I
v ‘| " I ' o-c.

 

 

.
' .
. .
.
u .
, O
.
‘ 0
. -
~
.
' Q
~~ .
. ' o.
' n
.'
.
. .
' a
u o .
. I . .
' . c .
a ,.
¢
. o
u
' u
|
.
h I.
I o
.
..
o .
.
o
.
..
u.
0
~.
. D
. I .
’ .
~ .
.
‘ ' ¢
. . I I I
.
- . I
. . ‘
. n
. . I
' o
- .
.
.
. .
, .
o .
.
u. . I I
I ‘l: .
.
O ' I
v- _ I
.
_.
1v . '.
A I. I I
.
h .
lb . ‘ I '
. v
.- _ I l
' .n . I
'--.. ' . . .
' ' .1 . '.'
€- ‘ 'r - .
. ‘ .
2 ‘I .
. . I ,_
, t
l I
' . . . ' fl.
,_( ’ . . 'Iv.
- ,. . I
n . .. .
.. .
I ‘I ‘
'.' - 0 ..
. ,._ .
l ' I
4
‘Ir . . ’
' I I.
.. ,
-. . . I .
. . . -
. .
. -.
. I I I
I . , I
‘ v
u
a

 

0-.» o

u
‘ .
‘
v
I
a
’ .
a
u 7
¢ .

'-

c.

 

O...

n-..

v

cu.

 

. t.....'I......'..“.,..94....3.,“"“'..,e"“'""‘f: $940.....2nut9cooO.OODQIOV‘cI~§;Qv

I
\V |.'-.'-“
. I

 

 

 

I .
.
.
’ o
. a
. . . I
. I I
r
‘ . u . .
. . - I I I I I
' . ' o .
O I I I
. I I
. o . . . . I II -
’ I u .
' . I .l ‘ D - . I
. . I I I I
. . A _ . . I .
.
. . . . . I . I
u I I . . I
' O
n - I I I
. . - ..I .
. t . ' ' -. nI
. I I - I
- I I I I
. I I I I I I I
D . - I I I
. _ , - I
- o ‘_
‘ . C n . ‘
- - . .- .
' - . . . ,
- ' ' ‘ . ‘ . _
- ' . I . . ‘ ‘ 0
. ' . - ' ‘ . .
.
- . I I I . I
. II I
u . ~ I I
' u . .‘ . _ I I
. ' - .. .
u . I . . .
- . I ' i . ‘ o o . .
‘ . u . _ _ .
. .. I I I I
V . . - . I I
. .u . _ I I I I ‘ . I I I
h u
. II . I I
o _ . I
. I . I
. . I I I I I I
‘ . . . . I .
‘ ‘ ' ‘ w u .
. .
I . . ‘ D .
. , I I I -
i . . a .
o . . I
. . . I I
. - . - . ‘ I . _
. . . _ I I .I .I
. . . I . I
' ' . . u ' '
. C
. -. -
. O
. ' I . I
. I. . . I I ‘ I
I . o .I . I I I I
. .
‘ . '. I
. . . I . . I
o
. I ‘ . I
. c , . .
l‘ . . " - - .
. . .
~ I ' I I n
. ‘ - . ' . .'_ .
.
o
. - ‘ o I
. , u . . '
.
- . . .
I I . o . ' I I
s.
.. . ‘ ' C .
. ‘ _ . . I ‘ I
o a . ‘ _ .- I I
.. u . . . I I I
. . A. . _ . -
. I . I -
~ I . I
. . I I
. . _' . - I .
I . . .
. . O - . I .
. .
V - . I - _
‘ .
- _ . . I
c
A I _ ' .
‘ . , I . . I
‘, . I
-
. o
. fl
. I . '
o
1
O
.
l
- 9
O
F
A .
a .
~ .
.
o .
. , I
. I . ~
.‘
. I I I .
. ‘ I
. I I
. . . . I I
,-
. . n u .
- I I I I I
. I I o I
‘ a v _ - '. - I I
. . II
. . - . ~ I . I . I, I I
. . . . P I I I
' . ' c . . .
. ‘1’ ' - I I I I I
. . . I . I I
. - . I I I . I II
. . ~ . . ... . . . I _ _
. . . - . - . . . I _ . I I I
. . . . : - , .. . . I . . I II I
~ -— u I I . - .
. . -'. . . I I II I
' ' ' ' I - . l ’ . . l 0 v -
. I . . . . . I .. . I I. I
. . o , _ _ . . - .._ I
l I D n . .
I . . n I — I - - -
I ‘ - - 1 I A . -
I '. - ‘ ....- . n. ' _ a
. l . _ ‘ - . I . . I
. . . - . . , ~ . I ‘. . . . I I . I A
. . , _ _ . . - . , _ .' .. _
. . . ~ . . II. -.
. 9.. ' I I I
.- . ‘ I

 

IIIIUHIIHHIIIIIIHHHIHIllIllllIl’lllUlllIlllllllHHl

LERRARY 300779 3015

52:“

Mici'zigan gia’z-e
University

 

M-D .

This is to certify that the

dissertation entitled
RAILROAD COMMON COSTS AND FACILITY ABANDONMENTS
presented by
Theodore Robert Bolema
has been accepted towards fulfillment

of the requirements for

Ph . D . degree in Economics

 

law): A.I%

Major professor

 

Date Ila. / S; I???

 

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

PLACE IN RETURN BOX to remove this checkout from your record.

TO AVOID FINES return on or before dds due.

DATE DUE DATE DUE

         
  
   

  

DATE DUE

 

 

 

 

 

 

 

 

 

 

C3! \
Lj-D-
-\ l
l l l
T J— E 1

MSU Is An Afflrrndlve Adlai/Equal Opportunity lmtltuflon
c-Wma-M

w___.._——--_

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RAILROAD COMMON COSTS AND FACILITY.ABANDONMENTS

Theodore Robert Bolema

A.DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR.OF PHILOSOPHY

Department of Econanics

1989

5¢73523

ABSTRACT
RAILROAD COMMON COSTS AND FACILITY ABANDONMENTS
By
Theodore Robert Bolema

Allocating railroad common costs to specific traffic flows is an
old problem in the economics literature. Recently, economists and the
Interstate Commerce Commission have given high priority to avoiding
cross-subsidization of one set of shippers by another set of shippers
when allocating these common costs. Under the current regulatory
institutions, the problem of avoiding cross-subsidization can better
be understood as a problem of finding a cost allocation which leads to
the shipment of the most efficient traffic quantities over the most
efficient transportation network configuration.

The existing economic literature on this problem generally
assumes no abandonment of transportation facilities. This assumption
may have been appropriate earlier in this century, when rail links
were abandoned far less frequently. Under this assumption, the
problem of recovering the common costs of maintaining and operating
the rail network with no abandonment of track (except in the case of
failing railroads) is basically the familiar natural monopoly cost
recovery problem. However, assuming no facility abandonments is
inappropriate today because of the large number of track miles which
have been abandoned during the 19705 and 19803.

When a cost allocation is found which encourages carriers and
shippers to transport the most efficient shipments quantities over the
most efficient network, then that cost allocation is non-subsidizing.
A procedure for finding such a cost allocation is found and applied to
a sample from the 1984 Michigan rail shipments. It was found to be
Pareto efficient to abandon some Michigan facilities and reroute some

shipments over the remaining rail links.

This dissertation is dedicated to my parents, for all of their

love and support while I was caupleting it.

iii

AW

Ioweagreatdealtothemembersofmydissertationcormnittee
and want to acknowledge all of the contributions they made. They are
Dr. John Wolfe, Dr. Harry Trebing, and Dr. Bruce Allen of the Michigan
State University Department of Eoonanics. I especially want to give
credit to the chair of my committee, Dr. Kenneth Boyer of Michigan
State University for all of his ideas, support, and patience. I also
received substantial support and assistance frcnn Dr. John Williams,
Dr. Daniel Christiansen, Dr. James McCarley, and Dr. Larry Steinhauer
of Albion College. Of course, any errors or omissions are not
attributable to any of them.

iv

TABIEOFCDNI‘ENIS

CHAPI‘ERI: PROBIHHSTA'IWI‘ANDBACIWIND“ .................... 1

PURPOSE........................................... ............. 4
IROPOSEDHXJPERI'IESOFANEFFICIENI'CDSTALIOCATIONH .......... 5
DEFINING EFFICIENCY............................................ 6
CRCBS-SUBSIDIZATIONANDEFFICIENCYHHHH...”................. 7
JUSTIFICATION OF THE PROPERTIES OF AN EFFICIENT ALIDCATION..... 9
DDDELING RAIIROAD NEIWRIG..................................... l2
mmmmwsmDJS'I'I‘IUI'IONS................. 13
W(DS'I‘SANDECDNCMICTHEDRY............................... 16
MARGINALCDST H2ICING.......................................... 18
RAMSEY PRICING ................................................. 20
OIHERCIJSTAIIOCATIONAPPKDAGIES... ............................ 22
NONUNIFORM PRICES .............................................. 23
OVERVIEWOFTHEREMAININGCHAPI‘ERS ............................. 24

CHAPTER 2: OTHER RAIL TRANSPORTATION (DST ALLOCATION PROPOSALS. . 26

‘IHERAMSEY PRICING PROPOSAL ................................... 26
'I‘HEUNIFOH’IRATIOKIIE” ........ .......... .................. .. 29
'I'HEFANARAANDGRIMMPHDPOSAL ...................... . .......... 3O
CDNCIUSIONW ......................................... 33

CHAPIER3: EFTICIENI‘CDSTAIIOCATIONANDABANIDNMEN’I‘S ........... 35

'Il-IEPROBIBIDESCRIPI'IONWHHH...” ..... .............. 35
‘IHE NEI‘VDRK.......... 36
THE PARTICIPANTS INTI-IE NEIWDRK............................... 36
SMPPEE'BENEFITSEEFOREAIIOCATINGUNIRACEABIECIE‘ISHHHH 38
CARRIERS'mSTSANDBENEFITS...”...................... ....... 41
‘II'IECHARACI'ERISTICHINCI‘IONW ...... ................. 44
TIIECDREOF'IHEGAME.......... .......... ................ ..... . 46
SPUJIDAILPIAYERSANDFACIII‘I'IESBEDICIUDEDDIIHEGAME?.... 49
'IHED'DSTEFFICIENI'NEIWW.. ..... . ........ 51
WSIONH.................................................. 55

CHAPTER“ ANAPPIICATION'IO'IHEMIQ‘IIGANRAILNEIWM .......... 57

'IHEPDIELAND‘IHE DATA”...................................... 57
'IHEMBTEFFICIENTNEIVDRKHH..................... ...... 67
SENSITIVITYTOTHEDDIANDEIASIICI’I'IESANDCIBTOFQPITALUH 74
UPPERHIJNISONEFFICIENI‘CDSTAIIOQTIONS...” ......... . ..... 75
AILOCATINGTHEFDfEDCDS'IS .................................... 79
CDI‘JCIIJSION.................. ...... .. .......................... 84

CHAPTER 5: CDNCIIJSION ........................................... 85

uerFRm® ...... ......OOOOOOOO ........................... 90

vi

LIST OF FIGURES

_FLG_U__RE 22:51:
Figure 1: A Hypothetical Network. . . . . . ...................... 3
Figure 2: The Available Rail Links .......................... 65
Figure 3: The Most Efficient Network ........................ 69

vii

Table

Table

Table

Table

Table

Table

IIST OF'TABLES

TABLE

1:

Commodity Categories ...............................

'Michigan Transportation Regions ....................

Transportation Regions Outside of Michigan .........

Routes and Quantities ..............................

Upper Bounds on the Cost Allocation ................

Cost Allocation Ranges .............................

viii

PAGE

60

61

62

71

77

80

'IABIEOF SW18

InChapterl

Ci ......the narginal transportatim cost per unit for shipper 1.

e1 ......elasticity of demand for shipper 1.

Pi . ..... the transportation price for shipper i.

A ......a constant for all shippers whichisdeterminedbythe
revenue requirenent. If more (less) revenue is
required, Ais sin'ply increased.

InChaptersBand4

Afijkm ...the allocation to the shippers of Xijkm for the fixed
costs of the facilities in Li km

C(LS,S) ..the total variable transporta ion costs of serving
coalition S over network LS.

Cih ...... fikvlariable cost of shipping a unit of product i over

C*ijlon ...the variable cost of shipping Xi'km over route m.

(Sijkm ...the carriers' gross benefits (be ore fixed costs are
allocated) frcm carrying shipment Xijknv

E(L*,S) ..the upper bound on fixed costs of operating network L*
which can be allocated to coalition S(L*) , so that
E(L*,S) = min( Fr(L5), GB(L*,S)).

Fr(L) ....the total fixed costs of operating all rail links in
network L.

fh .......the fixed cost; associated with rail link h, where
h = 1,2,...,H .

Gijk .....the increase in social surplus (before fixed costs of
the shared facilities are allocated) frcm the shipping
productibetweenj arrikcverthenostefficientroute
(which may or may not include rail links) instead of
over the most efficient route which includes no rail
links.

GB(L,S) ..the gross benefits (gross rail surplus gain) to all
shippers in coalition S(L) frm the shipment of X8 over
the rail facilities in L.

H ........ the nurtber of links between cities in the network.

Hr .......the nunber of rail links.

I-It .......the mmber of truck routes, with Hr + Ht = H.

ix

h ........ the index for links, with h = 1,...,I-Ir for rail links,
and h = Hr+1,...,I-I for truck links. h will generally
refer to a member of set Lijkm'

I ........the mnnber of products shipped over the network.

i ........the product index, i = 1,2,...,I.

J ........the number of cities (or nodes) served by the network.

Ji .......the set of all nodes where shipments enter the network.

j ........ a member of set Ji-

Ki .......the set of all nodes where shipments enter the network.

k ........a member of set Ki-

L ........the set of all links available for shipments.

Lijkm ....the set of all links used when commodity i is shipped
from j to k over route m.

LS ....... a subset of L.

L* . .. . . . .the most efficient network configuration.

Mijk .....the number of routes over which product i can be
carried from j to k.

m ........ the index for the routes, with m = 1,2,...,Mijk.

N(L) .....the set of all shippers and carriers in network L

N (L) ....the most subset of players in N(L) who are served over
the Host efficient network LS.

NB(L,S) ..the net benefits (surplus gain) to group S, where
NB(L,S) = GB(L,S) - R(L,S) _>_ o.

n ...i....s a member of set N(L).

Pijk ..... the price per unit paid for transportation service from
] tokbythe shippers ofproduct l.

R(L,S) ...the allocation of the fixed costs to group S.

S(L) ..... a subset of N(L) .

SAC(XS) . .the stand-alone cost of providing transportation
services to coalition S.

SAFC(XS) .the stand-alone fixed cost of service Xijkm-

T ........a subset of N(L) or of S(LS).

Tsijk ....the surplus from shipping product i between j and k
over the most efficient non-rail mode of
transportation.

135in ...the surplus which would be received if all shipments
are carried by the intermodal competitor.

v(L,S) ...the characteristic function which defines the maximum
benefits (or gross rail surplus gain) to all members of
S(L) from the operation of the facilities in L.

Xijkm ....the quantity of product i shipped from j to k over
route m.

X ...“...the set of all xijkm'

X5 .......a subset of X.

Xsijkm ...a service in XS which can be shipped by the players
in S(L) .

y5 .......the number of members in S(L‘kl.

yn .......the number of members in N (L).

CHM’I'ERI: PROBLEMSI'ATEMENI‘ANDBACKGIHJND

The recent regulatory reform legislation in the railroad
irdustryhasledtoincreasedenrhasisbyregulatorscnthe
profitability of railroads and on the ecormic efficiency of rail
rates. In particular, the Railroad Revitalization and Regulatory
Reform Act of 1976 and the Staggers Rail Act of 1980 have directed the
Interstate Cameroe Camission to allow railroads to abandon
mlprofitable services, to take the profitability of railroads into
account when making regulatory decisions, and to determine reasonable
rates for services which do not face competition (Railroads are
allowed to determine their own rates on competitive traffic under the
Staggers Act). In its recent statement on guidelines for determining
rates on coal shipments not facing carpetition, or market dominant
traffic, the ICII has decided that rates should not exceed the
stand-alone cost (SAC) of providing the service and should be

apportioned according to the individual demands of the shippers. 1

 

1Coa1 shippers and electrical utilities have complained that as
captive shippers, they are charged very high monopoly rates. In
response, the ICC on September 3, 1985 issued the following
clarification of their guidelines for coal shipment rates:

—Captive shippers should not. be required to pay more than
necessary for the rail carrier(s) involved to earn adequate
revenues.

-Captiveshippers shouldnotbearthecostofany
facilities or services frm which no benefits are derived.
-A captive shipper's responsibility for payment for
facilities of services that are beneficially shared by other
shippers shatld be apportioned according to the individual
demands of the various shippers. 'Ihus, railroads will have
an incentive to insure that competitive traffic contributes
as much as possible toward facility or service costs.
-Changes incoalrates shouldnotbesoprecipitousthat
they cause severe economic distortions .

1

2

Theseregulatorydaargesintherailroadindustryarethe
regulators' attetptstobetterallocatethefixedardcarmoncosts in
a railroad network. As such, the problens with which the rail
iniustryregulatorsarecaaceniedarethesanesortsofprrblans
discussed in the long literature of calmer: cost allocatiors. Almaxgh
thefoazshereisontheallocaticnofrail networksharedcosts, many
of the conclusions below are also applicable to other irdustries with
similar network structures, such as pipelines, power transmission, and
telephone networks. '

Intherail industry, theprcblemarisesbecausethereare
substantial costs of operating and maintaining facilities used in
camonbyseveral services. InFigure 1belcw, therail linkbetween
city1andcity3wouldbeusedforshiptents fromcity1tocity3
andalso forshiprents frcmcityltccity4. Therail linkbetween
cities3and4wouldbeusedforshipnentfrcxncity1tocity4and

also for shipments between cities 2 and 4. If the cannon costs of

 

fran "ch: News: Decisions and Orders," Traffic World,
September 9, 1985.

ItshouldbenotedthattheICChasnotextendedtheseguidelines
to shipnents of carnedities otherthan coal. The ICChad earlier
issued the following statement on SAC theory:

The ' -alone cost to any given shipper (or shipper
group) isthecostofservingthatshipperalone, asif it
were isolated frcm the railroad's other custaners. It
represents that level at which the shipper could provide the
service itself. No shipper would reasonably agree to pay
more to a railroad for trarsportaticn than it would cost to
produce in isolation itself, or more than it would cost a
carpetitor of the railroad to produce the service to it.
Thus, the stand-alone cost serves as a surrogate for
carpetition; it enforces a competitive standard on rail
rates in the absence of any real carpetitive alternative.

fran Interstate Camerce Oatmission (1983) .

 

 

 

Ea Tam. Em

Figure 1

operating these shared rail facilities do not vary substantially with
the levelof service (an assuming that marginal cost pricing is not
feasible), there will be no clear cost-based way to allocate these
costs.

Earlier contributions to the theory of efficient pricing with
shared costs have advocated recovering the unallocatable shared costs
with charges that vary with the demands for the service or with the
stand-alone cost of providing the service. 2 However, previous work
was based upon the assumption that all facilities will be used. This
may have been a reasonable assurrption before the Staggers Act was
inplemented, because the ICC allowed few service abandonments. But
the Staggers Act liberalized the abardomnent procedures, so now rail
carriers have more freedan to eliminate services and facilities which
cannot be provided profitably. By abandoning all services using a
certain facility, a carrier can avoid the fixed costs of cperating
that facility.

Therefore, cost allocation proposals for rail trarsportation must

 

ZThese allocations will be discussed in detail in chapter 2.

