457 and 458:
(2)marginal productivity of the boa
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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
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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
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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
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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