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

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(5 ) . ‘11 Setting equation (3) equal to equation (4) gives: ajaqA ir. 6(4 • tst +a 2112s 60. ^ (14:46t ,Q,xr Q+44 Adding and subtracting the proper terms to both sides yields: ( 7 ). i7° a- laGls QA (6) . koqs -1)qr-r 6;7)4 c%4Xrit which says Only when net prices are equal can modal splitting occur and if 13 71Tik and 11 s , This may not be a relevant profit position if the net discounted demand curves intersect after the respective net discounted marginal revenue curves become negative. Note 10. Consider the case where the demand curve exists daily and the firm is considering splitting modes. The firm will be satisfying a certain amount of demand today with Q A units, <strong>for</strong> which they receive a price P A =a-bQ A and a net price P A =a-bQ A -T. In a. days Q reaches the market <strong>for</strong> which they receive a price P and a net discounted price Ps = Profits are: (1). IT= Q# 1")°‘ 58.
k The optimal amounts of QA and Q s are found by taking •the partials: (2) . 1" 611C 'IT (45* QA) = rtT Q." 51, (3). , (Iasi 614 =0 Equating ')Q.A and 1,ct s yields: (4) . which says only split modes when net discounted marginal revenues are equal and IT 1Th and ITs. Note 11. Consider two markets and two modes. The firm must look at, (1). + = mc MR A (2): . MC (3). „1 ,c A i'vmS (4). '‘Mit2 + Mki = MC A In cases (1) and (3) it is possible to notice a firm shipping by different modes. However, this is an aggregation problem because of the two markets involved. ...sewooMem. 59
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c,q /kao, PROPERTY OF THF H S. GOVE
Page 3 and 4:
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
Page 11 and 12:
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
Page 17 and 18:
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
Page 81 and 82:
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
Page 217 and 218: • For instance, suppose a firm ha
Page 219 and 220: eceive the same criticisms as above
Page 221 and 222: Per Cent WA Decrease From Current L
Page 223 and 224: • Cargo . Brewer's analysis depen
Page 225 and 226: A different type of approach, is ta
Page 227 and 228: These substantial estimates of elas
Page 229 and 230: and the consumption points. These a
Page 231 and 232: Initially, the determinants of a fi
Page 233 and 234: axis. Q is the quantity the firm wo
Page 235 and 236: Arc elasticity of the associated tr
Page 237 and 238: • same A*es (-p)/-11 Skto 4441.
Page 239 and 240: Suppose that the range of one choic
Page 241 and 242: is better than getting P 2 tomorrow
Page 243 and 244: A, At the kink P . Any_further rais
Page 245 and 246: market price; or inventory costs ma
Page 247 and 248: The shipper must pay a transport bi
Page 249 and 250: quantity transported of Z decreases
Page 251 and 252: The analysis yields a downward slop
Page 253 and 254: of each market and calculates each
Page 255 and 256: If more consumption points ,are add
Page 257 and 258: or ( 5 1) . 1. Q-14.)4 `("P)EXarg (
Page 259 and 260: 4. 0 -A? 040- Net MR 1 0 so. Ira."
