CSIS Discussion Paper No. 40

Regulatory Reform and the Congestion of Urban Railways
Yukihiro Kidokoro∗

Abstract: Using a spatial model with a railway line in which the congestion rate, defined as the ratioof the number of commuters to a railway’s nominal capacity, is explicitly included, this paper
numerically simulates the impacts of railway regulation reform in Japan. We show that while theregulatory shift from rate-of-return regulation to price-cap regulation makes railway firms operate
efficiently, it substantially shrinks railway capacity and lowers social welfare. We then consider
modified versions of price-cap regulation, which are consistent with relief of congestion.

Keywords: price-cap regulation; rate-of-return regulation; congestion; railways∗

Center for Spatial Information Science (CSIS), University of Tokyo

Mailing Address: Faculty of Economics, University of Tokyo, 7-3-1, Hongo, Bunkyo, Tokyo, 113-0033, Japan
Tel & Fax: +81-3-5841-5641, e-mail: kidokoro@csis.u-tokyo.ac.jp
This paper is a product of CSIS joint research project, “Spatial Information Database for Transportation Systems.” I would like tothank Yoshitsugu Kanemoto for helpful suggestions and discussions. I owe special thanks to Hajime Miyazaki for his extensive
comments. I would also like to thank Ken Brevoort and Tatsuo Hatta for their remarks. Of course, I am solely responsible for any
errors and omissions.

11 Introduction
Extremely high population densities in Japan’s large cities2 have made it possible for many
private railways to provide transportation services. Urban railways, including public and private
railways, play an important role in Japan’s urban transit system. For example, railways in the Tokyo
metropolitan area provide 56% of travel needs. Such a high concentration of population, however,causes extreme railway congestion during rush hours. The congestion rate, which is the ratio of thenumber of commuters to a railway’s nominal capacity, is about 200% on almost every line in theTokyo metropolitan area. Typically, Tokyo railway firms have been operating their lines with very
short headway and very long train configurations during peak time. Therefore, peak-time congestion
cannot be relieved without constructing new lines or enhancing the current double-track lines tofour-track lines.
Why is the transportation capacity of urban railways in Japan’s large cities too small for thedemand? This problem is analysed by Kanemoto and Kiyono (1993, 1995) and Kidokoro (1998), allof whom demonstrate that the present regulation imposed on railway firms increases congestion.
Kanemoto and Kiyono (1993, 1995) point out that under the present regulation system, i.e.,
rate-of-return (ROR) regulation, the regulator sets the rate of return on capital investments lower than
the true cost of capital, taking into account the profits from side businesses associated with therailway business. They suggest that this low rate of return on capital investment hinders railway
firms from enhancing their capacity. Kidokoro (1998) focuses on another aspect of the present ROR
regulation. The present ROR regulation values railroad right-of-way (the land used for running thetrains) at its book value, which is much lower than its market value.

He shows that thisunder-valuation of railroad right-of-way decreases profits substantially and thus railway firms’
incentives to enhance their capacity are very much weakened.
The purpose of this paper is to investigate whether or not the congestion problem stated above

2

For example, the population density in Tokyo was 5384/km2 and that in Osaka was 4650/km2 in 1995.

2

can be resolved in the current era of regulatory reform in Japan, and to propose a regulatory methodthat is consistent with the relief of congestion. The paper focuses on the regulatory reform from ROR
regulation to price-cap (PC) regulation, which is now under way in many industrialized countries.
Many authors, such as Train (1991), Braeutigam and Panzar (1993), Liston (1993), and Bös (1994),
have discussed the merits and demerits of ROR and PC regulations. However, they do not provide acomprehensive analysis that explains the effects of the regulatory shift from ROR regulation to PC
regulation on railways’ performances, explicitly taking into account the congestion problem. Thus,
we here narrowly focus on the regulatory reform for congested urban railways, rather than address thegeneral regulatory reforms that are now taking place in many regulated industries3. For that purpose,
we build a simple spatial land-use model of a commuter railway. The reason why we employ a spatial
land-use model is that the current bottleneck input in Japan, which hinders an enhancement oftransportation capacity from the current double-track to four-track lines, is railroad right-of-way.
Using a spatial model also enables us to implement a cost-benefit analysis of various regulatory
methods in a closed-form system and to show the impacts of the regulatory change.
Using data from the Tokyu To-Yoko line, which is one of the major railway lines in the Tokyo
metropolitan area, we numerically simulate the various regulatory methods and examine the effectsof the regulatory change in terms of social welfare. Our main results are as follows:(1) Introducing PC regulation without properly addressing the congestion problem is problematic,
because it enhances a railway firm’s cost-reducing efforts and increases efficiency, but cannot relieve
congestion.
(2) PC regulation with a cap contingent on transportation quality, which is the inverse of thecongestion rate, can relieve congestion without distorting cost-reducing efforts.
(3) PC regulation, in which the cap is made contingent on investment, can also correct the congestion,
but decreases railway firms’ cost-reducing efforts and thus has an adverse influence on their efficient

3

See, for example, Armstrong et al. (1994) and Helm and Jenkinson (1998).