4
consider the possibility that the allocation of costs might lead the
carrier(s) to operate an inefficient: network (to operate facilities
which should not be used and to abandon facilities that could be
operated profitably).
HJRPCBE

The purpose here is to show
1) that in previous contributions to the theory of efficient pricing
with shared fixed costs, the importance of facility abandonments in
allocating shared fixed costs has not been recognized;
2) when efficient operation (or efficient abandcrmlent) of facilities
is considered, a first-best allocation of cannon costs can be found
which is less arbitrary than was previously thought possible: and
3) this proposed allocation can be applied to a specific shared
facility cost allocation problem based upon the Michigan rail
transportation, and therefore, the proposed allocation has practical
applications.

Many of these econanic principles behind the deregulatory changes
have been described as satisfying efficiency and equity criteria. 3 In
this dissertation, however, these principles are interpreted as

efficiency considerations, and the cost allocation proposal developed

 

3See for exarrple:
Fanara and Grim: (1985) p. 298.

The Moriarity Rule satisfies the following axioms of fairness:
1. No project pays more than its stand-alone cost
2. Every project pays sane cannon cost
3. Every project shares sane of the joint saving
4. Tiesrmoftheallocationsequalsthetotalccstof
providing the joint project. Therefore, no excess over
thetotalcostisdnarged, ardmoutsidesubsidyis

required _ .
5. The allocation is hanogeneous ofdegree 1 incosts...

5

here will be based upon efficiency grounds only. In other words,
questions involving the fairness of rates and the distribution of
incatewillnotbecorsideredwhenevaluatingthisaniothercost
allocation proposals.
mmmm OFANEFFICIENI'CDSTAIIOQTION

It will be argued that the first-best allocation should have the
following prcperties:
1) The provider(s) of the service stmld be allowed to recover all
costs (fixed and variable).
2) It should induce the provider(s) of the transportation services to
provide the traffic flows over the network which maximize social
surplus.
3) It should induce the provider(s) of the trarsportaticn services to
operate the facilities so that social surplus is maximized. In other
words, if the total surplus for all who benefit fran the rail
facilities can be increased by abandoning a service, the provider(s)
shouldhavetheincentivetcdoso. Itisthispropertythathasbeen
ignored in previous work.

Itwill alsobeshownthatacostallocationwhichhasthethree
properties above also has the following desirable properties:
4) It will lead to a non-subsidizing cost allocation (by proof in
chapter 3 and through an application in chapter 4).
5) It will allocate the fixed costs with less arbitrariness or
equity-based elanents than allocations which ignore possible efficient
facility abandonments (by proof in diapter 3 and by an application in
dnpter 4) -

6
An additional desirable property is:
6) It should be at least as practical to implement as previous cost
allocation proposals (as demonstrated by an application to the
Michigan transportation network) .
DEFINING EFFICIENCY

In order to cotpare the cost allocation proposals surveyed and
developed in the next two chapters, some measure of the efficiency of
the proposal is needed. Pareto efficiency will be used as the
standard here. The nest Pareto efficient cost allocation is the one
that leadstotraffic flmlswhiducaruetbedlarlgedwitlmtrnakiuugat
least one party worse off without being carpensated by the gainers.
In other words, the nest Pareto efficient cost allocation and traffic
flows are those which lead to the greatest total surplus.

The Pareto efficiency standard can be extended to permit policy
changes which lead to potential Pareto improvements, or policy changes
improving total surplus for which those who benefit from the change
could hypothetically corpensate those who are made worse off. This
avoids the problem of determining whether such compensation is given
and how the compensation will be made, and reduces the problem to
finding the flows which maxiumize total surplus for all who benefit
from the rail facilities.

Besides igrering the problem of coipersating those made worse
off, defining the nest efficient flows as those which maximize total
surplus (as a measure of social welfare) also requires the assumption
thattheonlyinterperscnalcorparisonsarethcsebasedupontheir
market behavior (and not on their ireone or preferences). Therefore,
the nest efficient traffic flows are those which best take advantage

7
of gains from trade, and not necessarily those which lead to utility
maximization. Itisassumedherethattotalsurplusisthebest
available approximation of social welfare, despite the problems
outlined above.4
CROSS-SUBSIDIZATICN AND EFFICIENCY

Recently, ecommists have developed theories of cross-
subsidization that depend upon whether or ret individual or groups of
consumershaveanireentivetobreakaway fromthesupplierandbe
served by another firm, provide the service for themselves, or ret
receivetheservice.5 Ifaconsumerorgroupofconsumershassuchan
incentive, that consumer or group is said to be cross-subsidizing
other users.

This definition of cross-subsidization was first proposed by
Faulhaber (1974), who defined cross-subsidization as when at least one
consumers (or group of consumers) pays mere than their "stand alone
cost", or more than they would pay if they alone were served. It may
be the case that when the nest Pareto efficient rates are calculated
for traffic on a given network, some consumers or groups of consumers
may pay nere than their stand-alone cost. If these consumers are
prevented by regulators from switching to arether supplier, then the
regulators will have the luxury of maximizing efficiency with some
consrmerssubsidizingotherconsrmers. Itmaybethecasethatthe
subsidized consumers and the subsidizing consumers purchase different

 

4See Zajac (1979), chapters 2 and 5, Brown and Sibley (1986),
pp. 8-18, and Varian (1984), pp. 198-209 and 268-276 for a more
detailed discussion of the use and implicatiors of Pareto efficiency.

58ee Faulhaber (1980), Sharkey (1982), Zajac (1979), and Brown
and Sibley (1986) .

services from the supplier.

If, however, the consumers are able to switch to other suppliers,
then rates set by the supplier or regulators to maximize efficiency
which do ret consider cross—subsidization may lead to constmers
droppingtheirservice. Inthiscase, therateswhich leadto
cross-subsidization cannot be considered to be optimal because they
arenotsustainablearriwillnotrecoverallofthefixedcostsifthe
cross-subsidizing costumers choose ret to be served by this supplier.

If the objective is to prevent cross-subsidization, then an upper
bound equal to the stand-alone cost of providing a service (or group
ofservices) canbeconsideredtobeaconstraintonthecost
allocation. Such an upper bound can be calculated for every service
and every possible group of services.

Thestand-alorecostupperbouresarebasedupontheganetheory
conceptofthecore. Ifacostallocation isinthecore, thenno
users of the network will be able to increase their benefits by
breaking away from the grand coalition. If re service or group of
services is allocated mere tlen its stand-alone cost, then by
Faulhaber's definition of cross—subsidization, this is a subsidy-free
allocation, since re service pays mere than it would outside of the
network. The Faulhaber definition is based upon the cost of providing
the service.

Sharkey (1982) extended the definition to include cases in which
theseconsumerspaymerethanthebenefitstheyreceivefromthe
service. His definition of cross-subsidization looks at both stand-
alonecostsandatthedelendsoftheusersoftheservices.

Sharkey's extersion isbasedupontheret benefits ofthe users or

9
group of usersu The net benefits of the service are the incremental
benefits received from.the service minus the additional variable
production and transportation costs of adding the service minus the
costs allocated to the service. If, when the total surplus is
'maximdzed and the fixed costs are allocated, the net benefits fer all
services and.groups are positive (and no service pays more than its
standralone cost), the allocation is in the core and therefbre
subsidy-free.6 In other words, the nest efficient flows and cost
allocation must be in the core.
JUSTIFICATION OF THE PmPERI‘IES OF AN EFFICIENT ALLOCATION
Property 1: The provider(s) of the service should be allowed to
recover all costs.

In the familiar case of provision of a service by‘a natural
menopoly, a marginal cost pricing structure will be the nest
efficient, (will maximize social surplus) but will ret allow the
producer to recover its fixed costs. For’muCh of the analysis in
Chapter 3, it will be assumed that the providers of transportation
service have a constant.marginal cost function. ‘With.a constant
marginal cost and marginal cost pricing, there is no producers'
surplus fbr the carriers, so the carriers will be unable to cover any
fixed costs.

If the carriers in the rail industry'were government owned,
marginal cost pricing in the cases described in the previous paragraph
nught.be practical, because any operating losses could be recovered
through the general revenues of the government. But the carriers in
the rail industry are private carriers, so they will have no incentive

 

6Sharkey (1982) pp. 61-64.

10

to operate under marginal cost pricing, because they will ret be
operating profitably. 7 Given this institutional arrangement, carriers
mustbeallowedtorecoverall oftheircosts, orelsetheservice
will ret be provided—even when providing the service(s) maximizes
social surplus.
Property 2: The cost allocation should induce the provider(s) of the
service to provide the traffic flows over the network which maximize
social surplus.

SinceParetoefficieucyisthestandardusedheretoevaluatecost
allocation proposals, the nest efficient cost allocation must give the
provider(s) of the service the incentive to provide the nest efficient
traffic flows over a given network.
Property 3: The cost allocation should induce the provider(s) of the
service to operate the facilities which lead to social surplus
maximization.

Most of the approaches to allocating the rail transportation
costssurveyedinchapterZareattemptstofirdthepricestructure
which leads to the nest efficient traffic flows (or minimum distortion
away from the most efficient traffic flows) over a giyeg network.3
Thepurposehereistoconsideraneregereralcasewherethenetwork
structurecanbechanged. Iftotalsurpluscanbeincreasedby
changing the network structure, the cost allocation proposal should

 

7Unless they can cross-subsidize unprofitable services with
profits from other operations. Cross-subsidization will be
discussed further in subsequent chapters.

8See for erample, Baunel and Bradford (1970), Brautigam (1979) ,
the discussion of the various Ramsey pricing proposals in Tye (1985) ,
Danes (1984) and Roberts (1983), and the Fanara and Grimm proposal
1985).

11
give shippers and carriers the ireentive to make efficient
configuration duanges . Therefore, the problem is to simultaneously
find the nest efficient retwork structure and the nest efficient
traffic flows over that retmrk structure. Of course, the efficiency
of any network structure is defined by the nest efficient traffic
flows over the network, so the two problems are interdependent.

It will be shown in chapter 3 that a cost allocation which
satisfies the three properties above will also satisfy the following
two properties:

Prcperty 4: The cost allocation will lead to a non-subsidizing cost
allocation.

Cross-subsidization is a concern in many of the discussions of
efficient cost allocations in the economies literature9 and in the ICC
rulings.1° It will be shown that the issues involving dross-
subsidization (as defined by Sharkey (1982) only arise when the
problem is defined too narrowly. When the problem is defined as
finding a cost allocation which gives carriers the incentive to
operate the nest efficient network, then the efficient cost allocation
will also be a subsidy-free cost allocation.

Property 5: It will allocate the fixed costs with less arbitrariness
or equity-based elements than allocations winch igrere possible
efficient facility abandonments.

Multi-part tariffs with one part of the cost allocation

consisting of fixed charges will be more arbitrary or else mere

 

9See Tye (1984) and Fanara and Grim (1985) , for example.

1"’See Ex Parte 347 (1983) and the coal rate guidelines in
footnote 1 to this chapter.

12
dependent upon equity considerations rather than efficiency than a
per-unit cost allocation, since the allocation is likely not to be the
sameforallusersandisretdirectlydetermiredbytheecormic
decisiors of the users. However, a multipart tariff solution to the
rail cost allocation problem which satisfies properties 3 and 4 above
will be less arbitrary than a multi-part cost allocation which does
ret consider facility abandonments. To have the properties described
above, a cost allocation must include the constraints that no service
orgroupofservicesbeallocatedashareofthefixedcostswhich
lead to inefficient operation or abandonment of services, and these
constraints narrow the range of efficient cost allocations.
Property 6: It should be re mere difficult to implement than the
cost allocation proposals surveyed in dlapter 2.

Indapter4, theproposal developedherewillbeappliedtoa
simplified medel of the Michigan rail transportation system to show
that the proposal is indeed one which has practical applications. The
Ramsey—pricing proposals described below require excessive data
collection and rapidly becore mere coiplex to calculate as the size of
the problem increases. As a cost allocation becomes more difficult to
calculate, it becomes more difficult to implement. Therefore, the
cost allocation should economize on data collection and calculations
in order to be practical to apply.

MDDELING RAIIROAD NENDRIG

Thetechniquesdescribedinthisthesisaremeanttobearplied
to abstractions from actual rail networks. In these networks, a
typical railroadretworkconsistsofammberoflirflrsbetweenaset
of redes over which a variety of comedities are carried. The links

13
may have different lengths, costs of construction and operation, and
traffic densities. Commodities may follow routes over one or several
links and may often be classified as long hauls or short hauls. Each
comedities is produced at one set of redes and sold (demanded) at
another set of redes, arnd different comedities may be produced at
different redes and have different demand and cost functions.

The trarsportation costs consist of variable costs of carrying
cornedities aund fixed costs of operating links. It is assumed that
theccstsof operating linksdoretvarywiththeamomtoftraffic
carriedonthelink, butthesefixedcostscanbeavoidedby
abandoning the link. Variable transportation costs may include the
congestion costs (such as delays) imposed upon other users of the
network. There may also be economies of network operations, because
astheameuntoftraffic increases, thefixedcostscanbespreadover
more users.

RELEVANT RAILROAD REHHATIONS AND INS‘ITIUI'IONS

Until recently, railroads were heavily regulated by the
Interstate Conneroe Conmission, which exercised considerable control
over railroad rates, entry into new routes, and abandonment of old
routes. However, the industry has been partially deregulated in the
last decade.11

The first naj or piece of deregulation legislation was the
Railroad Revitalization and Regulatory Reform Act of 1976 (the 4R
Act). The 4R Act contained provisions for the elimination of rate

regulation where railroads did not possess market dominance (merepoly

 

11This discussion of the American railroad irdustry's structure
and recent regulatory reform is based primarily upon Keeler (1983) .

14
power), and for the ICC to consider the financial health of railroads
when making rate decisions. Before the 4R Act, few abandonments of
existing services were allowed for railroads if there:were any
significant protest from the affected users, but the 4Rs Act gave
railroads more freedom to abandon unprofitable services. An important
consideration behind the passage of the 4Rs Act was the poor financial
health of many railroads. However, even after the 4Rs Act.was
implemented, the financial condition of railroads continued to
deteriorate, partly because just about everywhere the railroads had
discretionary power to raise rates in accordance with.the act, the ICC
found the existence of market dominance.12

The deregulation process was continued with.the Staggers Rail Act
of 1980. The Staggers Act is based on.the premises that the rail
carriers no longer have the market.power they once had, that most
traffic is now corpetitive, arnd market forces will be more efficient
than regulation.13 Some of the major goals in section 3 of the Act
are to improve the financial conditions of railroads, to reform
regulation to reduce inefficiency, and to balance the goals of
carriers, Shippers, and the communities served.by railroads.

The Staggers Act.preserves rate regulation only to prevent rates
from.rising to monopoly rates on routes found to be market dominant,
and also to prevent ruinous competition from breaking out by requiring
rates to remain above the variable costs for each service. So long as

the extreme cases of market dominance on one hand and rate wars on the

 

12Keeler (1983) p. 97.

13See Section 2 of The Staggers Rail Act of 1980, Public Law
96-449 (1980).

15

otherdonotoccur, theActallowsrailroadstodeterminetheirom
rates. However, marketdominanceisnolongerdeterminedbytheICC:
it is based upon the ratio of a railroad's revenues to variable costs.
If this ratio does not exceed 1.8 (if rates are less than 80% higher
than variable costs) the railroad is net considered to have market
domirance. TheActalsoallowstheIcrtoexenptcertaincomedity
groups entirely from regulation. This provision was meant for
products such as fresh fruits ard vegetables for which internedal
(truck) competition is strong enough to provide a conpetitive standard
without rate regulation, making rate regulation unnecessary.

Abardonment procedures had already been simplified and
liberalizedurderthe4RsAct, buttheStaggersActfurtherreduced
the railroads' obligation to provide meney-losing services (to
cross-subsidize these unprofitable services). The abardonment process
was liumited to 255 days from application by the railroad to prevent
delaying tactics, ard the ICI: was required to take the financial
codition of the railroad into consideration when making the decision.

In his study of recent rail track abandonment, Due (1987) fond
that there have been many of these facility abandonments. Between
1976 am 1986, 35,000 miles of traCk were abandoned (about 20% of the
1976 total miles), and as of 1986, the railroads were considering
abandoning another 7,000 miles of track. Much of this abardonnent can
be attributed to railroad failures, and many of the facilities were
taken over by smaller competitors, but there have nonetheless been
considerable facility abandonments siree the abandonment procedures
were liberalized.

OnefinalprovisionoftheStaggersActisrelevanttothis

16

project. TheStaggersActencouragedcortractratesbetneenshippers
ard carriers, and the parties have considerably more flexibility over
hovtheysetuptheircontracts. Nowthesecontractscancontain
fixeddnargeswhichdoretdeperdupoutheanenmtcarried. Thus,
railroadcostscanberecoveredwithfixeddnargesonshipperswhich
will have less distortionary effect than per—unit charges which vary
with the level of service.

Keeler summarized the Staggers Act as follows:14

Overall, then, the Staggers Act gives belated recognition

tothefactthattherailroadirdustryisnologerthe

menopoly itwasinthenireteenthcenburyardreloger

able to cross-subsidize connen carrier obligations of all

sorts from profits on captive shippers. In fact, in

recognizing that cross-subsidies come at the expense of

captive shippers ard in placirg limits on prices they can

be charged, the act actually discourages cross-subsidization

and explicitly ereourages raisirg rates or terminating

meney-losilg services.
MON GDSTS AND WC ‘I‘HEDRY

This problem of allocating railroad costs can be traced back to
the T’aussig ard Pigou exchange (and earlier) 15. Taussig (1891) argued
that rail rates could be explained by the jointness of the costs of
providing services over the network. Pigou argued that the costs were
ret truly joint—except in a few cases such as backhauls—ard argued
that the explanation for rate discrimination could be found in the

standard case of nerepoly supplier discrimiunation.l6 “Their

 

14Kee1er (1983) p. 102.

15The origins of the problems discussed here can be traced back
to the famous T‘aussig—Pigou debate (ard earlier). Sane of the
articles surveyed in the first two dapters trace their origins back
to the Taussig-Pigou debate. See for example, Fanara ard Grimm (1985) .

16'I‘aussig (1891) , Pigou (1912) , and the Taussig ard Pigou
exchange in the 1913 mm Journal of My; .

17
underlying difference of opinion was whether the costs of serving
different railroad custoners may properly be regarded as joint. . . or
oomuon"17, where the distinction between joint and common costs
depends upon whether the products (different transportation services
in this case) are produced in fixed proportions (joint) or in variable
proportions (cannon).

Economists have also used the value of service to explain rates.
Ingenueral, iftheprioeofthecomodityshirpedishigh, thenthe
transportation charge will be a small peroentage of the total price,
and the shipper will pay a high transportation charge. These shippers
are likely to be less sensitive to additional transportation charges
thanthoseshippers formuanthesanetransportationduargewouldbea
higherperoentageofthetotalprioe, sothequantitydistortionis
lu'kelytobelower. Thevalueoftheservice isanupperboundonhow
hightheratecanbe (thevalueoftheservioeisnotthesameooncept
as the value (price) of the comedity) . A similar conespt is
"charging what the market will bear," whidh is the rate structure
whiduraisestlsnexinmannmtofrevenue (andisloverthanthe
value of the service unper bound).

Inrecentyears, theseoonoeptshavebeenextendedandformalized
in the public utility pricing and transportation econonics literature.
Efficiency is usually the standard used to evaluate rates in this
literature (and here as well). The brief discussion which follows is
meant to show the relationship between the proposed solutions to the
railroad ratemaking problan (discussed in chapter 2 and proposed in
chapter 3) and the traditional issues discussed of public utility

 

17Rahn (1970) footnote 11, pp. 93-94.

18
pricing problems.
MARGINAL (DST ERICING

Pricing at marginal cost is usually considered to be the most
efficient because then buyers pay a price equal to the cost of
supplying an increnenntal unit of output, so that the most efficient
output is supplied. Producers supply that output because it is
profitable for than to produce up to that output level, but beyond the
ontpntatwhichtheprioeequalsthemarginal cost, thecostsexoeed
theincrementalrevenuefortheproducer, sonoadditionaloutpntis
supplied. This is the most efficient output level because the sum of
producer surplus and consumer surplus is maximized.