Page 261 and 262: To determine the demand curve for t
Page 263 and 264: I • The above equations (1-4) wer
Page 265 and 266: (I). 1■1 (7). Id. (8). •a 0.0.1
Page 267: • goods arrive (so that Q A+Q S g
Page 271 and 272: it has been used in economics. Basi
Page 273 and 274: An analogous relationship exists fo
Page 275 and 276: • • (11). Now a probability dis
Page 277 and 278: --_.—..---...........AawmarA D SA
Page 279 and 280: , (1). APPENDIX TO CHAPTER III SENS
Page 281 and 282: decreases. Proper choice of P rA (X
Page 283 and 284: products, have different cost funct
Page 285 and 286: The above data falls short of the q
Page 287 and 288: lower than air rates. It rises more
Page 289 and 290: One of the objectives of the study
Page 291 and 292: a. Regression equation TABLE IV-1 r
Page 293 and 294: significant. 8 It was, therefore, d
Page 295 and 296: in large tonnages tend to have a lo
Page 297 and 298: T .A T ° S Highest value per pound
Page 299 and 300: . In addition, only the smallest qu
Page 301 and 302: Here the deviations are zero. The r
Page 303 and 304: certain range, the demand estimates
Page 305 and 306: expected as goods in the discrimina
Page 307 and 308: • BIBLIOGRAPHY [1] Air Cargo Maga
Page 309 and 310: [24] 2 Study of the Possibilities f
Page 311 and 312: [42] Dawson, Michael, "A Technique
Page 313 and 314: [62] Gorham, G., Sealy, K.R. 1 and
Page 315 and 316: ■•■•■■•••••
Page 317 and 318: [100] Richards, Anthony, The Role o
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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
Page 363 and 364:
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
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 (
Page 401 and 402:
Squaring both sides, one obtains an
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interesting expressions. However, t
Page 405 and 406:
CHAPTER V. This chapter attempts to
Page 407 and 408:
TOTAL . COST D = -(L r - L t ) 2 Th
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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
Page 419 and 420:
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
Page 425 and 426:
DIAGRAM 21 Figure T shows the actua
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truck sample is small ( 148 origins
Page 429 and 430:
In this application of the spatial
Page 431 and 432:
NORTHWESTERN UNIVERSITY LIBRARY Man
Page 433 and 434:
in the dissertation. In addition, h
Page 435 and 436:
Analysis of Tow in Motion 66 Introd
Page 437 and 438:
Table • TABLES Statistical Result
Page 439 and 440:
deepening or widening the channel,
Page 441 and 442:
lines and isoquants. This locus is
Page 443 and 444:
limited to the cost and production
Page 445 and 446:
problem because engineers also atte
Page 447 and 448:
are ignored. Making sure that the r
Page 449 and 450:
variables, the form of the basic re
Page 451 and 452:
family of cost curves obtained in t
Page 453 and 454:
economies of scale exist in ihe tra
Page 455 and 456:
in which R = resistance, in taw-rop
Page 457 and 458:
(2)marginal productivity of the boa
Page 459 and 460:
conditions are not always met in pr
Page 461 and 462:
production relationship, e.g., a ma
Page 463 and 464:
Howe's production and planning mode
Page 465 and 466:
of the barge coefficient seemed to
Page 467 and 468:
1962 counterparts. However, only (1
Page 469 and 470:
A 10 peicont increase in all inputs
Page 471 and 472:
proportion of constant costs. Typic
Page 473 and 474:
In short, cost was estimated as a f
Page 475 and 476:
o f cars, etc.). Each is then multi
Page 477 and 478:
haul. The variable (Z/X) was used i
Page 479 and 480:
In the switching process--which con
Page 481 and 482:
defined to be the percentage change
Page 483 and 484:
other production analysis of rail i
Page 485 and 486:
of transportation, the inputs contr
Page 487 and 488:
It will be convenient to define T f
Page 489 and 490:
vchicles, is considered to be a poi
Page 491 and 492:
F t (v) = B/v. 6 Therefore, the equ
Page 493 and 494:
The graphical expression of Equatio
Page 495 and 496:
And the distance traveled, D c , du
Page 497 and 498:
CHAPTER IV LINEHAUL PROCESS FUNCTIO
Page 499 and 500:
Form of Process Function The proces
Page 501 and 502:
particular . trip', that tonnage ma
Page 503 and 504:
ostimated from a capacity cable for
Page 505 and 506:
The function was originaliy fit by
Page 507 and 508:
were greater than 11 miles per hour
Page 509 and 510:
effective-push functions will be ex
Page 511 and 512:
ilotilla. These assumptions will no
Page 513 and 514:
Upon testing the hypotheses indicat
Page 515 and 516:
for in the first case tows were sem
Page 517 and 518:
a 0 / V I HP 3000 - 12 - 225 • H
Page 519 and 520:
3.5 3.0 1.5 5.. 2.0 7, 4.0 ■•
Page 521 and 522:
A final note concerning the effect
Page 523 and 524:
predict the time required for trave
Page 525 and 526:
Given the tonnage, 0, to be carried
Page 527 and 528:
existence. For example, the locks o
Page 529 and 530:
If all locks on the waterway arc tr
Page 531 and 532:
loaded ones in 1950; therefore p is
Page 533 and 534:
T L -2; Single Double Locking Locki
Page 535 and 536:
u T L 1 Table 4.7 INDIVIDUAL AND SY
Page 537 and 538:
it would leave the system. Alternat
Page 539 and 540:
The government should incur the cos
Page 541 and 542:
I si,:e was 3.1 bares. The small av
Page 543 and 544:
To simplify the analysis all delay-
Page 545 and 546:
characteristics and delays. Therefo
Page 547 and 548:
Equation (4.37) divides the total :
Page 549 and 550:
Xore confidence may be attached to
Page 551 and 552:
Recapitulation of Tow Linehaul Proc
Page 553 and 554:
function. The difference beiween th
Page 555 and 556:
S -, speed of water, in miles per h
Page 557 and 558:
y the above analysis, but for more
Page 559 and 560:
econoinic analysis of the rail linc
Page 561 and 562:
deceleration, Equation (3.8). Moreo
Page 563 and 564:
Then the cargo weight of the ith ca
Page 565 and 566:
(4, 6, or 8), the weight of the loc
Page 567 and 568:
Analysis of Train in Motion Introdu
Page 569 and 570:
and F(v) = 1.3w c + 29a 0.045w c v
Page 571 and 572:
Adiustment for Grade and Curvature.