3

operations.
(4) PC regulation, in which investment levels are fixed in advance and cost pass-through forinvestments is allowed, can correct the congestion without damaging cost-reducing efforts, if theelasticity of substitution among inputs is low and the regulator properly determines the target
investment level.
Although our primary concern is the regulatory reform for congested urban railways in Japan,
our analysis is relevant for other countries for several reasons. First, in the UK, the owner of therailway network (Railtrack) is vertically separated from train operators. As Welsby and Nichols(1999) point out, Railtrack has no incentives to provide additional railway capacity under the current
regulatory regime. In fact, the Booz Allen Report (1999) shows that there has been little increase inrailway network capability. Our analysis gives hints on how to provide appropriate investment
incentives to the owners of railway networks, such as Railtrack. Second, although our analysis
focuses on the congestion problem, it can easily be extended to other dimensions of transport quality,
such as delays, comfort, and safety, which would be more important policy targets outside of Japan.
Third, in many countries, urban railways are operated by the public sector. Even in this case, how toprovide appropriate incentives to a railway operator is a significant issue and mechanisms similar to
the regulatory method proposed in this paper are promising alternatives.
The structure of the paper is as follows. In Section 2, we set up a simple spatial model. In
Section 3, we briefly summarize the merits and the demerits of various regulatory methods. In
Section 4, we conduct a numerical simulation and show the effects of the regulatory change on social
welfare. Section 5 concludes our analysis.

2 ModelOur model is a variant of the model, outlined in Kidokoro (1998), that is based on an open-city4and absentee-landlord model used in the urban economics literature4. Before explaining the details of
our model, let us briefly state the main characteristics of the model. In our model, a railway andhousing development are perfectly complementary, and a railway provides positive externality to its
surrounding area. The total social welfare is the sum of the railway firm’s profits and the residential
land rents along the railway line. If the railway firm owned all of its surrounding area, then marginal
cost pricing would hold. The reason is as follows. If the railway firm raises its fare and gains
monopoly profits, land rents in the residential area decrease. Given that a railway and housingdevelopment are perfectly complementary in our model, the upshot is that raising the fare is a meretransfer of profits from the residential land rents to the railway’s profits. Thus, a railway firm would
have no incentives to distort the fare above its marginal costs. In reality, however, a railway firmowns a tiny fraction of the residential area along its line, which means that the externality is only
partly internalized. Thus, in market equilibrium, railway capacity is underprovided and the fare ishigher than its marginal cost. This market failure is the reason for the regulation. Throughout ouranalysis, the regulation is partial in the sense that the regulator regulates only the railway sector. This
corresponds to the actual situation in Japan. The Ministry of Land, Infrastructure, and Transport can
impose regulations on its railway business, but it cannot impose them on its side businesses, whichare, for example, housing development and running department stores.
Now we describe our model in detail. Consider a residential city of fixed size H . All residents
in this city, N in number, commute to the central business district (CBD) by commuter railway. A
single railway firm connects the city with the CBD. For simplicity, there are no transportation costs
within the residential city. We assume that many competitive absentee-landlords own the residential
city as well as the railway firm.
The utility level outside the city is given by u . Residents and potential residents can freely
move out of and into the residential city. As a result, residents attain exactly u in equilibrium. The

4See, for example, Kanemoto (1980).

