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

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in order. The sample size is quite small (36 observations). With the relatively large number of variables used the number of degrees of freedom is quite small. On the positive side it is worth noting that the regression results are significant. F-values for the analysis of variance of the three regressions are presented in Table 20. Although care must be exercised in using the regressions for predictive purposes, the results are quite consistent with a priori expectations and can be used to estimate the direction and magnitude of changes in cost due to specified changes in the variables. Direct Barge Costs The results for the direct barge cost estimation are presented in Table 17. Direct barge costs include all those costs we would expect to change if one additional ton of cargo was transported. As expected, short-run average costs are falling as current output increases. The range of output produced by the firm is between 200,000 and 400,000 EBM's. Average cost for this firm thus varies from $2.86 per EBM to $1.54 per EBM. Assuming an EBM to be 1400 cargo ton-miles, average cost per ton-mile ranges from 2.1 mills to 1.1 mill. Recall that the costs reported by Meyer ranged from 2 to 2.5 mills per ton-mile? These estimates reported here are to be preferred to Meyer's, first, since they are more current and - secondly, because the relationship between average cost and output is explicit. The relationship of the estimates presented here and past estimates, such as Meyer's, that are available,Imme been influenced in three important ways. First, the barge industry has experienced 112
TABLE 17 DIRECT BARGE EXPENSE r 2 = .94 • Sample size = 36 Standard Error of Estimate = 0.03498 Intercept = -0.23800 Variable Name Mean Regression Coefficient t-Value Commodity Shipped (percent times 10 -2 ) Grain 0.30111 -0.22344 -1.06479 Coal ' 0.00806 -1.05039 -0.69376 Other Bulk 0.12583 -0.15056 -0.55241 Petroleum products 0.08917 -0.48547 . . -0.85037 Other liquid bulk 0.08861 -0.40087 -0.98271 .River Districts (percent times 10 -2 ) tower Illinois 0.14694 0.21486 0.27631 Chicago Port 0.02417 1.77304 1.04040 Tennessee 0.04111 -0.49696 -0.30993 WICC , 0.04250 -1.16258 -0.88053 E1CC ' 0.00222 -2.14679 -0.72300 Gulf i . 0.06833 -0.64112 -1.12297 Cairo - St. Louis 0.10556 -0.47782 -.0.35987 . St. Louis - Grafton 0.02278 -4.28935 -1.75228 Grafton - Minneapolis 0.00278 -1.75541 -0.56699 Cairo - Cincinnati - 0.03833 2.04464 1.65515 Monthly Dummy Variables • January February March Apr-Li May June ' July August September October November . 0.08333 0.08333. 0.08333 0.08333 0.08333 0:08333 0.08333 0.08333 0.08333 0.08333 0.08333 -0.11094 -0.09831 -0,07816 -0.03305 -0.07039 -0.12112 -0.08488 -0.02014 -0.03360 -0.04345 -0.04931 1 -1.46574 -1.94714 -1.76284 -0.59840 -1.25853 -1.90933 -1.54296 -0.40840 -0.43063 -0.91529 -1.28813 logio EBM (times 10 -6 ) log io Net Tons of Cargo , -0.56578 -0:90051 -3.49150 Capacity (times 10 -') Dependent Variable: logio 0.56021 -0.74976 -0.22836 Cost/EBM (times 10°) 0.33743 . 113
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c,q /kao, PROPERTY OF THF H S. GOVE
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INSTITUTE FOR WATER RESOURCES In 19
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NORTHWESTERN UNIVERSITY AN ECONOMET
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ACKNOWLEDGMENTS LIST OF FIGURES •
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Figure FIGURES Page 3.1 Two-Market
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Table Page 4.12 Rail Rate Regressio
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Table 4.A.5 Rate Regression Rail Qu
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This paper presents an economic mod
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All transport modes are designed to
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CHAPTER II REVIEW OF THE LITERATURE
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The first significant generalizatio
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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
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- 15 In a recent volume on the de=a
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aggregation over regions for each c
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for each of the modes under the ass
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ail rates, and here he encountered
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had statistical significance; howev
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flows with actual shipments. 21 The
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CHAPTER III THE TWO-MARKET MULTI-MO
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the market price in A it is obvious
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P b P o P a T r 0 Fig. 3.4 -- Equil
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for all quantities, we conceive of
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0 (3.6.A) (3.6.B) Q 2 Fig. 3.6 -- T
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• Q2 Qi Q0 Fig. 3.7 -- Two-Mode M
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preference. He pays money today for
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Situation II: Producer Ownership. T
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little consideration will reveal th
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considered these costs in several f
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Then, to calculate the rate of chan
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(T1) (T2) The effect upon Q of an i
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(3.A.7) (3.A.8) APPENDIX A TO CHAPT
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(3.A.17) (3.A.18) ■FQ 5-(43-- -7,
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term more negative and, since it is
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and its inverse (3.B.8) T c • C(Q
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Now, going back to equation (3.3.7)
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APPENDIX C TO CHAPTER THREE The Two
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product to be transported, Q1 units
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(3.C. 3) ,(3.C.6) The monopolist's
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To obtain the greatest profits, the
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.1., OA The sign of — is only sli
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(4.11) (4.12) (4.13) (4.14) 111 Tc
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(4.26) (4.27) (4.28) (4.29) (4.30)
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The tons figure is the total tonnag
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Since the aim of this study is to e
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Distance ' Quantity Rate Eq. (4.33)
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Distance Quantity Rate Eq. (4.33) (
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Distance Quantity Rate Eq. , Source
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Distance Quantity Rate . Eq. Distan
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where R E average, revenue received
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• 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
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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
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Summary of the Empirical Results In
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Table 4.45 FREIGHT RATE DATA ANALYS
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Commodity Group II III IV V Total C
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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
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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
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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
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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
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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
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production relationship, e.g., a ma
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Howe's production and planning mode
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of the barge coefficient seemed to
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1962 counterparts. However, only (1
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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
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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
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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
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The function was originaliy fit by
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were greater than 11 miles per hour
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effective-push functions will be ex
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ilotilla. These assumptions will no
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Upon testing the hypotheses indicat
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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 ■•
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A final note concerning the effect
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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
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If all locks on the waterway arc tr
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loaded ones in 1950; therefore p is
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T L -2; Single Double Locking Locki
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u T L 1 Table 4.7 INDIVIDUAL AND SY
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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
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To simplify the analysis all delay-
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characteristics and delays. Therefo
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Equation (4.37) divides the total :
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Xore confidence may be attached to
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Recapitulation of Tow Linehaul Proc
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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
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Then the cargo weight of the ith ca
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(4, 6, or 8), the weight of the loc
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Analysis of Train in Motion Introdu
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and F(v) = 1.3w c + 29a 0.045w c v
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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
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N t = number of trains on a given r
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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
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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
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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
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Tab1e 5.8 LONG-RUN MARGINAL COST OF
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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
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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
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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
Page 665 and 666:
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
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from variations in rates based on v
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service the firm would want to set
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oat output, or effort, is not propo
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this level of disaggregation are ex
Page 687 and 688:
CHAPTER III A STATISTICAL PRODUCTIO
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A second way of generating data inv
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variables, even if it is not accura
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Three major inland waterway firms p
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from changing depth or stream flow.
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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
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: estimated was the same for all thre
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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Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

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