Althouglu the above analysis provides a starting point for
determining rail rates, Kahn (1970) discusses several sets of issues
which must be addressed before the implications of marginal cost
pricing may be determined.

The firstsetof issues involvetlspropermeasuranent of
marginal cost. Kahn cites two economic principles for determining
whatshouldandshculdnotbeincludedinthemarginualoostfor
pricing purposes.18 The first is that everyone should bear the causal
responsibility for all costs inposed by the provision of an additional
unitofoutput, andtheseoondisthatpricingshouldbeattheshort
run marginal cost, because the properly defined short run marginal
oost(SIMC)isthesocialopporomityoostatthetinethedecisio1is
made. TheSRuCcaninclLdeoostsincurredafterthedecisionismade,
such as depreciation, maintenance, and repair costs, so long as these
costsvarywiththeontputlevelandcanbeanticipatedwhenthe

 

131cm (1970) vol. 1, p. 71.

19

decision is made.” The sun: should be based on the smallest possible
incrauentalunitofoutprt. Astheincrementalunitgets larger, more
costsbecouevariableandthecoumonorsharedcostsbecouesmaller.
For rail transportation, sane possible increuents are space allocated
toaconmodityonatrain, onetripbyanentiretrain, andthe
operationofaroutewhichmanytrainswill use. These increnuental
uunits reflect different decisions; whether to ship a comedity by
train, whethertoalterthe frequencyofthetrain service, orwhether
tooperateatrainroute. Itwillbeassunedinthemodeldeveloped
induapterBthattheincrenentalumitsareunitsofspaceonatrain,
which is the smallest possible umit.

Thesecondsetofissuesareconcernedwithwhetherevenproperly
defined marginal cost pricing is desirable by criteria other than
(Pareto) efficiency. An exanple of this type of issue is whether
consumers are capable of determining the value (what they are willing
to pay) of an incrauent of output. Such calculations may be too
complicated, or consumers may simply make the wrong choices because
theydonotknowwhatisintheirbestinterestordonctagreewith
the economists' definition of their best interest. Ancther exanple is
whether or not the income distribution for a society is optimal. If
incone is distributed differently, consuumers may make different
aggregate choices and may provide the producer with a different demand
curve, so the price will equal marginal cost at a different output
level. Econonistsgenerallydonctaddresstheseissues, atleastnct

 

19Thereisafurthersetofissueswhiduinwolvestheduoice
of depreciation neasuurements and other problaus of defining the costs
associated with the fixed investment but still included in the SRMC.
See Tye (1985) for a discussion of these problaus.

20

when evaluating whether marginal cost pricing is desirable. Since the
efficiency criteria for evaluating cost allocations is being
considered here, the desirability of pricing at marginal cost will
henceforth be evaluated by efficiency standards alone, but it is
acknowledged that there are other considerations than efficiency.

Ancthersetofissuues isconcernedwithwhattodom'enmarginal
cost pricing is not a viable option.20 It may be possible but
prohibitively expensive to calculate all relevant marginal costs, or
elsethemarginalcostmaybevaryingandthesellermaynctwantto
altertheprice frequentlyasthemarginalcostduanges. Another
questioninthisgroupingisvery iuuportanttotheanalysisinthe
next two chapters: Marginal cost pricing may nct allow the rail
carriertorecover itstotalcosts, yetatthesanetine itmaybe
Pareto efficient for the firm to operate and charge more than its
SRMC, either by raising its price above the SRMC or by recovering the
RAMSEY PRICING

Baumcl and Bradford (1970) applied the Ransey pricing concept
from public finance literatuure to the problan which arises when
marginal cost pricing does nct allow the public utility (rail carrier
in this case) to operate profitably. They proposed using Ransey
pricing to find the met efficient rates above the marginal cost which
allow the utility to recover its fixed costs.

Ranrsey pricing originuates with Ransey' s (1926) classical

 

2°1<ahn (1970) Vol. 1, pp. 83-86.

21

discussionofcptimaleucisetannes.” Hearguedthatinorderfora
governmenttoraiseagivenancumtofrevenuefruncoumoditytaxes,
thetaxoneadncomcdityshouldbeinverselyprquortioualtothe
elasticity of denand for the councdity. In practice, Ransey pricing
maximizedtctalsurplussuubjecttoabreak-evencostraintforthe
supplier.

men Ransey pricing is applied to railroad rates, each service is
duargedthenarginalcostoftheserviceplusanadditionaldnargeper
umitshippedtocoverthefixedcostsoftheentirenetmrk. To
minimize the quantity distortions (and maximize total suurpluus) , these
Ramsey charges are inversely proportional to each shipper's elasticity
of dannand for transportation services. For eadn shipper (or shimer

group) i,theperoentagemarloupovercostis:

£1_§ = i

(1) P; i ei

In equuation 1, Pi, Ci, and e1 are the transportation price,
marginal cost, and elasticity of demand for shimer i, and A
isacostantforallshinpersumidnisdeterminedbythereveme
requireuent. If more (less) revenue is required, is sinply
increased (decreased) asmuohasisneededtocoverexactlythe
revenue requirenout.

Ranseypricinginthisformisdependentupontheassumptiouof
independent demands. Rohlfs (1979) developed a superelasticy whidn
rqulaces the elasticity in equuation 1. 1 to account for non-zero
cross-elasticities of denand. Howcrer, as more complicated flows and

 

leee Baumcl and Bradford (1970) and Brown and Sibley (1986) ,
pp. 39-44 for discussios of the origins of Ransey pricing.

22
interdependent denands are introduced, Ransey prices rapidly becone
difficult to calculate.”

Braeuutigam (1979) extended the Ramsey pricing theory to rail
transportation facing intermodal canpetition (and nc inntramodal
conpetition) . After applying Ransey pricing to a totally regulated
transportation systan (the totally regulated second best, or T183,
problon) , Braeuntigam developed a theory of partially regulated secod
best (PRSB) regulation for when the coupeting modes are not regulated.
Routes with more intermodal coupetition would have less ability to
raise rates above marginal cost (will face larger quuantity
distortions) , because the unnregulated intermodal coupetitors can take
away sole of the traffic by pricing at their marginal costs.
Innternucdal conpetition will also be cosidered in the proposal in
Chapter 3, but since two-part tariffs will be used to recover the
fixed costs, T1258 and H288 allocatios will not be necessary to
recover the fixed costs.

UI‘HER CIBI' AILOCATIQJ APPROACHES

Thebasic ideabehindRannseypricingistorecoverthe
unnallocatable fixed costs by raising the rates above the marginal cost
as efficiently as possible—which is to say, according to the
elasticities of demand of the users. In practice (and in the public
utilities literature), similar looking procedures have been used,
exceptwithratesbeingraisedabovethemarginalcostbyother

criteria . 23

 

22This discussion is based upon Brown and Sibleys' (1986)
account of Rohlf's article (1979) , pp. 42—43 and 197-199.

23See Brown and Sibley (1986) pp. 44-49, 51-54, and 59-60,
and Braeuutigam (1980) .

23

onesudnprocedureisbaseduponmllynistributedcosts, uunder
whidnconnoncostsaredistributedancngservicesinproportiontothe
service's share of total ton-miles, revenue, or other neasureunent
without much economic meaning“. Under another approach which comes
out of the theory of cowerative games, (see the discussion of the
FanaraandGrinnnproposalinchapterZ), thecomnoncostsare
allocated in a manner which avoids cross-subsidization (as defined by
Faulhaber) .

These approaches are less cocernned with econonic efficiency per
seandarelargelyarbitraryinthemannerinwhidncostsare
allocated. But they are generally easier to calculate than Ransey
pricing allocatios and can be designed to avoid any inefficient
cross-subsidization which might arise frcnu Ransey pricing.

NONUNIFUIM PRICES

Wienper-unitratesareraisedabovethemarginal cost, a
quuantity distortion and dead-weight loss are created. The Ranusey
pricing solution creates the minimum distortion while still alloving
theutilitytorecoverallcoststhrcughper-unitdnarges, since
maximizing total surplus subject to breakeven costraints also
minimizes the dead-weight loss created by the per-unit charges to
recover the fixai costs.

Coase (1946) suggested that even the minimum dead-weight loss
from Horsey-pricing rates could be reduced or eliminated with a
two-part tariff. It may be possible to recover all of the fixed costs
of operating a rail network using a Chase-type tho—part tariff. One

 

2“See Brown and Sibley (1985) for an extensive discussion of
the shortconings of Fully Distributed Costing.

24
partofthetariffwouldbeequaltothensrginalcostofproviding
theserviceandtheotherpartwouuldbeanaccess feechargedtothe
shippers or producers (and paid out of their surplus) to recover any
remaining deficit.

A two-part tariff suuch as this would be more Pareto efficient
thananyunifompricewhichrecoversthefixedcostsbecausethe
two-part tariff (if innplenented correctly) would not create any
quuantity distortios because the marginal rate per unnit could still be
equaltothemarginalcostperunit. Thecostallocationinchapter3
will be developed assuming that the fixed costs of operating
facilities can be recovered with access charges25 and the marginnal
costs can be recovered with variable charges.

OVERVIEW OF THE REMAINING QIAPI'ERS

In the next chapter, several cost allocatios froun the rail
transportation literature will be surveyed, including allocations
based uupon fuully distributed costs, Ransey-pricing, stand-alone costs,
and Rannsey pricing costrained by stand-alone costs. It will be shom
that in each of these proposals, either the possibility of service
abandonments is igncred, or else inefficient service abandonments are
not defined correctly.

The model of rail facilities and an efficient cost allocation
will be developed in chapter 3. This multi-part tariff will be shown
to be less arbitrary than was previously thought possible. It will
also be proven that an allocation with the first three properties

defined in this chapter will also avoid the problon of cross-

 

25these fixedcostswillbechosensothattheydonctleadto
cross-subsidization or inefficient abandonment of services.

25

cubsidization that is discussed so extensively in the previous
literature.

The fourth chapter will consist of a simulation based upon the
1984 Michigan rail transportation network. The optimal Michigan
railway network and the optimal cost allocation will be found for the
traffic flos. Although this chapter is nct necessary to justify the
coclusios fron chapter 3, it will show that the application rules

are in fact practical to apply.

CHAPTERZ: mmmmsmmnonoosrmmwmoposms

Problems in inplouenting the regulatory reform described in
chapterlwereencounteredwhencoalrateswerecontested. Muchof
the coal transportation is by rail over market-donninant routes to
cities where it is used by utilities to generate electrical power.
These utilities and their coal suppliers argued that they were being
charged unreasonably high rates because they are captive shippers. In
the econcuuies literature, several cost allocatios have been proposed
sincethepassageoftheStaggersRailActandthesubsequentdebate
overcoalrateswhidnareclainedtoallocatethesecomcncosts
efficiently and fairly. Three of these proposals will be cosidered
in this chapter.

'IHE RAPBEY PRICING PROPCBAL

When their coal rates were contested, the railroads’
representatives argued that railroads should be allowed to charge
whatthemarketwillbear, uptothepointatwhichtheyearnedan
adequuate return on their investment. In other words, they argued for
second best, or Ransey pricingl. However, the utilities and coal
shippers ’ representatives argued that pure Ransey pricing would often
resuult incoalshipperspayingmorethanthestand-alonecostofthe
service. The ICC also agreed that pure Ransey pricing rules for
determining rates might lead to sore rates exceeding the stand—alone

 

1A brief descriptios of Ransey pricing and how it relates to
marginal cost pricing principles was provided in chapter 1.

26

27
cost of the service2 (cross-subsidization by Faulhaber’s
definition3) .

The railroad representatives have modified their proposal to
advocate Ransey pricing rates in narket doninnated traffic with the
stand-alonecostsinposedasunperboundsonrates. Urdertheir
proposal, rates will be allocated initially according to the Rantsey
pricing rule, but if any services are allocated ncre than their
stand-aloe cost, the cost allocation will be recalculated with these
services paying their stand-alone cost and other services will pay a
larger share of the fixed costs.

Therefore, this ncdified Ramsey pricing proposal would have sore of
thecoal shipperspayingall ofthefixedcostsoftheroutesthey
use, even though these links are shared facilities.4

However the Ransey price allocation is determined, this type of
allocation assumes that the capital stock of the entire network is
homogeneous, souserspayaccordingtotheirdemandsandnctaccording
to what links they use. It is nct clear what is the relationship
between the stand-aloe cost for individuual services (or groups of
services) and a Ransey pricing break-even constraint for an entire

network. The former assumes that sore capital (but nnot all) is

 

2Interstate Oomeroe Conmission (1983) . See also Fanara and
Grim (1985), p. 297, and footncte l to chapter 1 for more on the ICC
statements on stand-aloe costs.

3See Tye (1985) for a discussion of the problens of measuring
stand-alone costs which are nct clarified in the ICC statauents. Note
alsothattheIOChasnctstatedthat itisusingFaulhaber’s
definition of cross-subsidization, especially in regards to grops of
shipper's paying ncre that the stand-alone cost of serving the entire
group aloe.

4Roberts (1983), p. 28.

28
shared, but not necessarily by all users, while a break-even
constraint inpflies that all capital is.homogeneous and snared.by all
users.

Thisassuunptionofahcmogeneouscapital stool-{maybe
appropriate for electrical utilities and sole other public utilities,
whereanincreaseintheoutputlevelmaybenefitanyoftheusersof
the utility. But the existence of stand-aloe costs for differennt
services over a network by definition denies that the capital stock is
honcgeneous. Unlike the case of power generation, if soue rail
facilities are abandoned, nct all users of the network will be
affected the sane by the reduction of service levels over the network.
Damusmadethispointwhenl'earguedthat'wnseypricingis
esseuntially a public finance tool or a pricing technique for a
nationalized industry. As such, it is not a suuitable response to
deregulation."5

The Rantsey pricing allocations are one-part tariff cost
allocations which are neant to be the nest efficieunt (least
distortionary) allocation of cannon costs using oe-part tariffs5.
However, thedistortioncreatedbytherecoveryofcomcncostsusing
per-unitchargescanbereducedevenfurther (oreliminnated
altogether) withatwoparttariff. Theper-unitchargeundersuoha
two—parttariffwouldbethecostswhichcanbeallocatedto
individual unnits of the services, and the fixed part of the tariff

wouldbetheshareofcounoncostsallocatedtotneservice. A

 

50amus (1984), p. 50.

6The Ransey prices may be tne most efficiennt allocation of cannon
costsonnlyundertheassumptionofahoucgeneouscapital stock.

29

 

tm—parttariffbasedontheFanaraandGriuumproposal belowwillbe
more efficient than any oe-part tariff7.
THE UNIFOH! RATIO HJIE

Merrill Roberts advocated using the uniform ratio rule8 to
allocate the shared facility costs. "He ‘Uniform Ratio Rule’. . .
treatsasaclassall shipperswhoarediscriminatedagainstas
identified by PM ratios above the systanwide av " (enpnasis
Roberts’s) .9 Under such a cost allocation, a uunniform price-to- H
marginal-cost ratio is calculated as a ceiling on tne per-unit
charges which is to be applied to all traffic.10

This proposal umuld divide the users into two classes; those
discriminated for (with donand elasticities for transportation
services greater than the system average) and those discrinuuinnated
against (whose donand elasticities are below the system average) .

 

7Other criticisns of the Ransey pricing allocations are raised by
nye (1985), pp. 9-12, Dams (1984), pp. 59-60, and Roberts (1983), pp.
27-29. Tye points out that the railroads’ representatives use a ncre
"permissive" definition of stand-alone costs (p. 9). Rather than
using the historical cost of the incmbent railroads, the railroads’
representatives propose using the replacenent costs of a hypothetical
entrant. Tyearguesthatthecostsofahypothetical entrantwouldbe
inflated because trey would include the costs of overcoming barriers
to enntry under coditios of market doninnance.

Danuus argues further that tle railroads’ representatives propose
applying the stand-aloe uupper bound on rates only to groups, and then
turn around and advocate fully—allocated costs (but nct Ransey
pricing) within the groups.

Roberts argues that tne Ramsey pricing allocatios igncres
intermodal competition (unless Braeuntiganns’ extension of Ransey
pricing is adopted), will require any service whidn is allocated more
thanitsSACunderuncostrainedRanseypricingtopayall ofthe
shared costs uunder this costrained Ransey pricing allocation, and
will be impossible to calculate if the traffic floats are too conplex.

8first proposed by Alfred Kahn (1970) , pp. 137-139.
9Rober‘t’s (1983), p. 28.
10Roberts (1987), p. 98.

30
Kahnproposeddnargingtl'elogrumaveragecosttoshipperswith less
elasticdemandstorecovertnefixedcostsanddnargingthelongrum
marginalcosttoshipperswithnoreelasticdemands. Thenall inthe
class discrinninated against pay a unniform markup over their marginnal
transportation cost.

Notethatbyadvocatingapplyingthisproceduretorailcost
allocation problens, Roberts makes tne sane assumption of honogeneous
capital as us Ransey pricing advocates, although re does exclude
"highly specialized facilities. "11 Therefore, the uniform ratio ruule
isverynuchliketheconstrainedRanseypricingproposal inthat it
alsomakestheassmptionthat capital ishcmcgeneous. Acoordingto
Roberts, "(t)hekeypreniset1stallshippershaveastakeintl'e
system as a whole (but not in facilities specialized to particular
users) realistically solves the allocation problem. "12

Burt shippers do not have a stake in facilities they do nct use
and requiring them to pay for these facilities could lead to
inefficient cross-subsidization and service abandonments. Also, if
demand curves for smaller grops of services can be estimated, the
uniform ratio rule will be less efficient than an allocation based
uponmore than two grops (but easier to calculate).

'IHE FANARA AND GRID“ PROHBAL

Fanara and Grinnn (1985) nnade ancther proposal for allocating the
fixed costs without causing sane services to subsidize others (by
Faullsber's definition). They poinnt out that there is a history of
using accounting rules based upon stand-alone costs to allocate shared

 

11Roberts (1983), p. 28.
12Roberts (1983), p. 29.

31
overhead costs. They propose first calculating the stand—aloe cost
for each service (or grop of services, depending upon tne allocation
ruule chosen) and then using an arbitrary allocation rule to allocate
thecosts inamannerwhichdoesnct leadtocross-subsidizationand
hasalluserspayingsoueshareofthecostsn. Inotherwords, they
propose first allocating all traceable costs to te appropriate
services, and theun allocating the fixed costs of tne network in
proportion to the stand-aloe costs of the services. The share of
fixed costs allocated to any service (or grops of services which are
cosidered in the allocation ruule) will be less than the stand-aloe
fixedcostoftheservice. Theirprocedurecanbeusedwhen
alternative sources of transportation services are available, such as
nctor carriers.

In this form, the Fanara and Grinmn allocation is recovered
through two—part tariffs (rather than as uniform prices). Under the
recent regulatory changes, contracts between shippers and carriers are
encouraged, and these contracts might include fixed charges. The
two-part tariff, would have the variable costs recovered froun a charge
which varies with the quuantity shipped and the fixed costs recovered
fronlump-sumdnargestotheshippers. Assmningthatthesechargesdo
nct divert any traffic because they are lump-sum charges (and
therefore lead to re inefficient service abandonments) , this
allocation will lead to no quantity distortios, and therefore this
allocation proceduure will be ncre efficient than the Ransey pricing or

Uniform Ratio allocatios.

 

13The characteristics of four such arbitrary allocation rules
were conpared by Hannlen, et.al. (1977) .

32

Thesechargescolldalsobepassedontothefinalconsmersas
nerkups over the variable cost (as per-unit charges). Either way the
costsarerecovered, underanallocationbaseduponFanaraandGrinnn’s
proposal, all shippers are paying less than tne stand-aloe cost of
their service (are not cross-subsidizing each other by Faulhaber’s
definition“) , and the total costs of the network are recovered frcnn
treshippers. Itisarguedherethattheseupperboundson
allocatios to flows are efficient because cross-subsidization (and
therefore loss of traffic to other carriers) is avoided so log as
none of these upper bounds is succeeded.