5

railway firm supplies transportation service by setting a nominal capacity, Q . This value Q isnominal in the sense that the railway firm can pack as many commuters as it wishes into railway cars,
providing that the congestion does not reduce the individual commuter’s overall utility below u . The
congestion rate is defined asrate, q ≡N
. To allow analytical simplicity, we use the inverse of the congestion
Q

Q, as the quality of transportation service. The production function for railway capacity isN

Q = F ( L, Z , e ) , where L is railroad right-of-way, Z is non-capital input, and e is cost-reducing∂F∂ 2F> 0 and Fii ≡ 2 < 0 , where i = L , Z , and e . Both theefforts. We assume that Fi ≡∂i∂icost-reducing efforts and the production function itself are unobservable to the regulator. This meansthat the regulator cannot calculate the value of e based on Q , L , and Z . Thus the regulator cannot
implement the regulation based on the level of e . We ignore capital inputs other than railroad
right-of-way for simplicity, because our focus is on railroad right-of-way, which is the bottleneck
input that hinders an enhancement of railway capacity. The price of Z is fixed and normalized at one.
A railway firm incurs disutility ϕ ( e ) from cost-reducing efforts, e , where we assume ϕ ′( e ) > 0 and

ϕ ′′( e ) > 0 .
Railway firms in Japan own much land along their railway lines. This is used as railroad
right-of-way or as residential land. The book value of the land they own is very low; for example, in
the Tokyo metropolitan area the book value is less than 10% of its market value using 1993 prices. To
replicate such a situation in our simulation, we assume that a railway firm owns αH of the residentialarea, the purchase price of which is zero ( α is any number between 0 and 1). The railway firm uses

αH in two ways: the railway firm uses α 1 H as its own railroad right-of-way, and α 2 H as
residential land that is rented to residents, where α 1 + α 2 = α . The railway firm’s revenue sources
are thus dual: railway fares and rental income from residential land. We assume that the regulatory
authority imposes regulations only on the firm’s railway sector, as is the case in Japan. For simplicity
6

we assume that the provision of residential land is the only side business.
We assume that all residents are homogeneous with a quasi-linear and additively separable
utility function, U ( z , h, q ) = z + u( h ) + v ( q ) , where h is residential lot size, z is the composite
consumer good including housing, and q is the quality of transportation service. This form of utility
function enables us to conduct a simulation based on the actual estimate of v ( q ) . We assume thatu( h ) and v ( q ) are strictly increasing and strictly concave: u′( h ) > 0 , u′′( h ) < 0 , v ′( q ) > 0 ,v ′′( q ) < 0 . As is well known, the income effects are zero under the quasi-linearity assumption5 andcross elasticities are zero under the separability assumption. As a result, this form of the utility
function yields a demand function for land that depends only on land rent, which simplifies ouranalysis. For simplicity, we assume that the composite consumer good is the same good as the
non-capital input. The price of the consumer good is therefore one.
Each resident solves his or her utility maximization problem subject to a budget constraint:z + Rh + t = w , where R , t , and w denote land rents, transportation fares, and the fixed income of aresident, respectively. Utility maximization under this budget constraint yields the bid rent function,

R ( y − t , q) , where y ( ≡ w − u ) denotes real income, and the transport demand function, N (t , q, L) ,the derivations of which are shown in Appendix 1.
Now we can express the profits of the railway firm as

π ( t , q, L, Z , e ) ≡ tN ( t , q, L ) + R( y - t , q )αH − Z − R( y - t , q ) L − ϕ ( e) .
In our closed-form model, social welfare is the sum of the railway firm’s profits and the residential
land rent that does not accrue to the railway firm. Social welfare is thenSW ( t , q, L, Z , e ) ≡ π ( t , q, L, Z , e ) + R( y - t , q )(1- α ) H .

5See, for example, Varian (1992).

7

3 The Merits and Demerits of Various Regulatory Methods
In this section, we consider the merits and demerits of various regulatory methods. For brevity,
we state the results only. A detailed theoretical analysis is in Kidokoro (2001).

3-1 ROR Regulation

First, we consider a railway firm’s behaviour under ROR regulation, the general formula forwhich is(allowed rate of return) ≥(revenue)-(non-capital cost)(value of capital stock=rate base) .
( = a firm's rate of return).