Page 573 and 574:
Curve resistance, like grade resist
Page 575 and 576:
F . 0 VI Fd(v) F (v) t Fig. 5.1 --
Page 577 and 578:
and (5.26), and 2-miles-per-hour sp
Page 579 and 580:
per trip into several components, e
Page 581 and 582:
N t = number of trains on a given r
Page 583 and 584:
Table 5.1 STATISTICAL ANALYSIS OF T
Page 585 and 586:
Each of the terms V f and C represe
Page 587 and 588:
nowever, in the case of the rail li
Page 589 and 590:
-, 1 9, D 0 ,- ._ 200 ! i 175 '—
Page 591 and 592:
Horsepowe r ( in t hou sa n ds ) 3
Page 593 and 594:
exceeded 6,000 horsepower, for at p
Page 595 and 596:
Curvatures of greater than 5 degree
Page 597 and 598:
hohavior of rail costs. First, the
Page 599 and 600:
eing charged at the higher rate. Th
Page 601 and 602:
2. If train speed is greater than o
Page 603 and 604:
maximula attainable horsepower of t
Page 605 and 606:
price for each locomotive unit from
Page 607 and 608:
I L' is given by (0.5)($94HP L - $4
Page 609 and 610:
Figure 5.4 displays a set of short-
Page 611 and 612:
Economics of scale, in fact, seem t
Page 613 and 614:
Tab1e 5.8 LONG-RUN MARGINAL COST OF
Page 615 and 616:
obtained this way may then be added
Page 617 and 618:
The estimating methods for each of
Page 619 and 620:
Cos t per ton -mi le (m ;1 1s ) 7.2
Page 621 and 622:
CHAPTER VI SUMMARY AND CONCLUSIONS
Page 623 and 624:
eached for acceleration, which take
Page 625 and 626:
wide range of output would have to
Page 627 and 628:
Isoquants between car and locomotiv
Page 629 and 630:
eported in the dissertation will in
Page 631 and 632:
10. M. Bronfenbrenner and P. H. Dou
Page 633 and 634:
13. A. V.ctor Cabot and Arthur P. H
Page 635 and 636:
7. There are in fact three differen
Page 637 and 638:
26. Eric Bottoms, "Practical Tonnag
Page 639 and 640:
19. Hay, An Introduction to Transpo
Page 641 and 642:
BIBLIOGRAPHY American Railway Engin
Page 643 and 644:
Howe, Charles M... "Methods for Equ
Page 645 and 646:
Soberman, Richard. "A Railway Perfo
Page 647 and 648:
NORTHWESTERN UNIVERSITY ESTIMATION
Page 649 and 650:
TABLE OF COIMETS Page Chapter I. In
Page 651 and 652:
CHAPTER I INTRODUCTION AND REVIEW O
Page 653 and 654:
On the other hand, the statistical
Page 655 and 656:
and capital Outlays are also treate
Page 657 and 658:
TABLE 1 SUMMARY ESTIMATES OF RAILRO
Page 659 and 660:
C (X) FIGURE • ■ 9
Page 661 and 662:
The effects of two types of classif
Page 663 and 664:
egression equations will produce bi
Page 665 and 666:
S = speed in miles per hour W = wid
Page 667 and 668:
(6) S = h(HP, L, B, H, D, W) The ac
Page 669 and 670:
stock which remains idle. Under the
Page 671 and 672:
The planning function also exhibite
Page 673 and 674:
Of the production functions, (13, 1
Page 675 and 676:
sources of data. Despite the use of
Page 677 and 678:
The reader should note several them
Page 679 and 680:
from variations in rates based on v
Page 681 and 682:
service the firm would want to set
Page 683 and 684:
oat output, or effort, is not propo
Page 685 and 686:
this level of disaggregation are ex
Page 687 and 688:
CHAPTER III A STATISTICAL PRODUCTIO
Page 689 and 690:
A second way of generating data inv
Page 691 and 692:
variables, even if it is not accura
Page 693 and 694:
Three major inland waterway firms p
Page 695 and 696:
from changing depth or stream flow.