Of the three cost allocation proposals discussed in this
chapter, theFanaraandGrinnnprcposalhastl‘eadvantageofbeingthe
easiest to apply, because it requires only information about us costs
of tne transportation service (while the others require information
about demand elasticities) . Tne Fanara and Grinrm proposal is
calculated in a manner which prevents cross-subsidization by
Faulhaber’s definition, while both the Roberts and tie Ransey pricing
proposals must be modified to prevent this cross-subsidization.

Later it will be argued that this range of efficient (in the
core) allocatios is too broad. Eyen if no service pays ncre than its
stand-aloe cost, the allocation may still be outside of the core,
leading to inefficient loss of traffic. The Fanara and Grimm proposal
is based solely upon the costs of providing the service, and therefore

may lead to cross-subsidization by Sharkey’s definition, because tne

 

14It should be noted that by using a Moriarity rule allocation,
Fanara and Grinum are only considering whether individual shippers (and
notanyshippergrops) arepaynorethantheirstand-alonecosts, so
their final allocation proposal really may not avoid cross-
subsidization by Faulhaber’s definition.

33

benefits (demands) of each service group are not cosidered when the
rate are determined.
WCIIJSION

Therehavebeenseveralproposalsmadeadvocatingthe
replacement of the current nethods of allocating rail costs with less
arbitrary costing ruule. Tne Ramsey pricing proposals are the most
efficient (by definition) of tne per-unit allocatios which assure a
fixed network configuuration, but it is net clear how the most
efficient rate for the entire network are related to individual rate
when there are corplex interwoven traffic flows. Roberts advocate
tne umiform ratio rule first proposed by Kahn because it would lead to
more efficient rate than the Rail-Form-A rate15 which are currently
used, butthisproposal retainsnuudnofttearbitrarinesofthe
current rate by using the Rail-Form-A rate as the starting point.
BoththeRanseypricingandtheRoberts’ proposaldependuponkncwing
tne demands of the users in order to calculate tne denuand elasticities
of each service. TheFanaraandGrinumproposal wouldbemucheasier
to apply, because it requires only information about the costs of tie
transportation service. The Fanara and Grim proposal by definition
leads to no service group paying more than its stand-alone cost (one
ofthe Ia: guidelines), whilebothtneRoberts andtheRanuseypricing
prquosals must be modified to prevent cross-subsidization. However,
tl'e Fanara and Grinm proposal may lead to cross-subsidization by
Sharkey’s definition, because the benefits of each service grop are
not cosidered when the rate are determined.

 

15Rail-Form-A rate are a form of fully distributed costing
which allocate costs in proportios whidn have little economic neaning.

34

Aswillbeseeninthenextchapter, alloftheseproposalsas
deigned for fixed networks. Hodever, it may nct be optimal to
provide all service, and under tl'e Staggers Act, carriers are given
tnefreedontoabandonunprofitable service inmostcase. Inthe
next dnapter, it will be shown that a more efficient cost allocation
procedurecanbefoundduentl'eproblenofavoidingcross-
subsidization is properly defined as a problen of finding a cost
allocation which leads to both the most efficient network structure

and the nest traffic flows over this network struucture.

QIAPI'ERB: EFFICIENTCIBTAIIOGX‘ITCNANDABANWI‘S

In the literature of efficient pricing with shared fixed costsl,
facility abandoments have not been properly cosidered when
allocatingsharedfixedcosts. Tnepurposeofthisd‘uapteristosnm
that when the possibility of abandonments is cosidered, a first-bet
allocation of cannon costs can be found which is nore efficient and
les arbitrary than was previously thought possible. Since the
railroad industry following tre Staggers Rail Act of 1980 is an
industry in which such facility abando'ments are inportant, much of
the discussion of this allocation problen will be related to railroad
institutios.

THE PROBLEM DESCRIPTIQI

In chapter 2, it was shown that previous atteupts to solve this
rail cost allocation problem have assumed a fixed network structure,
and therefore have failed to cosider the possibility of facility
abandoments. Inthischapter, sudnabandonmentswillbeallowed, so
that the incentive to operate a facility must be cosidered in any
attenpt to allocate uuntraceable cannon costs. Therefore, tne problen
istostartfronagivensetofshippers, carriers, andsetof
facilitie, find the nost efficient network structure and set of
players that is in the core, and finally, to find a cost allocation
that allows all of the fixed transportation costs to be recovered
(with nnon-distortionary fixed charges) while encouraging the carriers
to operate tne nost efficient network and provide tne nost efficient

services levels.

 

1Thisliteraturewasdiscussedinctnaprterz.

35

36

TEE NEIVDRK

'BereareIproductsproducedandshippedoverthenetmrk.
There may be different transportation denands and costs for different
product shipnents. Let i be the product index, i = 1,2,...,I. The
network over which the connoditie will be shipped consists of J
citie and H links between citie. All traffic between citie is
carriedoveroeornore links, andtheremaynctbealinukbetween
everypairofcitie. OuutoftneHlinks, Hrarerail linksandHt
are truck.routes between nodes, with.nr + at =:H. let.h.be the index
for linnks, with h = 1,...,Hr for rail links, and h = Hr+1,...,H for
truucklinks. Itisassmedthatncnewrail ortrucklinnkswillbe
added to the netmrk. Let L = tne set of all links available for
shipments, and let a superscript on L (such as 1?) indicate a subset
of the facilitie.
TIE PARTICIPANTS IN TIE NEIVDRK

Following the literature applying gane theory cocepts to public
utility pricing probleusz, the shippers and the carriers of products
over the network will be nodeled as participants in a transferable
utilitygane. Theshipperswillbethecosunerswhodenand
transportation service, and the carriers will be the producers who
spply transportation service over the given set of facilitie. Iet
N(L) denote the set of all shippers and carriers in network L, with
n e N(L): and let S(L) be a subset of N(L). Note that the set of
players is a function which depends upon the facilitie available.
Tnerefore, for a subset LS of L, the set N(LS) may be smaller then the
set N(L) , because any menbers of N(L) which are not in N(LS) will be

 

2Faulhaber (1975), Zajac (1978) and Sharkey (1982)

37

excluded when tne facilitie in Ifi are not sufficient to provide
transportation servicetotheemeubersof N(L).

Tnereareshippersofproductiinseveralcitie. Ietj=the
indexforoeofthencdemerecomodityieitterentersorexits
tenetmrk,andletJi=t1esetofallindexmnubersoftlssemde
repreentedbythejindex,sothatjeJi. Perhaszicouldbethe
setofallncdewheretnecouuodityisproducedorentersthe
network, or,asinthecaseinchapter4, eithertheoriginor
destinationnodeof.theshipnent,dependinguponwhidlhasthelower
indexnumber. Alsoletk=theotherindexforncdewhere
conmoditie either enter or exit the network and let Ki = the set of
allncderepreentedbyk,wherekeKi. ThisKicouldbethesetof
allncdewherethecomodityexitsthenetwork,or,as(hapter4,the
ncdefortheshipuentwhiohhasthegreaterindexnumber. Inorder
for this problen to be of interest as a transportation problen, there
should be at least several overlapping shipments which share
transportation facil itie .

Therennaybeseveralpossiblerouteforproductitobeshipped
fronnjtok. Theseroutecanbeoverraillinnks,trucklinks, or
both. IetMijk=tlenumberofrourteoverwhichproducticanbe
carriedfromjtok,andletmbetheindexfortheroute,withm=
1,2,...,Mijk. Itmaybethecasethatproducticanbeshippedover
routemfronjtok,butanctherproductcannctbecarriedoverthe
sameroute.3 IetIijhn=thesetofalllinksusedwhencomodityi

 

3Perhapsittakesseveraldaysforaproducttobecarriedfronj
tokoveraroute, soaproduuctlikecoalcouldbecarriedoverthe
route, butanctherproductlikefrehfruitwouldspoil ifcarried
overthisrouute.

38
isshippedfronjtokoverroutem. 'nueshippersofcounnodityifron
jtokwillbenodeledasoeplayerinthisgane.

Ietxijm=thequantityofproduuctishippedfronj tokover
route 111, with Xijkm Z 0. If any of the links in Lijkm are abandoed,
then route m for this service will not be available, and Xijkm = 0.

It is inportant to note that these service are available over the
given network, but there may not be a solution in the core in which
oneornore Xijkm is shipped, inwhich case, soneofthe flowswillbe
set equal to zero. For larger networks, Xijkm will typically be zero
for many of the flovs. To sinplify the notation, let a dot subscript
indicate a sum of shipments, so that xijk. = the smu of all connodity
flows fronj tokoveranyroute“. Alsolethenotethesetofall
xijkm, and let x5 denote a subset of x.

W' BENEFITS BEFORE ALLOCATING UNTRACEABIE CDSTS

Bothshippersandcarriersintheganeareinteretedin
maximizing their surplus fronn their activity in the gane. As in
previous gane theory applications to public utility pricing problens,
shipperandcarriersurplusisneasuredinnonetaryternsandassmed
to be transferable. Therefore, every collection of players is
intereted in maximizing the total surplus the entire collection
receive, althouqu side payunents may be needed to maximize their total

surplus .

 

4Under the assumption of costant variable transportation costs,
there will alnost always be a unique nost efficient (least expensive)
route m between two citie, so Xijk. = Xijkm for m = the uniquue nost
efficient route between j and k.

39

The gross rail surplus gains to shippers will be the additional
cosumer surplus trey receive from their shipments of the product by
rail instead of by truuck or sale other competitive non-rail node of
transportation. Tne shippers' denands for transportation service are
deriveddemaudsfronthedenandsofbnyersandthecostsofproducers,
sincethisdifferenceisthemaxinunutnebnyersandsellerswouldbe
willing to pay for the service. The producers or final buyers may
thenselve be tne shippers, but tteir denands for transportation
servicearekeptdistinctfrontheir finaldenandsfortheproductor
costs of produucing the product.

Thedenandforservicexijk. isassmedtobeindependentofthe
demand for any other transportation service. That is to say,
shipments between two different pairs of citie are not substitute or
conpleuent transportation services (although shipments of a connodity
between the same two citie but over different route are perfect
substitute for each other). This is a rather strong assmption,
because there clearly are substitute and conplenents for
transportation service. However, this assmuption may be relaxed in a
nore complex nodel by replacing shipper demands with the product
demands and production costs froun which they are derived. It is also

 

5"Gross rail surplus gain" here nears the area under the
transportation demand curve minus the allocable (variable)
transportation costs and minnuus the benefits which would have been
realized from shipping the product by truuck or sore other non-rail
coupetitor. Tne net rail surplus gain will be this gross rail surplus
gainminustheallocationof fixedcoststothis shipperorgropof
shippers. later in this chapter, the gross rail surplus gain will be
oeoftheuupperboundsontheallocationof fixedcoststoashipper
grop, since if tne shipper grop is allocated nore than its surplus
gainfrounusingarail carrierinsteadofancthernodeof
transportation, the grop will. be better off either by using tne other
transportation mode or by not shipping the product.

Ir.- ‘-

4O

assumed that there are no income effects. When the variable
transportation costs per unit are assumed to be constant, it will be
unost efficient to have service Xijk. carried between citie j and k
over the shortet route over the available facilitie.

let Pijk(Xijk.) = the inverse demand function for transportation
services for product i between citie j and k, and let Pijk = the
price per unit paid by the shippers of this service. Then they pay
Pijkxijk. plus the fixed costs allocated to them for their shipments
of product i between citie j and k. The demand function is assumed
to be downward-sloping. let Tsijk = the surplus from shipping product
1 between j and k over the most efficient non-rail mode of
transportation. This alternative mode of transportation is modeled in
the next Chapter as a perfectly competitive set of truck
transportation service over the shortet route between every pair of
citie. Then the willingnes to pay of the shippers of a service is
the area under their demand curve for the service, or
Jxljsiljsloc(xijk.)dxijk.r and their rail surplus gain (before they are
aglocated a share of the fixed costs of the shared facilitie) is
Gijk = Jxfiiljsh(xijk.)dxijk. - Pijkxijk. - Tsijk-

letoGB(L,S) = the gross benefits (gross rail surplus gain) to all
shippers in coalition S(L) from the shipment of XS over the rail
facilitie in L, let Xsijkm 6 X5 be a service which can be shipped by
the players in S(L) , and let 155in be the surplus which would be
received if all shipnents are carried by the intermodal competitor.
When Xijkm is a service carried by members of S(L) , then Xsijkm =
Xijlcm' When Xijkm is not a service carried by members of set S(L) ,

then xsijkm = 0. Then

41

I l-Xsijk.
(2) GS(L,S) = 2 ,2 3 Pijk(Xijk.)dXijk.
i=1 j eJikeKiJ o

I I

- z z zpijkxsijk. - 2 2 2155in
i=1 jeJikeKi i=1 jeJikeKi

For the grand coalition N(L) ,
I ijk.
(3) GS(LuN) =1; 3.211]:th J[xl’ijldxijle)dxijk.
o
I I
- 1:1 jEJikiKiij kxijk' - 1:1 ijikEK?ijk

Sincetheproductdemandfunctionsareassumedtobedownward
sloping, Gijk for any i and k will be a concave function, and
therefore, GS(L,S) and GS(L,N) will also be concave functions.
CARRIERS' CDS'IS AND BENEFITS

Itisassnnedthattherearetwotypeofcostsassociatedwith
transportation services. There is a fixed cost fh associated with all
rail links (h = 1,2,...,Hr). This fixed cost is an avoidable fixed
cost, sudnasmaintenancecosts, andrctthesunkcostfrcmbuilding
the rail link. Therefore, if a link is not used, thee fixed costs
willnctbeincurred. Itisassmedthatthereisrcfixedoostof
operatingatruckmutebetweentwolinks. Ofcourse, theproblenin
Ransey-pricing and other previous literature has been to find the nost
efficient cost allocation which allows the carriers to recover thee
fixed costs. let Fr(L) = the total fixed costs of operating all rail

links in network L, where,

42
H

(4) Fr(L) = 2 fh
h=l

There is also a variable transportation cost of shipping each
product over each link. let Cih = the variable cost of shipping a
unit of product i over link h. It has been assumed that the variable
trausportation costs are constant. This assumption insure that
marginal cost pricing (at the variable cost) will lead to economic
losse for carriers with positive fixed costs, and therefore, marginal
cost pricing will not allow shippers to recover their fixed costs. To
simplify the notation, let C*ijkm = hEch1 = the variable cost of
shipping a unit of product i frcml j t: kjlgvner route m. Of course, the
rail cost allocation problem will only be intereting if the
transportation costs over at least some rail links are les than the
costs over truck route. It is further assumed that any difference
in the quality of transportation services over different route will
be reflected in the transportation costs. Thee differences in
service quality might include reliability, damage from movement, and
sped of delivery.6

let C(L,N) = the total variable transportation costs of shipping
all products over the network. Since the variable transportation
costs are assured in this chapter to be constant, then,

I My

3k...
(5) C(L,N) = 2 z 2 2 c ijkmxijkm
i=1 jeJikeKinFl

 

6For example, if rail transportation does more damage between two
ncde to freh fruits and vegetable than truck transportation between
the same two node (Perhaps more of the shipment will spoiled because
of tiune delays if rail transportation is used than if trucks carrier
the shipnent) , then the additional damage from rail transportation
would be considered by the shippers to be part of the cost of using a
rail carrier.

43

 

The stand-alone cost of providing a transportation service or
groupofserviceisdefinedasthesnnofthestand—alouecostsof
operating the rail links over which the service is carried plus the
total variable (allocatable) transportation cost of the service. For

a single service, the stand-alone cost is

(6) SAC<Xijkm) = °*ijkmxijkm + Z fh
helijkm

Of more interet in this cost allocation problem is the stand-

alone cost for a set of shipments XS. let IF be the facilitie needed

r—
i

‘. . ..M‘h’ . f}
'5

to ship XS. The general form of the stand-alone costs for a group of
service will be
(7) SAC(XS) = i z 2 Mijlé‘ijhpcsijm + Fr(LS)

i=1 jeJikeKim=1

A distinction will be made between the stand-alone cost of a
service (including the variable cost) and the stand-alone fixed costs
(not including the variable costs, which can be traced to individual
service). let SAFC(Xijkm) be the stand-alone fixed cost of service
Xijkm' so that
(8) SAFC(Xijkm) = E fh

heLijkm
Similarly, the stand-alone fixed costs for a set of service X5 is
(9) SAFC(XS) = Fm?)

The carrier(s) who operate the rail links over which any service
Xijkm is carried will be cosidered to be players in this game. Each
of the carriers will want to maximize their surplus fron providing
transportation services . Before allocating the fixed transportation
costs, the carriers' surplus, or gross rail surplus gain fron service

. *
Xijkm Will be C‘Sijkm = Pijkxijkm - C ijkmxijkm - E fh-
heLijl-zm

44
Under marginal cost pricing, C*ijkm = Pijkr so the carriers'
gross benefits (Gijkm) will be equal to - 2 fh (a negative
hELijkm
quantity). Carriers will not be willing to provide transportation
service if their carrier surplus is negative, so in order to maximize
efficiency with marginal cost pricing, the fixed costs must be
allocated to the shippers. The carriers' gross rail surplus will be
exactly zero after the fixed costs are allocated. let Afijkm = the
allocation to the shippers of Xijkm for the fixed costs of the
facilitie in Lijkm (this allocation will be discussed below). If
this is the only service carried over the network, the shippers'
contribution for the fixed costs will be all of the fixed costs
(Afijkm = SAFC(Xijkm)). For a set of service XS, the allocation will

be isAfijm _<_ snows) .

THE QIARACI‘ERISTIC FUNCTION

A gane is defined by a network L (or subnetwork LS), a set of
shippers and carriers N(L) or subset S(L) of N(L) , and a
characteristic funnction v(L,S) which define the maximum benefits (or
gross rail surplus gain) to all mannbers of S(L) from the operation of
the facilitie in L. Before defining the general characteristic
function, a few specific characteristic functions will be considered.

If S(L) consists of only shippers, then they will have only non-
rail transportation service available to them, so their v(L,S) = O
for rail transportation service. Similarly, if S(L) consists of only
carriers, then they will receive nc revenue fronn rail transportation
service, and v(L,S) = 0. If there is one shipper and one carrier of
thesameproductinS(L), buttheshipperdoenotdemandthesane

service which the carrier is providing, then v(L,S) = 0. Therefore, a

45
necessary condition for v(L,S) > 0 is for the morbership in S(L) to
cosistofatleastashirperandaerrieroftheservicemichthe
shimerdeunands. Ifthereisoneshipperandonecarrierwhidn
provide a single service over a given route which the shipper wishes
to use, then the characteristic function will be

(10) v(LrS) = nxugm Eigfiixijk.)dxijk. - C*ijnonxsijnon
- Tsijk - Afijkm}

In equation 10, Afijkm is the share of the fixed costs allocated
to the shippers of Xijknuv The allocation of thee costs has nct yet
been determined, so they will be considered to be given at this point.

Consider next a larger S(L) for which there are at least one
combination of shippers and carriers of the saute service. Again let
Xsijkm be a shipnent by the players in coalition S(L) , and let LS =
the subnetwork of links that will be used by the shippers in coalition
S(L) . The general fornn of the characteristic function for any S(L)
will be

I ijk.

(11) v(L,S) = max { >3 8 2 Pijk(Xijnou)dXijk.
i=1 jeJikeKi 0

I My)“ I S f
-.2 .2 X C ijlmxsijkm -.2 .2 2 TS ijk - Z A ijkm}

l=1 j eJikeKim=1 i=1 j eJikeKi XS

Equation 11 define the maximum benefits that the menbers of

coalition S (L) receive from the facilitie in L, given sore allocation
of fixed costs whidn has nct yet been defined. Note that attaining
this maximum net benefit may require that only the menubers of players'
subset T of S(L) participate and the matters of S(L) not in T

voluntarily not participate in the game. Since this is a transferable

 

46

utility gane, the players in T will be able to coupensate non-
participating players and all players will be better off than if all
players participate. Since GS(L,S) is concave and C(L,S) has a
costant slope, the v(L,S) is a coneve function. If the allocation
is the stand-alone fixed transportation charge for the service the
shippers are able to provide, tren :SAfijlon = SAFC(XS) . By
Faulhaber's (1975) definition of cross-subsidization in public utility
pricing, cross-subsidization occurs (a cost allocation is not in the
core) whenanyshipperorgrouupofshipperspaysmorethanthestand-
alone cost of serving only that shipper or group of shippers. If
cross-subsidization is to be avoided, then it is necesary to have
isAfijh“ _<_ snows) .

