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with the transport demand curve, is not identical with one of the supply curves. curves. The culmination of our geometrical model is presented in Fig. 3.7 where we have two modes supplying transport services with differing levels of quality costs. The diagram has become rather cluttered but the method of solution should now be obvious. As the shipper is in- terested in all transport costs, we first sum the supply curve and the quality cost curve vertically for each mode to obtain the unit trans- c c port cost curves, T 1 and T. Then, to find the competitive market solution, we sum these transport cost curves horizontally to obtain a "transport - supply curve" and find the point where this curve intersects the transport demand curve. As Fig. 3.7 is constructed, this is at a quantity of Q and transport costs of T. This yields a modal-split . of Q 1 and Q 2 . Then, working back to the modal supply curves, we see that the rate Charged by - Mode One 'will be Tr and that of Mode Two T. 1 2 In general these rates will not be equal. The conditions for a modal- split are, again, that S t be rising and that its intersection with the demand for transportation occur at a point where both modes are rep- resented. These simple diagrams have served nicely in illustrating the development of our'analysis. However, when the full Model is . presented, as in 'Fig. 3.7, the diagram becomes rather confused, even when dealing only With linear curves. After a discussion of the measure and form of our associated costs, we shall utilize mathematical methods in discussing the model And tracing the effects of shifting the various 45
• Q2 Qi Q0 Fig. 3.7 -- Two-Mode Model with Quality Associated Costs Transportation Associated Costs We now take a closer look at the associated costs of transportation and the way we have entered them in our model. Markets A and B are separate points and the physical movement of goods from one market to the other requires time and effort. The effort is supplied, over time, by the transportation industry. The transport rate is reimbursement received by this industry for the effort it expends. During the time the goods are in transit from A to B they are unavailable for use. This unavailability may incur several alternative forms of economic costs, 46
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 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: 0 (3.6.A) (3.6.B) Q 2 Fig. 3.6 -- T
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
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269.02 931.44 900.75 0.98 0.98 0.97
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Table 4.12 RAIL RATE REGRESSIONS FI
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1. date of the freight bill. 2. ori
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(4.41) Rik ■ 0 30 + 0 31 Mik + 0
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making is usually taken to refer to
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Total 728 79,603 Reduction due to m
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Source of Variance Total Reduction
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there is a wide difference between
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All Commodity Classes. Table 4.20 c
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Source of Variance Total 100 599,25
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Intercept Distance Quantity Density
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Intercept Distance Quantity Density
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stability and density showed very l
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groups into STCC commodity groups,
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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
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Regression Distance Rail Motor Dist
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increase with distances. This is ra
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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
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Commodity Group Table 4.50 DEMAND A
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APPENDIX A TO CHAPTER FOUR The Effe
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Table 4.A.2 RATE REGRESSION RAIL QU
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Table 4.A.4 RATE REGRESSION RAIL QU
Page 193 and 194:
The overall tendency appears to be
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CHAPTER V SUMMARY AND CONCLUSIONS R
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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
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United States Department of Commerc
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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
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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
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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."
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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
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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
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[62] Gorham, G., Sealy, K.R. 1 and
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■•■•■■•••••
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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
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While working on this dissertation
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BIBLIOGRAPHY Anderson, T.W. "An Int
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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
Page 345 and 346:
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
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Table II. Rail Time Regressions: Ti
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3. The Statistical Results. After t
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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
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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
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CHAPTER IV. A Predictive Model of R
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C ab /C a is smaller than one, the
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II. Rail-Water Competition: One Por
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Until now, no attention has been pa
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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
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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
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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
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In this application of the spatial
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NORTHWESTERN UNIVERSITY LIBRARY Man
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in the dissertation. In addition, h
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Analysis of Tow in Motion 66 Introd
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Table • TABLES Statistical Result
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deepening or widening the channel,
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lines and isoquants. This locus is
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limited to the cost and production
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problem because engineers also atte
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are ignored. Making sure that the r
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variables, the form of the basic re
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family of cost curves obtained in t
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economies of scale exist in ihe tra
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in which R = resistance, in taw-rop
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(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
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1962 counterparts. However, only (1
Page 469 and 470:
A 10 peicont increase in all inputs
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proportion of constant costs. Typic
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In short, cost was estimated as a f
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o f cars, etc.). Each is then multi
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haul. The variable (Z/X) was used i
Page 479 and 480:
In the switching process--which con
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defined to be the percentage change
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other production analysis of rail i
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of transportation, the inputs contr
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It will be convenient to define T f
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vchicles, is considered to be a poi
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F t (v) = B/v. 6 Therefore, the equ
Page 493 and 494:
The graphical expression of Equatio
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And the distance traveled, D c , du
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CHAPTER IV LINEHAUL PROCESS FUNCTIO
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Form of Process Function The proces
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particular . trip', that tonnage ma
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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
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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
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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
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Given the tonnage, 0, to be carried
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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
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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
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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
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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
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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.
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Curve resistance, like grade resist
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F . 0 VI Fd(v) F (v) t Fig. 5.1 --
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and (5.26), and 2-miles-per-hour sp
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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
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Each of the terms V f and C represe
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nowever, in the case of the rail li
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-, 1 9, D 0 ,- ._ 200 ! i 175 '—
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Horsepowe r ( in t hou sa n ds ) 3
Page 593 and 594:
exceeded 6,000 horsepower, for at p
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Curvatures of greater than 5 degree
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hohavior of rail costs. First, the
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eing charged at the higher rate. Th
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2. If train speed is greater than o
Page 603 and 604:
maximula attainable horsepower of t
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price for each locomotive unit from
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I L' is given by (0.5)($94HP L - $4
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Figure 5.4 displays a set of short-
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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
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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
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egression equations will produce bi
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S = speed in miles per hour W = wid
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(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
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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
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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
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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
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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
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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
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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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