ROR regulation has the following properties:(1) The marginal benefit of the investment in the non-capital input, Z , equals its marginal cost.
(2) If the allowed rate of return, ρ , is higher (lower) than the true cost of capital, r , then themarginal rate of technical substitution between the non-capital input, Z , and railroad right-of-way, L ,is lower (higher) than their relative price. If ρ = r , then the marginal rate of technical substitution
equals their relative price.
(3) The marginal rate of technical substitution between the non-capital input, Z , and cost-reducing
efforts, e , exceeds their relative price.
The first point shows that ROR regulation provides no incentive to lower non-capital input. Thisis because the railway firm is allowed to raise its price when investing in non-capital input. The
second point shows the modified Averch-Johnson effect, originally pointed out by Kanemoto andKiyono (1993, 1995). As Averch and Johnson (1962) showed, capital input is over-invested
compared with non-capital input, if the allowed rate of return exceeds the true cost of capital.
However, if the allowed rate of return is set lower than the true cost of capital by the regulator who
implicitly takes the profits of side businesses into consideration, which would be the case in Japan,
capital input is under-invested compared with non-capital input. This under-investment in capital
input, which results in a lack of railway capacity, is one of the major causes of congestion on urban
8railways6. When the allowed rate of return equals the true cost of capital, the choice of capital input is
not distorted. The third point shows that ROR regulation distorts cost-reducing efforts. If a railway
firm reduces its costs by its effort, its profits increase. However, given this increase in profits, a firm’s
actual rate of return goes up and becomes higher than the allowed rate of return. In this case, the firmmust reduce its revenue to meet ROR regulation. This implies that the railway firm cannot capture
the increase in profits that cost-reduction yields, and has weaker incentives for cost-reduction. Thus,
under ROR regulation, the railway firm operates inefficiently.

3-2 PC Regulation

Second, we consider a railway firm’s behaviour under PC regulation, which can be written as

tcap ≥ twhere tcap is the fixed ceiling price.
PC regulation has the following properties:(1)

The marginal benefit of the investment in the non-capital input, Z , exceeds its marginal cost.

(2)

The marginal rate of technical substitution between the non-capital input, Z , and railroad

right-of-way, L , equals their relative price.
(3)

The marginal rate of technical substitution between the non-capital input, Z , and cost-reducing

efforts, e , equals their relative price.
The first point shows that PC regulation causes under-investment in non-capital input. Thisdistortion occurs for the following reason. As long as the transportation fare is suppressed by PC
regulation, the railway firm cannot raise the fare even though it invests in non-capital input. The
incentive to invest in non-capital input is then discouraged. The second and third points state themerits of PC regulation; under PC regulation, the railway firm employs the optimal input mix of
non-capital input, Z , railroad right-of-way, L , and cost-reducing efforts, e , because it regulates the6

Kidokoro (1998) focuses on another cause of the lack of railway capacity. He shows that book-based valuation of rate base results in9

ceiling price only.
The above results demonstrate that the regulatory shift to PC regulation causes another source ofdistortion in investments, which leads to congestion. Under PC regulation, non-capital inputs areunder-invested, which also leads to under-investment in railroad right-of-way and cost-reducing
efforts, provided that the marginal rates of technical substitution among all inputs are optimal. That is,
as long as the ceiling price is binding, PC regulation causes under-investment in all inputs and thus
causes congestion. The congestion problem never disappears as a result of the regulatory shift from
ROR to PC regulation.

3-3 Modified PC Regulation

The analyses in Section 3-2 show that the regulatory shift to PC regulation cannot alleviate
congestion. We consider here “PC-like” regulation that is consistent with the relief of the congestion.
First, let us focus on PC regulation with a cap contingent on transportation quality, which is theinverse of the congestion rate. PC regulation thus modified can be written as
tcap + t ( q) ≥ t ,where t ( q) is the variable part of the ceiling price that depends on transportation quality, q . We callthis quality-contingent PC regulation (QPC).

Quality-contingent PC regulation eliminates theunder-investment in non-capital input, without damaging the input mix. Under quality-contingent PC
regulation, a railway firm is allowed to set a higher price when alleviating congestion. Since therailway firm can obtain profits from its investments in railway capacity, it has no actual incentive todecrease the investment in railway capacity (which thereby increases congestion). Thus, the railway
firm has no incentive to under-invest in non-capital inputs. If t ′( q ) = v ′( q ) , i.e., the marginalincrease in the cap equals a commuter’s marginal benefit of transportation quality, then a commuter’s
cost accompanied by decreasing congestion equals his or her received benefit and all input choices

under-investment in railroad right-of-way when land prices rise.

10

become optimal.
In many cases, it would be difficult to measure a commuter’s marginal benefit of transportation
quality, v ′( q ) .

Then, we consider PC regulation in which the cap is contingent on capacity

investment, which would be easier to implement, because the data on investment are easier for the
regulatory authority to obtain. This kind of PC regulation can be written as
tcap + t ( L, Z ) ≥ t ,where t ( L, Z ) is the variable part of the ceiling price that depends on railroad right-of-way, L , andthe non-capital input, Z .

We call this method investment-contingent PC regulation (IPC).