Finally, tle maximum benefits to all numbers of the grand
coalition N(L) are

I [Xijk.
(12) v(L,N) = max ( >3 , E >3 Pijk(xijkm)dxijk.
X l=1 jeJikeKi O
-; 2 2'. Hygijhnxijhn -§J 2 2 TSin - Fr(L)}
i=1 jeJikeKinFl i=1 jeJikeKi

This v(L,N) will also be a concave fuunction. Note that all of
thefixedcostsofthelinksthatareused (whichmaybeasmallerset
than L if not all links are needed to efficiently serve all players in
N(L)) must be recovered frontierrembers ianho participate in this
gane.
THE (DRE OF THE GAME

The core of tne gene is defined by network L, players N(L), and
characteristic vector v. Eadn shipper and carrier is iuntereted in

maximizing its gross rail surplus gain. To siunplify tie notation

47
below, no distinction will be made between carrier and shimer
surplus. let GB(L,n) = tl‘e gross rail benefits gain to shipper or
carrier n in N(L) fron the facilities in L7. Then GB(L,S) = the gross
benefits to all numbers of coalition S(L) when all heaters in N(L)
participate in tie coalition (or voluuntarily do nct participate) . For
a shipper in N(L), that shipper's gross benefits are denoted by
GB(L,n) = Gijk‘

Under Sharkey's (1982) definition of cross-subsidization, a non-
cross-subsidizing cost allocation is one in which re shipper or group
of shippers pays more than either its stand-aloe cost or its gross
benefits. Under this definition of ores-subsidization, a core
allocationisoe inwhichncshipperorgroupof shippers is
allocatedashareof fixedcostsgreaterthanthemininumof itsSAFC
and GB(L,S) .

The core of tie gane is based upon Sharkey's definition of cross-
subsidization. let R(L,S) = the allocation of the fixed costs to
group S. Then for the grand coalition, R(L,N) = Fr(L); and for a
groupScosistiugofoneproducer, onebuuyer, andoneshipperbetween
the producer and the buyer, R(L,S) = Afijkm. me net benefits
(surplusgain) togroupSarethendefinedas
(13) NB(L,S) = max {GB(L,S) - R(L,S), 0)
or (14) NB(L,S) = v(L,N) - v(L,N-S)

Note that v(L,N) and v(L,N-S) both include allocated share of
tie fixed costs. Thuus, eitrer definition of the net benefits is the
anticipated gains to numbers of coalition S fron participating in te
grand coalition N(L) . So long as tie cost allocation is in He core,

 

7Player n may voluuntarily dcose nnot to participate in the gane

48
the numbers of coalition S will be willing to pay R(L,S) _>_ 0, so for a
cost allocation in the core, equation 13 may be rewritten as
(15) NB(L,S) = GB(L,S) - R(L,S) _>_ o
Ttecoreofagauuecanbedefinedbyasetofnnetbenefitsvectors
NB(L,S) for which
(16) NB(L,S) _>_ v(L,S) for all subsets S(L) of N(L)

(17) NB(LIN) = v(LIN)

~—

Equuation 17 sinply state that tl‘e benefits to all participants
in N(L) are divided uup among the mennbers of N(L) . Equation 16 state

that nc subset of players S(L) would be better of after dropping out
of the grand coalition. Equations 16 and 17 can be rearranged as:
(18) v(L,N) _>_ v(L,N-S), for all subsets S(L) of N(L)
Proposition 1: A cost allocation R(L,S) which satisfie equuations 16
and 17 is net a cross-subsidizing cost allocation (is in te core) .
Proof: If equuation 16 is satisfied, then re coalition pays more than
its gross benefits, so every possible coalition receive positive net
benefits froun membership in the coalition and therefore, the net
benefits definition of non-cross-subsidization will nct be violated.
Also, if equuatios 15 and 16 are satisfied, then
GB(L,S) - R(L,S) = NB(L,S) 3 v(L,S) = GB(L,S) - Fr(LS)
'Iherefore, R(L,S) 5 Fr(L5) = snows), and GB(L,S) include variable
transportation costs, so no coalition is requuired to pay more than its
stand-aloe cost. Since R(L,S) 5 seems) , then the net benefits
constraintinl6isanucrerestrictiverequirementthanaSAC
constraint on cost allocatios as proposed in previous rail cost
allocation proposals.

Insnchacore, all fixedtransportationcostswouldhavetobe

49
allocated in such a way as to insuure that equation 16 is satisfied for
all possible coalitions. Even if a cost allocation exists so that all
menbers of N(L) have an incentive to participate in the gaune, a
different allocation of tre sane costs may cause sore numbers of N(L)
todrquoutoftheganeandleadtolesbenefits forallureu'bersthan
v(L,N) . However, tne quuetion of tre existence of a core involving
all numbers of N(L) will be considered first.
SI-IIJID ALL PLAYERS AND FACILITIES BE INCIDIED IN THE GAME?
Proposition 2: The necesary and sufficient condition for all
facilitie to be used is
(19) v(L,N) 3 v(lfi,$) for all possible subsets L5 of L and all
possible subsets S of N.

That is, the benefits after subtracting all costs to all numbers
of the grand coalition N (sore of whouu may choose nct to participate
intheganue) mustbeat leastasgreatasthebenefitstoanysubset
of N fron the facilitie in a subset of L, or else efficiency could be
increased by abandoning facilitie.

Proof: Equation 19 is a necesary condition to serve all players
because if it is not satisfied, then v(LS,S) > v(L,N) for some subset
S(L) of N(L) , which will tnen have tie incentive to withdraw fron
coalition N. Then by equuatios 16 and 17, NB(LS,S) _>_ v(LS,S) > v(L,N)
= NB(L,N) . Therefore, nc allocation in the core exists, because the
numbers of S(L) will be able to increase their net benefits by
withdrawing frouu the network and operating only network L5.

Equation 19 is a sufficient condition because if it is satisfied,
then GB(L,N) - era.) 3 GB(LS,S) - F1713), and
GB(L,N) - GB(l§,S) 3 Fr(L) - Frans). let T = N(L) - S(L). Then

50
GB(L,N) = GB(L,S) + GB(L,T), and
GB(L,S) + GB(L,T) - GB(LS,S) 3 Fr(L) - Fr(LS). Rearranging slightly,
(20) [GB(L,S) - GB(LS,S)] + GB(L,T‘) _>_ Fr(L) - Fr(LS)

The right side of Equuation 20 is the cost savings if the
facilitie in L buut not in 1.5 are abandoned, perhaps because coalition
S(L) breaks away fron the grand coalition. The term GB(L,S) -
GB(LS,S) is the benefits to numbers of S(L) fron staying in the
network and using the facilities in L buut not in If. It is also the
maximum that the meuubers of S(L) will be willing to pay for any
additional facilities not in L5. The term GB(L,T') is the benefits to
the numbers of T frouu participating in the coalition (or fron
coalition S(L) nnot defeating fron the coalition). The maximum that
the meuubers of T will be willing to pay for any additional facilitie
nct in 15 is the mm of GB(L,T) and nr(LT) . If GB(L,T') g Fr(LT),
then by Equation 20, the sum of what the numbers of S(L) are willing
topaytowardthe facilitie ianutnot inLS pluswhatnembersofT
are willing to pay for those facilitie is at least as great as the
cost of providing those facilitie, so both numbers of S(L) and T‘ will
have the incentive to contribute enough to pay for those facilite.

If GB(L,T) > Fr(LT) , then the members of T will be willing to pay at
most Fr(LT). Note that Fr(LT) 3 Fr(L) - Fr(LS). Therefore, the
numbersofTarewillingtopayatleastasmuuchasthecostof
providing the facilities in L bunt nct in 1:5, even if the members of
S(L) do nnot contribute anything toward the cost of those facilitie.
Either way, Equation 20 shows that those facilitie will be provided,
so Equation 19 is a sufficient codition for all facilitie in L to

used.

51

The proposals surveyed in the previous chapter all assume that no
facilities or services will be abandoned. If equation 19 can be
satisfied for all possible coalitions of players, then some or all of
these allocation proposals may lead to efficient provision of
services. Hewever, if equation 19 cannot be satisfied for all
possible coalitions of players, then by definition, any of the
proposals in the previous chapter'will lead to inefficient provision
of some services. Many facilities and services have been abandoned
since the passage of the Staggers Rail Act, so it is argued in the
next section that the prdblem of allocating fixed costs cannot be
separated from the problem of determining the most efficient network
structure.

'IHE PEST EFFICIENT NEIWORK

If equation 19 is satisfied.for the existing set of facilities L
and.players N(L), allowing for voluntary nonparticipation, then
Proposition 1 Shows that a twoepart tariff in the core exists, so the
prOblem is simply to find such a cost allocation. Several approaches
to the problem of finding a cost allocation in the core will be
proposed in the final section of this chapter.

Suppose, however, that equation 19 is not satisfied for L.and
N(Lo. There will always be some network for which a core solution
exists, because equation 19 will certainly be satisfied for L3 = g.
If'1§ =lfl, then Fr(DS) = 0, so equation 19 will be satisfied for an
empty set of players. Of course, this will not be a rail
transportation.problem. But there will always be a set of players and
facilities fOr'whiCh a core allocation exists, since this condition is

always satisfied.by an empty set of rail facilities.

 

52

Another case, where condition 19 is not satisfied for L and all
menbers of N(L), but may be satisfied for L and a subset S(L) of N(L) ,
has already been considered, since the analysis above allows for
nonparticipation of members of N(L) . The previous analysis also
considers (in equation 13) which subset of N(L) for which a core
solution exists is most efficient. In this case, let N*(L) be the
subset of players in N(L) who participate in the game over the set of
links L. Of course, the solution will be the same for N(L) and N*(L) ,
since participation ,is always voluntary in this game.

But the more interesting cases are where equation 19 cannot be
satisfied for L and any S(L) , or else where a more efficient solution
can be found when links are abandoned. To solve such a problem, the
characteristic function can be rewritten as:

I [J‘*ijk.
(21) v(L*,N*) = nix {51 .2 . Z . Pijk(Xijkm)dXijk.
— jEJ 1kosKl J O
I Mi'k * I r *
- .2 .2 2 C ijkmxijkm - .2 .2 Z Tsijk - F (L )}
l=l jeJikeKim=1 l=1 jeJikeKi

This is still the same characteristic function that was defined
in equation 13, but in equation 21, L*, N*(L*), and X*ijk. are
included for emphasis on the services and facilities that are included
in the game. However, this distinction between L and subset L* of L
will be used in the next section when finding ranges of cost
allocations in the core.

It should be noted that with constant variable transportation
costs, then there may not be a unique most efficient network. If

alternative routes have the sane variable transportation cost (if

C*ijka = °*ijkb for a 75 b regardless of X*ijka and X*ijkb) , then there

 

53

may be more than one set of most efficient facilities and traffic
flows. However, there will be only one X*ijk.8- There will be no
inefficient exclusion of shippers, because all shippers that are able
to able to use a route at least as inexpensive as the best alternative
shipper (using either transportation mode) will add to the total
consumer surplus (and contribute to the recovery of the fixed costs),
which is maximized for the most efficient network.
FINDING AN ALLOCATION IN THE (DRE

A non-subsidizing cost allocation exists for L* and N*(L*) , so
the last stage of the problem is to find a cost allocation in the core
for sore L* and N*(L*)9. It has been argued in this chapter that this
discussion of non-subsidizing networks cannot be separated from the
discussion of the most efficient network configuration. This close
relationship between the two concepts made the discussion of the
theory of the most efficient network structure rather complicated, but
the benefit of that discussion is that in the process of determining
the most efficient network structure, the constraints on the cost
allocation are determined. A non-subsidizing cost allocation is one
which gives the shippers and carriers the incentive to operate the
most efficient network, so a cost allocation which satisfies equations
16 and 17 will be a non-subsidizing cost allocation. In other words,
the problem of avoiding cross-subsidization is redefined as a problem
of maximizing the efficiency of the network structure.

Such a non-subsidizing (or core) allocation was found to be one

 

8See Theorem 8 in Shapley (1965) for an existence proof which is
applicable to Xijk. and the most efficient network, but not applicable

to xijkm'
9This L* may be the empty set of facilities.

54
in which all fixed costs are allocated to shippers so that no shipper
or grunp of shippers pays more than either its stand-alone cost or the
gross rail surplus gain received from participation. Thus, a cost
allocation in the core would be one for which:

(22) R(L*,S) 5 min(Fr(LS),GB(L*,S) for all subsets S(L*) of N(L*)
Therefore, once the constraints in equation 22 (which must be
satisfied for the most efficient network) are found, these constraints
can be used to find a core allocation. Sinnce both rail benefits and

stand-alone costs are used to define upper bound constraints, this
cost allocation based upon avoiding innefficient abandonment of
facilities allows the fixed costs of the network to be recovered in a
less arbitrary manner than would be possible without considering the
abandonment of facilities.

By definition, this process of finding the most efficient network
will also generate a set of lower bound constraints, since the
existennce of a maximum allocation for one set of shippers S(L*)
imposes the requirement that the remaining shippers in N(L*) pay any
fixed costs that the shippers in S(L*) are unwilling to pay.
Therefore,

(23) R(L*,'r) _>_ max{Fr(L*) - R(L*,S), 0) for T = N(L*) - S(L*)

Any cost allocation using fixed charges which do not violate the
constraints in 22 and 23 is a non-subsidizing cost allocation. A
number of cost allocation rules have been proposed elsewhere to
arbitrarily allocate costs subject to constraints such as the upper
bounds on allocations to groups in equation 22. Hamlen, et. a1.
(1977) use core theory to evaluate at length four allocation rules,

including the Moriarity Rule used by Fanara and Grimm. To use these

55
allocation rules, the unallocatable costs nr(L*) of the network are
added up and allocated according to some predetermined weights. let
E(L*,S) be the upper bound on fixed costs of operating network L*
allocated to coalition S(L*) , so that E(L*,S) = min( Fr(LS),
GB(L*,S) ) .

Hamlen, et. al. , find that three of the allocation rules produce
allocations in the core (and therefore are appropriate to use in this
problem), but the Moriarity Rule may not. An example of a cost
allocation which is always in the core is based upon the Shapely10
value (based upon the benefits to buyers and sellers of Xijkm) . This
allocation rule has each shipper in N*(L*) allocated its Shapely value

so that
(YS-l) ! (Y'Lys) !

(24) Afijkm = (E(L*,S) - E(L*,s-n))

y"!

whereys=thenmnberofmembersinS(L*)andyn=thenumberof

 

members in N* (L*) . This Shapely-value allocation will always be in
the core, but it mores increasingly difficult to calculate as the
number of members in N*(L*) increases.
(IDNCIUSION

In this chapter, it was shown that the largest L8 for which
equation 19 can be satisfied will be the most efficient subset of
network L, and efficiency can be increased by abandoning all
facilities in L but not in LS. Allowing for facilities abandonments
also narrows the range of the fixed charges which may be charged to

shippers in order to allocate the shared costs of the facilities in

 

10Slnapely (1953) proposed this value as a method for potential
players to decide whether to enter a game by finding a priori their
expected benefits fron playing the game.

56
l§, because allocating more than the upper bound to a facility or set
of facilities will lead to inefficient facility abandonments.

This cost allocation based upon avoiding inefficient abandonment
of facilities allows the fixed costs of the network to be recovered in
a less arbitrary manner than would be possible without considering the
abandonment of facilities. Under this allocation, the problem of
avoiding cross-subsidization is redefined as a prOblem of maximizing
efficiency. SuCh an approach by itself leads to a non-subsidizing

allocation, so it is not necessary to consider issues of cross-

 

subsidization separately, as was the case with proposals based upon ;

Ramseyepricing‘with stand-alone cost constraints.

CHAPTER“ ANAPPIICATICN‘IO‘IHEMQ‘IIGANRAILNEIWRK

In this chapter, the first-beet allocation of fixed costs
developed in the previous dnapter will be applied to tie 1984
Michiganrailshiplents. Itwillbeshownthatwhentteabandoment
of rail facilities is pr'onbted if such abandonments will increase
efficiency, then a first-best cost allocation may be found which is
more efficiennt and less arbitrary than was previously though possible.
Theprimarypnrposeofthischapteristoshowthattreapproadnto

 

allocatingcostsproposedindnaptechanindeedbeappliedto
existing traffic flows.
THE mom. AND THE HAIR

Although all railroad services would have different
transportation demands and costs, data limitations and the costs of
annalyzing a highly conplex network make it desirable to aggregate
shipnents into a set of relatively few honogeneous product categories
and origins and destinations into a smaller number of regions. Since
the purpose of this application is to show prinarily how such a first-
best cost allocation would be fond for an existing transportation
system, the services to which the cost allocation are applied are
aggregated into a relatively small number of services. This
relatively high level of aggregation sinplifies the cost allocations
procedure, making the cost savings from efficient abandonment of
services more apparent, while still demonstrating how such a cost
allocation could be found for a more conplicated (less aggregated) set
of traffic flows.

'nnecombditiesshippedintoandantcfuidniganwereaggregated

57

58
intofolrcomoditygronpschosentoroghlycorrespodwithtle
cannodity groups defined by Friedlaender and spadyl. Tne conuodity
groupsaredefinedinTablelbelow. IntlenotationofChapter3, I
= 4, with i = 1 for durable manufactures, i = 2 for nodurable
manufactures, i = 3 for petroleum and related products, and i = 4 for
minerals, chemicals, and all other shipments.

Origins and destinations of controdities in the lower penninsula of r
Michigan were divided innto six regions: Sonthvnstern Michigan 5—
(inchding Kalamazoo), Southeastern Michigan (including Detroit), the T

 

"Thlmb" region (extending to Flint and the Northern Detroit suburbs), L.
Nortlern Michigan, Western Michigan (the area around Grand Rapids),
and Central Michigan (including Lansing). Each of the six regions is
cosideredtobeoelocaticn, sothatall shipments intoandoutof
theregionswillberegardedasiftleyhadttesamepointoforigin
or destination. These regions are shown in Table 2.

Origins and destinations of freight shipments entering or leaving
tle lower penninsula of Michigan were also divided into six regios.
Two of these regios include the areas which have Michigan borders and
thus, relatively short stripping distances . (re of these regios
borders on tie Soutleastern Michigan region and cosists of Ohio,
Western Pennsylvania, West Virginia, Eastern Kentucky, and Ontario,
andtrectterregicnbordersontleSonthwesternMichiganregionand
consists of Indiana, Illinnois, and Western Kenmcky. Tne states west
of tl'e Mississippi River plus Wisconsin, tie Upper Peninsula of
Michigan, andtleCanadianProvinceswestofandincludingManitcba
aredividedintotworegios. 'neranainingstatesnorthandeastof

 

1F‘riedlaender and Spady (1981), p. 57.

59
Virginia plus the Canadian Provinces east of Ontario are tie fifth
rm-Midnigan region, and the final region cosist of the retaining
sontlern states west of tte Mississippi River. These six regios
ontside of Michigan are shown in Table 3, and the conbinatios of i,
j, and k for counodities and tteir origins and destinations are srmn
in Table 4.