Page 697 and 698:
made for each. (In the log-linear r
Page 699 and 700:
•Ps Variable Name Riven Districts
Page 701 and 702:
Variable Name River Districts Port
Page 703 and 704:
La Variable Name River Districts TA
Page 705 and 706:
Variable Name River Districts TABLE
Page 707 and 708:
t..n .....1 TABLE 6 . . VARIABLE ME
Page 709 and 710:
A. Linear Regression (Arithi.etic M
Page 711 and 712:
are roughly comparable across all c
Page 713 and 714:
termed "labor embodied technologica
Page 715 and 716:
TABLE 8 COMPANY ONE LINEAR REGRESSI
Page 717 and 718:
the other monthly coefficients indi
Page 719 and 720:
CHAPTER IV AN ANALYSIS OF DIRECT TO
Page 721 and 722:
with the use of dummy variables. To
Page 723 and 724:
A more direct method, and the one e
Page 725 and 726:
. cost In using; for example, , cro
Page 727 and 728:
• ,,, • .. -Excluded Variables
Page 729 and 730:
200,000 EBM per year) comes to abou
Page 731 and 732:
Form C weights have limited accurac
Page 733 and 734:
study as to the level of output to
Page 735 and 736:
The firm in the sample operates a l
Page 737 and 738:
would tend to be slightly higher co
Page 739 and 740:
3. other bulk 4. petroleum products
Page 741 and 742:
In addition, river districts with s
Page 743 and 744:
where: Cost = annual total direct b
Page 745 and 746:
1964 1965 Variable Name Barge Type
Page 747 and 748:
TABLE 13 F-TESTS FOR BARGE COST REG
Page 749 and 750:
tend to rise with increases in barg
Page 751 and 752:
ing is quite consistent with a prio
Page 753 and 754:
TABLE 16 PERCENT COMMODITY REGRESSI
Page 755 and 756:
arge was to ship one more commodity
Page 757 and 758:
1 are the costs of operating and ma
Page 759 and 760:
preparation of barges is necessary
Page 761 and 762:
estimated was the same for all thre
Page 763 and 764:
TABLE 17 DIRECT BARGE EXPENSE r 2 =
Page 765 and 766:
Variable Name TABLE 19 TERMINAL EXP
Page 767 and 768:
considerable growth in the past twe
Page 769 and 770:
also be used in conjunction with di
Page 771 and 772:
to an already scheduled tow). Two k
Page 773 and 774:
The terminal results are quite tent
Page 775 and 776:
The five firms in the sample repres
Page 777 and 778:
sure the extent of this activity, a
Page 779 and 780:
1 linear form of- the functions hav
Page 781 and 782:
C. Net Tons of Barge Capacity TABLE
Page 783 and 784:
Indirect cost is the same for towbo
Page 785 and 786:
A. Total Horsepower TABLE 22 CROSS
Page 787 and 788:
1 .‘ A. Total Horsepower TABLE 23
Page 789 and 790:
to scheduling. In addition, we obse
Page 791 and 792:
:CHAPTER VII SUMMARY AND CONCLUSION
Page 793 and 794:
the coefficients of the dummy varia
Page 795 and 796:
. The coefficients of the dummy var
Page 797 and 798:
Supporting results for neutral tech
Page 799 and 800:
port agencies. A considerable amoun
Page 801 and 802:
I to inland waterway operators, sin
Page 803 and 804:
Footnotes--Continued 7 Howe, Jan.,
Page 805 and 806:
Footnotes--Continued This is also w
Page 807 and 808:
Bibliography--Continued Interstate
Page 809 and 810:
UNCLASSIFIED Security Classificatio
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Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

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