Theraillinksbetweentheselccatio'sarehypotheticalrail
linnks. If two Midnigan regios share a border, it was assuned that
thereisoerail linkbetweenthem. Thelinksbetweenanytwo
Michigan locations are cosidered to be abandonable links. It is
assumed that trere is enogh traffic over all links partially or
entirelyoltsideoftIeMidnigan lonerpeninsulatomakeabandonmenrt
of any of then inefficient. Only the fixed costs fron tte 9 available
Michigan rail links will be recovered in this exercise. The fixed
costsoftheotherlinksareignoredbecausethedatausedbelovare
forshipnnentsintoandontofMichiganonly, sotnerecoveryoftle
fixed costs of tre non-Michigan linnks will also include allocatios to
shipmentswhidnarenotintnesanple.

Tne principal sonroe of data is tre chi's Annnual Rail Waybill
Sannple Master File for 1984 , which provides comedity codes, actual
and short-line distances, weights, and transportation revenues on rail
shipments between differennt origins and destinations. The shipments
inthissanrpleareaoe—peroentsanpleofthetotalshipnentsintoor
out of the lover peninsula of Michigan. Out of this sanple of 18178
shipments which had Michigan lower Peninsula origins or destinatios ,
36 were ronoved because they had nno reported origin, destination,
conncdity code, or shipment weight, and another 1481 were renoved

with Two Digit Census Codes and W of Shipments

Category 1: Dirable Manufactures (7894 Shipments in the Sample)
W _chamwdi
nnetal alloys and fabricated products 618
34 fabricated netal products 13
35 non-electrical machinery 24
36 electrical machinery and products 91
37 transportation equipment (including autos) 7148

60

Table 1: Comodity Categories

Category 2: Nondurable Manufactures (1361 Shipments)

MEL—s _dei

22
23
24
25
26
27
3O

anrmunition 3
textiles and finished textile products 18
finished textile products 101
lumber and wood products 206
furniture and fixtures 29
paper and paper products 902
printed matter 1
rubber and plastic products 101

Category 3: Petroleum and Related (380 Shipments)
gamed—11:11.4 __tyOonmodi

29 petroleum products
category 4: Mineral, Chemical, and Other (5815 Shipments)
Oonucdig Code Comnodig Number of Shim
1 farm products 244
10 iron ore, aluminum, bauxite 687
11 coal 1190
14 nonnetallic minerals 319
20 food and kindred products 711
28 chemicals 399
32 stone, clay, glass, concrete 376
39 misc. products 10
40 waste and scrap 591
41 miSC. 347
42 returned containers 238
43 mail 9
44 freight forwarded 1
45 shipper association 48
46 mixed shipments 629
47 small packages 16

Number of Shimts

Number of Shimts

 

61

Table 2: Michigan Transportation Regions
with Fonr-Digit Standard Point Location Codes (SPIC)

Region 1: Nortrern Michigan

hidden—Comfy SPIC .Mieuigenm _SPIC W _SPIC
Presque Isle 3111 Cheboygan 3112 Alpena 3113
Montmorency 3114 Otsego 3116 Alcona 3117
Oscoda 3118 Crawford 3119 Emmet 3121
Charlevoix 3122 Antrim 3124 Ieelanau 3125
Kalkaska 3126 Grand Traverse 3128 Benzie 3129
Icsco 3131 Ogemaw 3132 Rosconmon 3133
Arenac 3134 Gladwin 3135 Clare 3136
Bay 3137 Midland 3138 Isabella 3139
Missaukee 3141 Wexford 3142 mistee 3143
Osceola 3144 lake 3145 Mason 3146
Mecosta 3147 Newaygo 3148 Oceana 3149

Region 2: The "Thumb" Region (including Flint)

W 8_P_I_C Wm £11; Melon—11191 gm
3151 Salinac 3152 T'uscola 3153
St. Claire 3154 Iapeer 3155 Genese 3156-3157
Phconb 3158 Oakland 3159

Region 3: Mid-State Region (including Lansing)

Michiga_n Conny SPIC Midnng County SPLC Michigan 99mg SPLC
Saginaw 3161-3162 Gratiot 3163 Shiawassee 3164
Clinton 3165 Livingston 3166 Ingham 3167-3168
Eaton 3169

Region 4: Western Michigan (including Grand Rapids)
mm County SPIC M_ichigg County SPIC Michigan Comm 2;

3171 mskegon 3172 Ionia 3173
Kent 3174-3175 Ottawa 3176 Barry 3178
Allegan 3179

W _SPIC new 0am _SPLC w $.11;
Wayne 3181-3183 Washtenaw 3184 Jackson 3186
Monroe 3187 Ienawee 3188 Hillsdale 3189

Region 6: Sontl'mester'n Michigan (including Kalamazoo)

W _$__PIC new _SPIC __gen____tyMi<—‘hi Conn _8

3191 Kalamazoo 3192-3193 Van Buren 3194
Branch 3196 St. Joseph 3197 Cas 3198

Berrien 3199

 

Table 3:

62

Transportation Regions Outside of Michigan

with Two-Digit Standard Point Location Codes (SPLC)

Region 7: Ohio Border
fits gr Province SPLC State or Province SPLC

Ontario 04 Western Pennsylvania 21
West Virginia 27 Eastern Kentucky 28
Ohio 34-35

Region 8: Indianna Border
State or; Province SPLC State or Province §PLC

Western Kenntucky 29 MI Upper Penninsula 30
Wisconsin 32-33 Indiana 36-37
Illinois 38-39

Region 9: Eastern U.S. and Canada
m or Province SPLC State or Province SPLC

Eastern Cannada 00-03 Maine 11
New Hampshire 12 Vermont 13
Massachusetts 14 Rhode Island 15
Connecticut 16 New York 17-18
New Jersey 19 Eastern Pennnsylvania 20
Delaware 22 Maryland 23

District of Columbia 24

Region 10: Soltheastern U.S.
State or Province SPLC State or Provinge SPLC

 

 

Virginia 25-26 North Carolina 40-41
Tennnnessee 42-43 Sonth Carolina 44
Georgia 45-46 Alabama 47
Mississippi 48 Florida 49

Region 11: Central U.S.

State or Province SPLC State or Province SPLC
Minnesota 50 North Dakota 51
South Dakota 52 Iowa 53-54
Nebraska 55 Missolri 56-57
Kansas 58-59 Arkansas 60-61
Oklahona 62-63

Region 12: Western U.S. and Canada
$2 or Province SPLC State or Province SPLC

Western Canada 05-09 Louisiana 64-65
Texas 66-69 Montana 70-71
Wyoming 72-73 Colorado 74-75
Utah 76 New Mexico 77-78
Arizona 79 Alaska 80-82
Idaho 83 Washington 84

Oregon 85 Nevada 86

California

87-88

63
after tte lower peninsula was divided into regios because their
origins and destinatios were in the sane region. Finally, many of
tie prices and shipments weights appeared to be inplausibly high, so
shipments were renoved until all shipments had prices (per ton-mile)
andshipmentweights lessthanStimestheneanpricesandshipment
weights. This led t0>the removal of the 358 shipmentS'with.the
highest prices and tie 853 shipments with the greatest weights. The
finnal sanple cosists of 15450 shipments.

Fixedtransportationcostswereestimated frondata inttelhrdn
of 1984 mm Statistics in the United States. The ICI'.‘ cost of
capital was 15.8% in 19842, so the cost of capital was defined as
15.8% of the Net (after depreciation) Road and Equipment entry for all
class 1 railroads in 1984. The total freight ways and structure
expenseandthetotal freightgeneralandadministrativeexpensewere
also defined as unallocatable overhead costs and the sum of these
costs was divided by tie miles of track operated by freight carriers.
This fixed cost was estimated as $82,608 per mile of track for each of
the nine Michigan facilities in 1984.

Variable transportation costs over rail links were estimated by
addingthetotalfreightequipnentexpenseandthetotal
transportationexpenseanddividingbyttegrcsston—miles ofrevenue
freight. This variable cost was 2.03 cennts per ton-mile of freight.

 

2Government Accounting Office Doonnents, Railroad Revenues;

M15 of Alternetive m to Measure Meme My, released
October 2, 1984.

 

64

 

Net Road and Equipment $42,115,494,ooo

(including passenger service) x .158
Cost of Capital $6,654,248,000
Freight Ways and Structures Expense 4,210,046,000
m and Administrative Eggs; 2 666 680 000
Total Fixed (Unallocatable) Costs $13,530,974 ,000

Average Fixed Costs per Mile
= $12,772,895,000 / 163,798

Total Fixed Cost / Track Miles
$82,608 per mile of track

Freight Equipment Expense $6,512,674 ,000
W M26 3 0
Total Variable Freight Cost $18,638,959,000

Average Variable Costs per Ton-Mile of Rail Traffic
= Total Variable Freight Costs / Gross Ton-Miles of Freight
= $18,638,959,000 / 918,672,776 = 2.03 cents per ton-mile

.. 'I‘Jur-FI

 

Distances between any pair of Michigan cities were estimated as
the average short-line miles fron shipments between us two regios in
tnechzsanple. Itwasobservedthattheshipnentswhidntendedto
traveltrefurthestwnenenteringorleavingthestatewerethosefron
theregiosonttesonthernMichigan border. Thus, for all shipments
to and fron a partionlar region ontside of Michigan by way of a
particular border region inside of the state (over links 10 to 18),
the the difference between the total short-line miles and the miles to
or fron the border region were calonlated. The average of these
differenceswasusedasttemilelengthofthelinkbetweentheregion
ontside oftlrestate (regios7t012) andtheMichigan borger region
(regios 2, 5, or 6). The rail links andthemiles assignedtothem
areshowninFigureZ.

Itwasassunedthatallshipxrentsnotcarriedbyrailconldbe
carriedbytruckcarrierscvertteshortestronte(orpartofaronte)
betweentnetwocities. Thedistancesbytruckbetweenntworegios
wereassnmedtobetlesaneastheshort—linerailtradcdistance

65

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Region 1:
J Northern
Linnk 2 Link 1
318 Miles 253 Miles-
Region 4: II Link 4 " Region 3: ll Link 3 [Region 2: '
Rapids II 112 Miles _I 67 Miles 9 —
Linnk 8 Link 7 Linnk 6 Link 5
67 Miles 106 Miles 112 Miles 65 Miles
, . H Link 9 _H‘ . ~
‘ Reglon 6: Reglon 5:
‘il mm... H Mae. 1| Dem.
Michigan I
(Loner
Penninsula)
_______ -.t_...-______._.....__________....
Outside of Link 16 Linnk 11
Michigan 215 Miles Link 12 288 Miles
264 Miles
Region 8: ‘ Region 7:
Indiana Ohio Border
Border
Link 13 Link 10
Link 17 636 Miles 694 Miles
Link 18 537 Miles N
1792 Miles Link 15 Region 9:
918 Miles Eastern
US & Cannada
‘ * ' Link 14 ,
Region 12: Region 11: 844 Miles
Western US Central US
8 Canada ’
Region 10:
Sontheast
US

Figure 2:

 

The Available Rail Links

 

66
between tle cities. Shipments could be carried part-way by truck and
part-waybyrail. Thesetruckcarrierswereassnmedtochargea
constantrateperto‘n-mileandnofixeddnarges. Tteestimateof
average revenue per ton-mile for Class I trucks was 9.9 cents3 for
1986. Deflating that estinnate by the producer price for 1986
(relative to 1984) , the 1984 average truck rate was estimated as 9.56
cents per ton-mile.

When estimating tre donand onrves for connodities carried over
tlenetwork, noattanptwasmadetodistinguishbetweenoriginand
destination locatios. All shipments in the sane commodity category
carried in eitl‘er direction between two locations were considered to
bepartofthesaneservice. Therelevantquantitiesarethetos
shipped of the connodity.

Ttedemandcurve foranygivenservicewas fondfronntle
average price charged for all shipnents of the partionlar conncdity
category between the two particular locations, the total (over all
shipments in the sanple) tons4 of the comnodity carried between the
two locations, and the elasticity of demand for the connodity category
which were estimated by Friedlaender and Spady5 for shipments in the
FasternUnited States. Thiselasticity isassnmedtobetne
elasticity of demand for a linear demand curve at tte point on the
demandcurvewherethepriceandquantityaretheaveragerateper
ton-mile (including the fixed cost allocation) and the total toe of

 

3Reported in W (March. 1988). page 11-

4Becauset1esanpleisofoe—percentoftheshipments, ttetons
in the sample were nultiplied by 100.

5Fried1aender and Spady (1981), p. 58.

 

67

the connodity shipped between tle two lccatios . Friedlaender and
Spady estimated that these elasticities were .8428 for conncdity class
1, .7022 for conmodity class 2, 1.1638 for camodity class 3, and
.5893 for ccmmodity class 4. Note that the elasticity of demand is
the smallest for the conmodity class which includes coal shipments.
THE MET EFFICIENT NEI‘VDRK

WithLdefinedasthesetof all 9Michigan railroad linnks, the
gross rail surplus gain for all possible sets6 of facilities LS e L
was fond by cosidering every possible Lfi. For each 115, the nest
efficient roltes and shipment qmntities were folnd and the gross rail
surplusgainfroneachshipmentquantitywereaddedtofindtnegross
rail benefits for tie subnetwork. This was acocmplished by first
finding the least expensive route for all shipments over LS, then
finding the consunner surplus maximizing quantity and respective
consumer surplus for each of these shipments. Finally, tle fixed
costscfoperatingLSweresubtractedfronthesnnnofthesecosnmer
surpluses over network Ins. Since the fixed costs are recovered
throngh fixed charges, the nost efficient shipment quantities are
those for which the variable rate per ton is equal to tie variable
costoftransportingatonofthecomcdityovertheleastexpensive

available rolte between tte two cities.7

 

5With 9 abandonable facilities, there were 29 = 512 possible 15
including L = (1,2,3,4,5,6,7,8,9) and 0. Each of these network were
considered when finding the most efficient network. If the network
were much larger than 9 abandonable links, a more efficient search
procedure would be needed to find the nost efficient network. Several
such procedures are described by Bazaraa and Jarvis (1977).

7Usingtheassnmptionofindependentdemandcnrves, themost
efficiennt quantities were found by setting the variable cost
allocation equal to the variable transportation cost.

 

68

The most efficiennt subset of facilities in L was found to be L* =
{1,3,5,7,8,9}. Therefore, it is be efficient to abandon rail linnks 2,
4, and 6. Equatios 16, 17, and 19 colld also be satisfied for any
subsetof L*, bntaccordingtoPmpositionz, thereisnoLfiwhich
includes link 2, 4, and/or 6 for which a cost allocation in us core
exists.

This L* spans all possible origin and destination links. Thus, I
the most efficient set of shipment quantities x* includes only r
shipments carried by Michigan rail links8 and shipments which can be i

 

carrieddirectlyfronaMichiganncdetoanontstatencdewithont i._
using Michigan rail facilities. Table 5 shows the nest efficient
roltes and shipment quantities over the existing network, the actual
average prices and total shipment quantities, tie most efficient
variable cost allocatios and shipment quantities over nost efficient
network, the total surplus if all Michigan rail linnks are closed
(truck benefits), and tie additional surplus (rail net benefits before
fixed costs are allocated) if transportation services over the six
links in L* are available to shippers. If the net benefits fron the
rail linnks are zero for a shipment, then that shipment can be carried
byrailbetweentletwonodeswithontusingaMichigan (abandonable)
raillinnk. Thegrossrailsurplusgainforall shiptentsoverL*is
$299,073,460 and the total fixed costs over this network are

$55,182,146. Therefore, willingness to pay exceeds the costs of

 

8This result is specific to this problem. With the truck
variablerateperton-milealnostStimesasgreatastlerail
variablecostperton-mileandallncdesconnectedtotlerail
network,tleshortesttruckrontewonldhavetobeshorterthanabont
20% of tie shortest available rail ronte in order to attract traffic
awayfrontterail carriers. Formshipments over L*istheshortest
railronteasnudnasStimesaslogastheshortesttruckronte.

 

 

69

 

Region 1:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Northern
Michigan
Link 1
253 Miles
Region 4: Region 3: ll Link 3 I Region 2: IL
Rapids 7 67 Miles —
Link 8 Link- 7 Link 5
67 Miles 106 Miles 65 Miles
’ . II Link 9 II .
‘ Reglon 6: Region 5:
—_H Kalamazoo H 110 Miles " Detroit
Michigan , l ,
(Lower
Penninsula)
_______ _.___-__.____ "F"-——-———"'"""
Outside of Link 16 Link 11
Michigan 215 Miles Link 12 288 Miles
264 Miles
Region 8: I Region 7:
Indiarna Ohio Border
Border , ,
Link 13 Link 10
Link 17 636 Miles 694 Miles
Link 18 537 Miles II ’
1792 Miles Link 15 Region 9:
918 Miles Eastern
‘ US & Canada
* 7 Link 14 a
Region 12: Region 11: 844 Miles
Western US ‘1[ Central US
& Canada , 7
Region 10:
Sontheast
US

Figure 3:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The Most Efficient Network

lax-d3
1arr14

larfls
lat-d7
lama

1ard9
1am10

lardll

Iani12

andB
and4
ands

NNN

and6
and?

NN

Zardlo

fiUNHbNHhUNHbUNH-FUNHDUNHfibNH-FHDHhNH-bNHhNHhNhNHbUNHfiNUNN-fl

Table 4:

70

Routes and Quantities

5833888882222838858

Sfififiggfififififififiqqmmmm

6.81 18.99 .
5.49 76.25 87.89
12.66 29.68 138.42
4.66 0 6.
26.34 0 244.99
34.29 0 249.82
49.54 0 98.
292.82 0 3,365.40
41. 0 34.
. 8 7,431.23
71.36 0 . 793.59
. 0 1,325.78
237.19 94.65 3,332.53
. 85.11 7,689.28
15.98 0 98.51
182.59 111.71 2,944.77
16. 66.90 3,348.70
17.83 0 110.
202.19 409.40 3,605.
476.26 2,786.28 9,502.48
48.50 117.30 880.
25.27 1,140.05 616.77
56.89 3,023.46 7,419.51
88.81 1,640.73 423.72
276.51 4.45 943.80
60. 740.13 637.82
10.34 88. 06.05
181.52 1,250.75 791.82
8. O 22.61
399.36 1,767.83 1,677.41
6.6 0 33.70
1,881.89 45,933.87 0
219. ,374.90 0
13. 75.19 0
2,039.04 34,197.00 0
1,354.32 30,737.60 15,976.82
95. 1,499.67 ,097.
17.27 94. 178.61
571.85 2,941.81 5,876.13
2,391.62 ,117. 0
172.38 5,518.22 0
6.39 26.40 0
396.16 17,419.40 0
2 736.21 93,638.60 12,971.78
.92 9,425. 1,211.13
.13 0 1.61
404. 5 7,872.26 1,880.02
2,078.51 71,110.41 25,172.99
207.73 5,692.70 2,482.15
346.43 14, 363. 97 4,239.23
232.13 174,027.17 28,031.57
143.41 ,2 . 8 1,561.58
20.06 . 1 164.51
260.47 19,868.92 3,268.76

 

3anda

3arx110

Jardll

ardS

ands
and 7

chub-lb

4ard10

4ard11

bNHhNt—J#UNHbNH-F-UMP-h'00-'thHuh»UNHfiNHhUNHbUNHhUHfiUHbH-FUt-hb

2323856355858uut3m
6 8.3838588893833338

0
0‘0
4

71

Table 4 (Continued)

3
am. i E 063mm iém I E E E mil: Emi
25. 3.51 31.73 48.85 168.28
35.65 2.68 59.82 406.79 409.61
6.99 2.68 8. 0 14.94
181.11 2.68 234.92 147.72 1,249.51
5.50 ,2.15 9. 92.6 66.96
3.30 2.15 5.0 89.90 36.97
216.59 7.21 350.06 7,319.17 1,679.45
6.80 7.21 10.54 50.0 45.
2281.86 7.21 2,913.59 29,461.81 13,440.25
91. 6.52 150. ,950.8 1,114.28
108.73 6.52 145.15 43.70 718.05
281.63 6.52 363.47 ,627.49 2,490.00
339.93 15.45 507.87 14,340.52 2,464.59
13.07 15.45 18.76 686. 91.
14.59 15.45 23.89 460. 114.
506.33 15.45 641.55 16,383.25 3,102.29
402.33 19.81 589.00 18,069. 8 4,480.43
216.20 19.81 215.11 1,519. 1,478.15
3.02 19.81 11. 0 5.
492.00 19.81 469.43 3,725.32 3,260.16
365.57 13.05 .25 ,900. 4,674.39
32.21 13.05 43.70 797. 321.
140.36 13.05 197.56 8,469.69 1,514.63
257.27 38.53 385.27 29,192.21 3,001.
54.45 38.53 71.83 4,213.18 556.
7. 38.53 . 0 .3
110.30 38.53 136.28 8,116.88 1,055.53
77.36 3.59 0. 1,031.36 ,429.
14.60 3.59 . 0 7.
7.10 1.36 10.76 101.79 49.
113.00 8.95 176.58 2,369.93 2,039.47
14.83 8.95 22.61 594.22 275.25
1308.73 8.95 1,110.27 0 5,690.26
235.10 5.72 329.79 1,575.52 1,433.87
93.84 5.72 112.56 305. 462.
9. 5.72 13.70 19. 52.
299.06 5.72 315.74 550.22 1,238.24
173.55 16.50 270.62 8, 43. ,342.11
99. 16.50 132.94 2,403.07 1,574.47
284.32 16.50 263.79 9.47 2,503.70
80.22 20.00 120.40 4,695.07 589.97
293.36 0.00 273.41 2, 72. 1,235.57
62.89 20.00 6.71 0 3.
2.80 . 268.49 2,431.75 1,229.26
170.68 12.26 282.80 14,058.17 1,393.
198.76 . 33.29 2,108. 1,067.
244.57 12.26 .74 4,098.22 1,377.33
50. 37.74 72.05 4,31 . 356.
225.93 37.74 176.49 2,004.48 820.25
26. 37.74 98. 6,172. 1, 29.

-3“.

5an19

Simdlfl

Siaflll

ESmdlz

6ani7

6am18

6an19

6 and 10

(Sadll

‘Smfilz

fiUNHhUNHfiNH-FNH#UNHfiNH-bUNHuhUNH-bUNHhtUNHhUNi-‘cb“Nb-‘0

72

Rflfle4 Knmjmmfl)

.Allocation Tons
5.66 38.80
19.12 2877.80
22.53 53.
19.87 3.
8.34 4838.84
26.54 1255.21
12.07 73.68
12.83 .65
10.16 772.61
29.26 2938.20
26.04 442.72
11.66 152.79
.83 744.18
36.77 1802.02
22.62 545.81
2 .8 620.80
24.33 1013.10
4 .89 2174.74
24.86 277.94
7.06 6.
17.17 998.36
101.89 1914.04
29.39 349.83
0.56 316.80
38.09 1444.99
31.99 144.28
9.99 52.35
11.72 827.57
7.56 266.56
10.84 58.38
9.26 8.30
8.23 997.40
38.61 95.20
25.56 139.
27.95 409.90
33.82 56.45
19.62 443.46
4.17 8.
59.18 98.08
22.31 261.11
22.64 4.
33.94 247.18
97.67 131.97
26.61 360.01
60.81 7.
54.92 185.70

if.

00000000000000000000

888 Gmfiflfiflflfibfifimmmdmmmmu

a:
egasaasmuuumuu53333323333333

h
0 0
UL)
mm

555555a&h 049

3,446.29
363.97

1,136.71
2,915.92
77

52928290
10,617.32

244,921.61
2 56

,4 .

3 ,853.44

4

5,557.52
12 19
5,150.01
2,200.87
907.53

° E
300000000

'1 N N
m r: we 30:1
N \l
0” 0:0. .004.”
h
N 0

‘

mum

K3

3‘3"!"
ooooooooooougwoooog

0U

 

73
Footnotes to Table 4

*Shigrants between regions may be in either direction. The routes
betweenthepairsofregionsarereported inTable4.3.

** The observed total oost allocation ton (in dollars) and the

 

observed tons shipped (in inthousandso ns) are estimated fran 1984
ICI: Waybill le data. Thee ICC f1e 1s a one- 53%;? so
the in the lied by 1 0. The cost
allocation is estimated 1viding ltal revenue from all
stugrants of a eseoodeig tworegions by theobserv

Sl‘L‘L cost allocation and quantities (a1ed

Lopped origemth
the elasticities for the commodity groups) are used tog danand
curves for each of the shigrant categor1es.

’ The variable cost allocation variable torate)per (tonin dollars
is the estimated variable costthe 0 ton shipmento thecarmodi
between the 1ons overthe1ve available route

%1mos‘t3 efficienrggnetmrk. The most ef icient routes are reported 1ni
e4

 

1r'Jihetonsofacorrrrrrodityshi betweentworegionsoverthemost
eff-entnetworkarethesurpusmaximizingshigrantsoverthenost
eff c ent route. The tons sh1 over the most efficient network are

 

 

 

found from the demand curves the variable costs for each shigrarrt

over its most efficient route. Surplus is maximized when the variable
toshi sequaltothevariablecostovertheleast

eiqrerrsive ava1 ablel route, which can be either a rail or truck route.

© The truck benefits (in thousands of dollars) are the benefits fran
worrying the most efficient quantity of the oamrodity over the most
efficient truck route (as 1f rail routes were not available). The
most efficient quantity when carried over truck routesma may not be the
rmilsarra 33113;. most effic1ent quantity when carr1ed over the available

 

§ Rail net benefits (in thousands of dollars

gain from usmggneil carriers instead of arealternative
thetotal fits (before the fixed oosts are allocated) net 0

the truck benefits. No shi W111 be willing to fig}: a

allocation that is greater its rail netbene

74

operatingtheseservioes (whid1uustbethecaseanytirreLirfp,
according to Proposition 2). The most efficient traffic routes over
thisnetworkandtlaSAFCoverthoseroutesaregiveninTableS.

Note that the average variable cost allocations per ton are lower
anduietctaltorsshirpedarehigheroverthisratworkthantheywere
overtheactualnetwork. Inthisexeroise,itwasassumedthatthe
fixedcostsoouldbeallocated with limp-sum charges. Recoveringthe
oostswithper—rmitdrargeswouldraisetheaveragerateperton,so pi
scma of the difference between the observed and most efficient rates :

 

pertoncsnbeexplairadbythechangetoalrmp—smuallocationof E...
fixed costs. I
SENSITIVITY'IOIHEDEMANDELASTICITIESANDGJSTOFCAPI‘IAL
The results described above are not highly sensitive to the
elasticities of danard. To check the sersitivity of the nost
efficient network structure to the demand elasticities, the most
efficient network was found for the same set of shignents with
different elasticities. When the four elasticities were all decreased
by 25% (rrultiplied by 3/4) , the most efficient network was again found
to be L* = {1,3,5,7,8,9}, because all regions are served by rail
facilities, so even with less demand sensitivity to the cost
allocation, there would be no additional rail surplus frcm providing
additional (and evidently redundant) facilities not in L*. The most
efficient network was also not affected when the elasticities were all
increased by a third (rrultiplied by 4/3). So when the shipment
derands are more sensitive to the cost allocation, intermodal
oarpetition would not make it sufficienly more efficient to provide
fewer links. If either of these changes in the danand elasticities

75
are made, the shigrant quantities and total surplus, will be affected,
ard the cost allocations described below will also be affected. But
even the fairly large changes in the demand elasticities described
above did not affect the most efficient network structure, so in that
sense, theoostallocationprooedureinthisd’zapterisnotvery
sensitive to the danand elasticities.

The Government Acoormting Office suggested that the ICC cost of
capital for 1984 may be too high. Ore alternative estimate produced
by the GAO was 11.35% as the cost of capital9. Using this lower cost
of capital of 11.85%, the most efficient network was again L* =
{1,3,5,7,8,9}. As was the case with changes in demand elasticities,
this shows that the most efficient network structure is not affected
bytheestimateoftheoostofcapitalbeingtoohigh. Achangein
thecostofcapitalwhididoesnotaffectthenetmrkstnlcturewill
also have no effect on the shigrent quantities. The only effect
before allocating the fixed costs will be an increase in the total
surplus after subtracting the lower fixed costs.

UPPERHIJNIBONEFFICIENI‘CDSTAIIDCATIONS

In order to silrplify the presentation of the cost allocation, the

155 traffic flows in Table 4 were aggregated into stellar sets of
shigrents in two steps. For the first aggregation, it has been
assured that different oarmodities carried between two regions have
the sane lowest cost route. Therefore, no distinction was made
betweencorlroditiesardberefitsardoostswereaggregatedoverall
shigrents carried between two regiors, which reduced the mmber of

 

9Government Accounting Office Documents, Railroad Revenues:

Analysis of Alternetive Methods to Measure Revenue m, October
2, 1986, p. 14.

V‘-

 

 

 

76

LpgrlhmfiscmtmecnaLMJaetkm

TafleS:

 

9879798865487 5 5446295315663Afi733181. 1 84....” 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7186721309 0mwobl79352890u695 70$95506004 mmo 6000
11 2 9062 1 82 7 6 8
8259m36” 61. 1.91. “MI 80“ 7111. 7564 1408w4 no 4“

I9 SI

5
6r1w1. 1 ”469641 81.71.32 1. 86
11.1. 2 1.1.

6399337852 9 522114741144676767779 9 999 9

0.4.9..000.00evbeeLOLOeLLoeaboofleorboooeLo-IM...thO‘%OO‘%obe‘%Ooboooo
99146116 4 9 9 22 4 22 an 4 444
96 1.5 553869 9 69955535555 1.21.1.3
IIIIIIIIIIIIII I IIIIIIIIIIIIIIIIIIIII I III
60606900995454 4 54499858998845u545559 9 999 9
2223223322 1 1 111 1 1
9989780 .865887 5 5AAO.19539966940733183 1 845 6
0... 0.9... o ......oo....... o ... 0
44891286 313090 .4624352230369570 955060 0048306000
99212911 493 D 9257062721134m82 307 6 flaw 8
149.101.291.74 I80I5.0I11"1.72564 140864 5 4
IIIIIII I I I IIIIII IIIIII I III I
1 1 2 1“... 1. 2 1.1.

680.16361337952 2 522234747344676767779 9 93°" 9
0 0 C 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C 0 0 0 O 0
818464P8I6I’05832 2 3222975759776565 555
05169.0I10fl95 54 4 SMAWL08585088454545559
233222322 1 1 1111 1 1 °.I 999 a."
60478 160‘. 8 604 8 6
H1111... 1111.111 nlllnl nlumnm nmnunuumnmnm
85 5 8
I111 11 I 3 1. 1.371.. 8 8 8

 

mmmmmmmwmwmmmmmmwmmmmmmmmwmwmmmmmwmmmmmmmmmmmmmmm

1111111112222222222333333333444444.445555555666666

77
Footnotes to Table 5

+Notethatthe Whetweentwo 1onsinTable5arenot
divided into tycategories as in le 4.

*‘Ihe most efficient route is the route over erthe nost efficient
network L which has the lowest variable .transporta t1on cost. The
most efficient network was found by oonsidermg all possible subsets
of Michigan rail faeilities and finding the gross ra1l surplusgam
rfnetvvommek most efficient shiprent quant1tias over every possiblegm'n

r .

"IheSAFC (inwthmsandsofdollars) isthefixedcostofthe
irumbent carrier: ting only those Michigan facilities needed to
provide the mfiartian ar service. The fixed costs of faculties not
chLang lirfl<s10t018areignored becausethereare
shipmen over these acilitias whi are not in the Michigan sample.

 

 

'IheSAFCis estimated tfil yingthe miles of Midngantrack

the route (from Figure )by: e average fixed cost per mile of track k.
of $82 608 which was estima earlier in this chapter. is assumed
that1acarr1er1s ingmo mrethanitsstarri-aloneoosts,then

wh11e chargmg a lower rate.
rail shisurplus gain fran using rail carriers over Michigan

links or all ts( tedov erooumodigl ) betweengan a
ir of citiesShl is the tota benefitsov from these .
fits from the next best transportation mode. 0 shipper would be
W1llmg to pay more than its gross ra1l surplus.

’7 CEhe SAFC and the rail surplus assumingno noabandonmentare for
all shi ts over Ellie], eastexpens1ve route when it is mare that
all of erail links (including links 2, and 6) W111 be operated
the carriers. 'Ihese columns are includ4 to show that the range
non-subsidizing cost allocations 15 narrower when the cost
allocation tés de51gned not to lead to inefficient facility uses or
abandonmen

 

 

78
shipnerrtstoso in'I‘able 5. Noshimervmldbewillingtopaya
cost allocation greater than either its SAFC or its benefits frcm rail
services (before fixed cost are allocated), so the upper constraint on
the cost allocation is the lower of a service's SAFC and benefits frcm
rail transportation. The SAFC and gross benefits for all services are
sham in Table 5.

In order to oarpare the range of cost allocations for individual
shipnentstotherargesfamdfranotheroostallocntions,thennst .
efficient traffic flows were found under the assumption of no facility . A1
abanioments,soshiptentsoverallnineMidiiganraillim<swere H

 

allowed. 'Ihe SAFC and gross rail surplus gains for these traffic
flows over the entire set of facilities in L are also shown in Table
5. IheSAFCupperban'dswouldbetheuzperbamdsmflertheFarara
andGrimmproposal, andtheminimmlofthetmupperbamdsvmldbe
the upper bounds on a core allocation if no facility abardonments are
allowed. Inbothcases, theupperbourdsmtheoostallocatimare
lower (the allocation rage is narrower) under the cost allocation
procedtneinchapter3, withtheexoeptionof shiptentsbetween
regions3andlo. ‘meSAFCvmldbelmerforshiptentsbetweenBarfl
lObecausetrafficisreroutedoverliIflcé, whichisanabanionedlink
in the most efficient network. Therefore, the lower bound on all
shipnents over link (3-to-4, 3-to-5, 3-to-9, and 3-to 10) will be
higher because they alone are responsible for this facility. However,
any shipments over facility 6 is not a core allocation if abardoment
is allowed, according to Proposition 2, since efficiency could be
inprovedbyabardonirglirflcs 2, 4, and6. Therefore, thislowerSAFC
forshiprentbetweenBaxrllOvmldmlongerbetheSAFCafter

79

facility 6 is abandoned.
W 'IHE FIXED GETS

Of course, it is the upper bounds on carbinations of facilities
which are more likely to constrain the cost allocation, but the upper
bounds on all possible cmbinationslo would be impossible to sunmarize
in a brief table. Therefore, the shipments were aggregated a second
time by collection all shipnents which share the same set of Michigan
rail facilities. This reduced the mmber of shipnerrts to 16, of which
15 use Michigan facilities. The upper bounds were calmlated for all
canbinations of these 15 facilities which had at least one facility in
conmon. Theupperbomriontheseshipnentsandccnbinatim'sof
shipments are shown in Table 6.

Theexistenceofanupperboundonasetofshiptentsalso
implies that all remaining shipments nust pay any fixed costs in
exm of that upper bound for facilities which they share with the
groupwhichhastheupperbom'dconstraint. Thelowerboundson
coubinations of facilities are also shown in Table 6 .

A Moriarity allocation is the easiest to calculate of the
allocations surveyed by Hamlen, et,a1. (1975), but is not necessarily
a core allocation. In this case, however, the Moriarity allocation
was found to be in the corell. Under the Moriarity rule allocation,
thesxmoftheupperbamisconstraintsontheoostallocationforthe

15 irdividual shipnents in Table 6 is $217,406,313 and the total costs

 

10With 41 of these 50 shipnents using Michigan rail facilities,
there would be 241 or 2.2x1012 different carbinations of shipnents and
upper bounds.

11If the Moriarity allocation had not been in the core, it vmld
mvebeennecessarytouseamoreoatplexallocationrule, suchasthe

Shapely rule.

 

 

 

80
Table 6: Cost Allocation Ranges

Shipments Sharing Michigan Link 1

 

Shifi over Gross 23m lus Hanan t A 00;:
20' 08 O
13 26 434.6 22 143.1 22,143.1 0 I
135 311804.1 61886.8 61886. 0 31322.3
4;. 33432-3 44432-3 44 3323 3
' O 0 O 83.4
1 8 13 26 434.6 22 231.0 22, 231. 0 0
1 8 135 311804.1 61974.7 61974.7 0 3136:25
1 8 17 29,656.3 24,343.1 241343.1 0 10,416.7
1 8 178 35,191.0 282.8 '282.8 0 121.0
13 8 135 31,804.1 29,029.9 29,029.9 0 12,422.2
13 8 17 35,191.0 46,398.3 35,191.0 13,730.2 19,854.4
13 8 178 40,725.7 22,338.0 22,338.0 0 9,558.7
135 8 17 40,560.5 31,142.0 31,142.0 0 13,226.0
135 8 178 46,095.3 7,081.7 ,081.7 0 3,030.3
17 8 178 35,191.0 24,450.1 24,450.1 0 10,462.5
1, 13 8 135 31,804.1 29,117.8 29, 117. 8 0 12 469 8
1 13 8 17 35 191.0 46 . . . ' °
11 13 8 178 401725.7 221235.; 33E}§%,3 13’813 1 13133323
, 135 8 17 40,560.5 31,336.9 31,336.9 0 13,363.6
1, 1;5&8 178 46,095.3 ,169.6 ,169.6 0 3,067.9
15 1135 1787 35,191.0 24,538.0 24,538.0 0 10,500.1
13, 135 8 178 40,560.5 53,285.1 40,5 .5 20,167.0 22,801.3
13 17 8 178 23'933'; ig'ggg'g ig'ggg'g 13 92g 1 13133733
135, 17 8 178 461095.3 311336.9 31133629 ' 0' 131409.4
1 13,135 8 17 40 560.5 53 373.0 40 . .
11 131 135 8 178 461095.3 291312.7 291313.; 20'703 9 §§122§,§
1'135 17 8 178 40,725.7 46,681.1 40,725.7 14,013.0 19,975.4
15 5 17 8 178 46,095.3 31,424.8 31,424.8 0 13,447.0
1 13 17 8 178 46,095.3 53,480.0 46,095.3 20,811.9 22,884.7
1, 13, 135, 17 8 178 46,095.3 53,567.9 46,095.3 20,899.8 22,922 3
Shipments Sharing Michigan Link 5
fllfi Qver Gross Sirglflus Aoca Coreon
35 10,904.2 101979.1 101 904. 2 4,663.3
5 5,369.5 181 556. 4 51369. 5 2,297.7
135 8 35 31,804.1 17,865. 9 17,865. 9 0 7,610.2
135 8 5 31,804.1 251443. 2 251 443. 2 0 5,244.6
35 8 5 10,904.2 291535. 5 101904. 2 0 6,961.0
135, 35 8 5 31,804.1 36,422.3 31,804.1 5,369.5 9,907.9

* Lixflcsaregrumedintosetsoflinksoverwhimtrafficis

carried,

sonderntesallshipuentscarriedoverniwiganlirflcslaIflBonly,

ard135denotesallshiptentscarriedoverlinksl, 3, ands.

81

Table 6 (Continued)

Shipments Sharing Michigan Link 3

Over Gross gag-p113 Maxim
26' .6 ' O I O

135 31,804.1 6,886.8 6,886.8
3 5,534. 22,305.9 5,534.7
35 10,904.3 10,897.9 10,897.9
37 14,291.2 80,050.3 14,291.2
378 19,82 .9 743.9 743.9
13 8 135 31,804.1 29,092.7 29,092.7
13 8 3 26,434.6 44,449.0 26,434.6
13 8 35 31,804.1 33,041. 31,804.1
13 8 37 35,191.0 102,193.4 35,191.0
13 8 378 40,725.7 ,887.0 22,887.0
135 8 3 31,804.1 29,192.7 29,192.7
135 8 35 31,804.1 17,784.7 17,784.7
135 8 37 40,560.5 86,937.1 40,560.5
135 8 378 46,095.3 7,630.7 7,630.7
3 8 3 10,904.3 33,203.8 10,904.3
3 8 37 14,291.2 102,356.2 14,291.2
3 8 378 19,825.9 23,049.8 19,825.9
35 8 37 19, .7 90,948.2 ,660.7
35 8 378 25,195.4 11,641.8 11,641.8
37 8 378 19,825.9 80,794.2 19,825.9
13, 135 8 3 31,804.1 51,335.8 31,804.1
13, 135 8 35 31,804.1 39,927.8 31,804.1
13, 135 8 37 40,560.5 109,080.2 40,560.5
13, 135 8 378 46,095.3 29,773.8 29,773.8
13, 3 8 35 31,804.1 55,346.9 31,804.1
13, 3 8 37 35,191.0 124,499.3 35,191.0
13, 3 8 378 40,725.7 45,192.9 40,725.7
13, 35 8 37 40,560.5 113,091.3 40,560.5
13, 35 8 378 46,095.3 33,784.9 33,784.9
13 37 8 378 40,725.7 102,937.3 40,725.7
135, 3 8 3 31,804.1 40,090.6 31,804.1
135, 3 8 37 40,560.5 109,243.0 40,560.5
135, 3 8 378 46,095.3 29,936.6 29,936.6
135, 35 8 37 40,560.5 97,835.0 40,560.5
135, 35 8 378 46,095.3 18,528.6 18,528.6
135 37 8 378 46,095.3 87,681.0 46,095.3
3, 35 8 37 19,660.7 113,254.1 19,660.7
3, 3s 8 378 25,195.4 33,947.7 25,195.4
3 37 8 378 19,825.9 103,100.1 19,825.9
35, 37 8 378 25,195.4 91,692.1 25,195.4
13, 135, 3 8 35 31,804.1 62,233.7 31,804.1
13, 135, 3 8 37 40,560.5 131,386.1 40,560.5
13, 135, 3 8 378 46,095.3 52,079.7 46,095.3
13, 135, 35 8 37 40,560.5 119,978.1 40,560.5
13, 135, 35 8 378 46,095.3 40,6 1.7 40,671.7
13, 135 37 8 378 46,095.3 109,824.1 46,095.3
13, 3, 55 8 37 40,560.5 135,397.2 40,560.5
13, 3, 35 8 378 46,095.3 56, 0.8 46,095.3
13, 3 37 8 378 40,725.7 125,243.2 40,725.7
13 35, 37 8 378 46,095.3 113,835.2 46,095.3
135, 3, 35 8 37 40,560.5 120,140.9 40,560.5
135, 3, 3s 8 378 46,095.3 40,834.5 40,834.5
135, 3 37 8 378 46,095.3 109,986.9 46,095.3
135 35 37 8 378 46,095.3 98,578.9 46,095.3
3, 55, 57 8 378 25,195.4 113,998.0 25,195.4
13 135 3 35 8 37 40,560.5 142,284.0 40,560.5
131 1351 31 35 8 378 46,095.3 62,977.6 46,095.3
13, 135, 3 37 8 378 46,095.3 132,130.0 46,095.3
13, 135 35 37 8 378 46,095.3 0,722.0 46,095.3
13 3 55 57 8 378 46,095.3 136,141.1 46,095.3
135, 5, 35, 37 8 378 46,095.3 , .8 46,095.3
13,135,3,35,37 8 378 46,095.3 143,027.9 46,095.3

ll. 0

was»

n

‘5
:3

00000? OOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOO'OO 00000
00

5,534.7

(I
U

5:55

P
O‘fiONQQU‘OQUHD

 

 

 

82

Table 6 (Continued)

Shipments Sharing Michigan Link 7

51.11 War

7,

371378 8 78
78 78

378, 7 8 78

17, 178, 37 8 378
17, 178,37 8 7
17, 178137 8 78

178, 371378 8 7
1781371378 8 78
1781 37' 78 78
1781375 7 8 78
37, '378, '7 8 78

17,178,37, 378
171 1781 37, 378
17, 178, 37 7 8
1L 178,375 7 8

'378 '7 8
175 2L 375 7 8 78

17,178,37,378,7 878

GrossSurplus Maxinun

55718532???

29, .3
351191.0

H
.5
MN
MO
UN"
N

5 '756I
141291.

35,191.
351191.
401725.
291656.
351191.
401725.
401725.
351191.0
351191.0
191 825. 9
14129L 2

\ILJOULIOO NUI‘O

401 725. 7
40,725.7

N
01
‘

£3
S"

‘09)
0001

H
H?
abut-x)
\OGND

hQO‘OQU'HD

m
‘0
~
U
h
0‘

113, 244.3
1281050.9

128, 794.
1131796

§
u:
U
Ho
moum qqummoemmomh

b
H
fifiB
O\

1291 151. 9
1051 091. 6

129,346.8

....
0
?

14, 29L
743.
8,756.

401 725. 7
40,725.7

0100000 000000000000000 00000

\I
N
0‘
\l

\3
:5
000080 0000‘0000000000

8,003.6
7,817.7

000000

8,203.5

8,013.6

8,561.6
0

8,756.5

 

20,879.4

83

Table 6 (Continued)

Shipments Sharing Mimigan Link 8

$1.11 . Qver Gross 1115 Maxim Hininum A Chg?
Wm 3588.0 ”$113 511%??? WW.
378 19,825.9 743.9 743.9 0 318.3
78 14,291. 552.0 552.0 0 236.2
5,534.7 12,740.3 , .7 0 2,368.4
89 14,621.6 16,862. 14,621.6 0 6,256.8
178 8 378 40,725.7 938.8 938.8 0 401.7
178 8 78 35,191.0 746. 746.9 0 319.6
178 8 8 35,191.0 ,935.2 12,935 2 0 2,451.8
178 8 89 44,277 9 17,057 0 17,057.0 0 6,340.2
378 8 78 19,825.9 1,295.9 1,295.9 0 554.5
378 8 8 19,825.9 13,484.2 13,484.2 0 2,686.7
378 8 89 28 9 .8 17,606.0 17,6 .0 0 6,575.1
78 8 8 14,291.2 13,292.3 13 292.3 0 2,604.6
78 8 89 23,378.1 17, .1 17,414.1 0 6,493.0
8 8 89 14,621.6 29, .4 14, .6 4,043.9 8,625.2
178, 378 8 78 40,725.7 1,490.8 1,490.8 0 637.9
, 3 8 40,725.7 13,679.1 13,679.1 0 2,770.1
178, 378 8 89 49,812.6 17,800.9 17,800.9 0 6,658.5
178, 78 8 8 35,191.0 13,487.2 13,487.2 0 2,688.0
178, 78 8 89 44,277.9 17,609.0 17,609.0 0 6,576.4
178, 8 89 44,277.9 29,797.3 29,797.3 4,238.8 8,708.6
378, 78 8 8 19,825.9 14,036.2 14,036.2 O 2,922.9
378, 78 8 89 28,9 .8 18,158.0 18,158.0 0 6,811.3
, 8 8 89 28,912.8 30,346.3 28,912 8 4,787.8 8,943.5
78, 8 89 23,378.1 , .4 23,378.1 4,595.9 8,861.4
178, 378, 78 8 8 40,725.7 14,231.1 14,231.1 0 3,006.3
178, 378, 78 8 89 49,812.6 18,352.9 18,352.9 0 6,894.7
178, 378, 8 8 89 49 812.6 30,541.2 30,541 2 4,982.7 9,026.9
178, 78, 8 8 89 44,277.9 30,349.0 30,349 0 4,790.8 8,944.8
378, 78, 8 8 89 49,8 .6 30,898.3 30,898.3 5,339.8 9,179.7
178, 378, 78, 8 8 89 49,812.6 31,093.2 31,093.2 5,534.7 9,263.1

Shipnents Sharing Michigan Link 9

~88- .... 885883.118 8888. 8888.8. W8
853m 14%6 AH—arrk—Tflfiz}?

9108619 114’39427 9’08629 .
39 8 9 141621.6 1311256.8 141621.6 9,086.9 101140.6

 

84

to be allocated are $55,182,146, so each service was allocated fixed
costs equal to 25.4% (= 55,182,146/217,406,313) of its willingness to
pay. This cost allocation is given in the far right-hand column in
Table 6. It can be verified in Table 6 that no set of traffic flows
is allocated a share of the costs that is outside of its allocation
range.
(DNCLUSION

In this chapter, it was demonstrated that the cost allocation
proposal indiaprtera canbeappliedtoanexistingnetmrk. Since it
was efficient to abandon links in this network, the cost allocation
proposals in the literature survey (Ransey-pricing, Fanara and Grim)
would not lead to an efficient cost allocation because they do not
consider the efficiency of facility abarxiomtents when allocating

oosts.

 

 

CHAPI'EIR 5: MISHJQ

Since the passage of the regulatory reform legislation of of 1976
and 1980, railroads have nuch more freedan to abandon unprofitable
services and set their own rates for nuch of their traffic. Thus, an
efficient solution to the old probl- of recovering the cannon costs
of rail carriers nust now include the corsideration of which
facilities and services should be abardcned to maximize efficiency and
the limits on cost allocations if inefficient abardonmem: is to be
avoided.

It was shown in chapter 2 that several rail cost allocations
proposedsincethepassageoftheStaggersActaremtefficientcost
allocations because they fail to consider whether efficiency can be
increased by abandomnent of facilities fran the existing network
structure. It was proven in Proposition 3.2 that if the existing
network is not the most efficient network, then no non-subsidizing
allocation will exist which allows all facilities to be used.

A procedure for finding an efficient cost allocation was
developed in chapter 3 and applied to the 1984 Michigan rail shipments
in chapter 4. Under this proposal, first the most efficient network
configuraticnisfcm'd, andthenupperbamdsonthefixedchargesto
shipnerrtsandgmipsofshimentsarefamdwhidlencmragethe
carriers to operate the most efficient network while recovering all
camloncosts. AccordingtoProposition3.2, thesearethesameupper
bounds that Sharkey finds for a non-subsidizing cost allocation.
Therefore, the problan of firding a non-subsidizing cost allocation
using fixed charges is identical to the problem of finding a set of

85

 

L

86
fixed charges which encourages the most efficient service provisions
and service levels.

This cost allocation satisfies each of the properties of an
efficient allocation proposed in chapter 1. This cost allocation
proposal satisfies property 1 by allowing the provider(s) of the
service to recover all costs. With private rail carriers, it is
efficient to allow carriers to recover all of their costs, or else the
carriers will not provide the service - even when providing the
service vmuld otherwise maximize social surplus.

The third property is satisfied because the most efficient set of
facilities is found in the first step of the cost allocation
procedure, and then the limits on a cost allocation (thcngh fixed
charges) are found which give carriers the incentive to provide the
social surplus maximizing network configuration. Property 2 is also
satisfied because the most efficient network is defined as the retmrk
over which the most efficient traffic flows may be carried. So long
as side-payments are allowed, the potential Pareto optimality standard
of efficiency insures that the winners fran any movanent closer to the
surplus-maximizing shipments levels over the most efficient set of
facilities (perhaps the captive shippers) will be able to cmpersate
the losers (perhaps the monopolist carriers) fran such a move. Even
if side payments are not made, the presence of carpetition for most
services and the ICC regulation of market daninated services insures
that rates will not be greatly different fruit the rates which lead to
the most efficient services.

It is proven in Proposition 3.2 that the cost allocation with the
first three properties of an efficient cost allocation also will lead

 

 

87
to a non-subsidizing cost allocation (property 4) ard will allocate
theccumoncostsusing fixeddzargeswithlessarbitrarinessor
equitybbased.elementsl than.allocations using fixed.charges which
ignore possible efficient facility abandonments (property 5) . 'Ihe
principlesusedtoallocatethefixedcostsinduaptersBani4were
based upon efficiency consideratiors only, rather than both efficiency
andequitycriteriaas intheFanaraandGrinmproposal. 'meseequity
criteria might be considered when choosing an arbitrary allocation
rulez, but the range of possible non-subsidizing allocations has been
narrowed, makingequityissuesless inportantwhenthecostsare
allocated.

In chapter 4, the cost allocation prqaosal was applied to the
Michigan tramportation network to demonstrates that the cost
allocation can be applied to existing transportation systans. 'Ihis
cost allocation requires less information than the Ransey-pricing
allocations advocated by the railroads' mresentatives and is also
less difficult to calculate than the Musey-pricing proposals.

'Ihe railroad regulatory reform legislation from the late 19703
places nudm nore arrhasis upon the profitability of railroads and the
econanic efficiency of rail rates. To the extent that maximizing the
efficiency of the provision of tramportatim services (while insuring

 

1It will allocate the fixed costs with less arbitrariness than
otherallocationsgiventhenetworkstmcture. Acasewasfoundin
diapter4wheretheupperbamicmstraintwaslessrestrictivemder
theproposal frondmapter3thanitwmldhavebeenunderanother
proposal,h1tthisresultwasbecausenetvnrkstrucu1reintheother
proposalswasmtthenostefficientstmcmre(sothatu1eothercost
allocation was not a core allocation).

2such as one fron the survey of such allocation rules by Hamlen,
et.al. (1975)

 

88
that railroads recover all of their costs) is the objective of
regulators, then the ICC was correct in requiring that no service or
service group pay more than its stand-alone cost for coal shipments3.
ItisarguedherethattheICCcmldproduceevenmreefficient
guidelines in two ways. First, the Ia: could apply these coal
shipnent guidelines to shipments of all products. Second, the ICC
could extending its concept of cross-subsidization to siulaticrs where
a shipper or shipper group pays more than either its stand-alone cost
or its additional shippers surplus frcm using rail carriers imtead of
the next best alternative“. The ICC in its coal rate guidelines
proposed that rates should be proportional to the individual demands
of shippers, which is related to (but less specific than) the cross-
subsidization concept based upon the shippers additional surplus frun
rail services5.

The chi's rate-making authority was limited by the Staggers Act
to railroads with market daninance6, so any non-subsidizing allocation
of costs to relatively ccmpetitive services could not be imposed by
the ICC. However, no shipper will pay more than its benefits fran
rail transportation and the definition of market daninance in the

Staggers Act slmld protect shippers frcm cost allocations in excess

 

3See footnotelinchapterl. Thisguideline foravoiding
cross-subsidization is consistent with Faulhaber ' 5 definition of
cross-subsidization.

4This definition of cross-subsidization is based upon Sharkey's
( 1982) analysis of cross—subsidization in public enterprises, which
wasusedtodevelopthecostallocationprocedureinchapterB.

5Noteinfootnote1todlapterlthattheICCdidmtexterd
thisguidelinetogrmpsofshippers.

6withmarketdaninancedefinedundertheStagger'sActasahigh
revenue-to—variable cost ratio

:1

89
of their stand-alone costs. Therefore, the railroads will have an
incentive to avoid cross-albeidizing cost allocations and will find
these guidelines for non-subsidizing allocations useful Mm
allocatingcoststoanyoftheshippersoverthene’mork. Alsounder
the Staggers Act, carriers and shippers are given more flexibility
Mlenmakingcmtracts. Thesecontractsmaynowbewrittento include
fixeddlargessudlasthoseindlapters3and4torecoverthecatmcn
costs shared by many users of the network.

LIST OF REFERENCES

LIST OF REFERENCES

Mokhtar S. Bazaraa and John J. Jarvis (1977)

1iaaareEr9grarming_end______rreflgu§ J9 n Wiley and Sons
Inc. , New York, 1977.

William J. Baumol and [hvid F. Bradford (1970)
"Cptinum Departures fran Marginal Cost Pricing", An_§_r__ican
W, Vol. 60, No. 3 (June), pp. 265-283.

Ronald R. Braeutigam (1979)
"Optimal Pricing with Intermodal Carpetiton" , American
Economic Review, Vol. 69, No. 1 (January), pp. 38-49.

Stephen J. Brown and David S. Sibley (1986)

The Theog of Public Utilig Pricm’ , Cambridge University
Press, New York, NY.

Ronald H. Ooase (1946)
"The Marginal Cost Controversy", Economica, Vol. 13, No. 1,
pp. 169-189.

Stuart Daggett (1955)

Principles of Inland Wration, Fourth Edition, Harper
and Brothers, New York.

Ronald R.Braeutigam (1979)
"Optimal Pricing with Intermodal Canpetition" , American
Economic Review, Vol. 69, No. 1, pp. 38-49.

Sylvester Dams (1984)
"Ransey Pricing by Railroads: Gan It Exist? ", Journal of
MR Em’es and Polig, Vol.17, No.1, pp. 51-61.

Phillip Fanara, Jr. and Curtis M. Grimm (1985)
" -Alcne Cost: Use and Abuse in Determining Maximum

U.S. Railroad Rates". W. Vol. 19A,
No. 4. pp. 297-303.

Gerald R.Fau.lhaber (1975)
"Cross-subsidization: Pricing in Public Enterprises",
American Economic Bgiew, Vol. 65, No. 5 (Dec.) pp. 966-977.

90

91

Ann F. Friedlaender and Richard H. Spady (1981)
WWW MIT Press Cambridge.MA

Susan S.Hamlen,William H.Hamlen,and John T‘.T’schirhart(1977)
"The Use of Core Theory in Evaluating Joint Cost Allocation
Sdlemes", The ma Review, Vol. 52, No. 3 (July).
pp.616-627.

Kent T. Healy (1957)
"Discriminatory and Cost Based Railroad Pricing," American
My, Vol.47, No. 2 (May). pp. 430-461.

m Parte No. 347: Cost-Rate Guidelines - Nationwide.
Interstates Camerce Oarmission, Washington, D.C., 1983.

Alfred E.Kahn (1970)

Me mics of Mation: Principles and Institutions.
Vol.1, John Wiley and Sons, Inc.,New York, 1970.

Alfred E.Kahn (1971)

The Economics of Mation: Principles and Institutions.
Vol.2, John Wiley and Sons, Inc.,New York, 1971.

Theodore E. Keeler (1983)

Railroads, Freight and Public Poligy. The Brookings
Institution, Washington, D.C. 1983.

Shane Moriarity (1975)
"Another Approach to Allocating Joint Costs", The Accountm'
Review, Vol. 50, No.4 (Oct) pp.79l-795.

Merrill J.Rcberts (1983)
"Railroad Maximum Rate and Discrimination Control",

mmtion Journal, Vol. 22 No. 1 (spring) pp. 23-33.

Merrill J. Roberts (1987)
"Residual Railroad Rate Control: The Unmet diallenge of

Deregulation", Lgisties and mmtion Review, Vol. 23, No.1,
(March), pp. 83-108.

J.H. Rohlfs (1979)
"Economically-Efficient Bell System Pricing", Bell Laboratories
Economies Discussion Paper No. 138.

Lloyd 8. Shapely (1953)
"A Value for N-Person Games", Coflibutions to the Theory of

Genes, Vol. 2, H. Kuhn and A.W. maker, eds., Princeton
University Press, Princeton, NJ.

92

w.W.Sharkey (1982)
"Suggestions for a Game-Theoreting Approach to Public Utility
Pricing and Cost Allocation", 1g 2;; Jam]. of Economics,
Vol. 14, No. 1 (spring) pp. 57-68.

w.W.Sharkey (1985)
"Cores and Inplications for Pricing in a Model of Production

with Fixed Costs and Shared Facilities", unpublished paper at
Bell Cmmmications Research.

William B.Tye (1985)
"Problems of Applying Stand-Alone Costs as an Indicator of
Market Daninance and Rail Rate Reasonableness", Integtional

MW. Vol. 12. No. 1 (Feb) 133- 7-30-
Hal Varian (1934)

W. second edition. WW Norton and
Carpany, New York, NY.

W.G. Waters II and A.D. Woodland (1984)
mmgic Analysis and Railway any“ , Centre for
Transportation Studies , University of British Columbia,
Vancouver, Canada.

Edward E. Zajac (1978)
am or Efficiency; fl; Wig to Public Utilig
m, Ballinger Rlblishing Carpany, Cambridge, 1%.

"‘WinfillllliflililfliES