Investment-contingent PC regulation can alleviate congestion, provided that the marginal investment
costs of non-capital and railroad right-of-way are fully recovered through the increase in the ceiling
price. In this case, the under-investment in non-capital input is removed, holding the marginal rate oftechnical substitution between the non-capital input and railroad right-of-way equal to their relative
price. However, it distorts the choice of cost-reducing efforts. This feature stems from the fact thatinvestment-contingent PC regulation lowers the investment costs of railroad right-of-way andnon-capital, but leaves the cost of cost-reducing efforts, e , unchanged. Suppose that the marginal
investment costs are fully recouped by the increase in the allowed price. In this case, if a railway firm
invests in non-capital and railroad right-of-way, the allowed price goes up and the investment costs
are virtually zero.

If it invests in cost-reducing efforts, however, the allowed price remains

unchanged. This asymmetry weakens cost-reducing incentives, and leads to the railway firm
operating less efficiently.

4 Numerical Simulations
In Section 3, we argued the merits and the demerits of ROR, PC, quality-contingent PC, andinvestment-contingent PC regulations. Now, we conduct a simulation to consider the effects of theregulatory change from the present ROR regulation on railways’ performances. We use data from the
Tokyu To-Yoko line in 1993, a typical railway line in the Tokyo metropolitan area, and apply the11transport-engineering studies by Shida et al. (1989) and Ieda (1995), which focus on the disutilities ofcongestion in Japanese urban railways. In many urban railways operating in the Tokyo metropolitanarea, railroad right-of-way is a bottleneck input, which cannot be substituted for other inputs. Thus,
the Leontief function is a natural candidate for the production function 7. In addition, we use the
Cobb-Douglas production function to ascertain the effects of the elasticity of substitution among
inputs. Table 1 summarizes the cases we consider in the simulation. The bases of the parameters are
justified in Appendix 2.
Table 1 is here.
First, we duplicate the present ROR regulation and compare the results with the actual data. The
results are presented in Table 2.
Table 2 is here.
In both the Leontief (Case 1-0) and Cobb-Douglas (Case 2-0) cases, our results duplicate theactual data satisfactorily. As Mizutani (1994) points out, Japanese urban railways are found to beseriously in deficit if we calculate depreciation based on replacement cost, i.e., economic opportunity
cost. It is, therefore, not surprising that the profits of railway businesses are negative in our results
when cost calculations are based on economic opportunity cost.

4-1 First BestWe obtain the first best optimum in both the Leontief (Case1-1) and Cobb-Douglas (Case 2-1)
cases as a policy target, given our parameters, assuming that a railway firm owns the entire city, i.e.,

α 2 = 1 − α1 = 0.983 . The results are presented in Table 3.
Table 3 is here.
These results show that social welfare increases by 24.1 - 26.4 (billion yen) a year in the Tokyu
To-Yoko line area if the first best is attained. In the first best situation, the congestion rate is about

7

All properties we obtained in Section 3 are valid even if the production function is the Leontief-type, because it is a limiting case of12

130%, which shows that congestion is noticeably relieved. We hereafter evaluate each regulatory
method based on the incremental social welfare that arises when the regulatory method is changed
from the present ROR regulation.

4-2 PC Regulation

We focus on the case where the authority changes the regulatory method from the present ROR
regulation to PC regulation. The results are shown in Table 4.
Table 4 is here.
First, we look at the results in the Leontief case. Case1-2-0 deals with the regulatory shift to PC
regulation in which the ceiling price is set at the same level as under the present ROR regulation. The
railway firm’s free choice of input mix under PC regulation enables the railway firm to operate
efficiently, and lowers operating costs. PC regulation, however, has a significant negative effect oncongestion through a substantial decrease in investment in railroad right-of-way. As a result, social
welfare would shrink compared to the present ROR regulation. This result supports Helm andThompson’s (1991) suggestion that under-investment in transport infrastructure is seriously harmful
to social welfare. This result holds true even if the ceiling price is set at the first best level (Case
1-2-1) or at lower than the present level, i.e., tcap = 0.8 × 8.13 (Case1-2-2), 0.6 × 8.13 (Case1-2-3).
The simulation results of Cases 1-2-2 and 1-2-3 show that a lower ceiling price leads to a higher
congestion rate and lower social welfare. This suggests that the disutility from the increase incongestion is so severe as to upset the gain from the decrease in the fare. Thus PC regulation would
not be suitable for crowded urban railways.
Even in the Cobb-Douglas production function case (Cases 2-2-0 - 2-2-3), the same results holdtrue, except that there exists an additional effect brought about by the substitution among inputs.
Under the present ROR regulation, in which the allowed rate of return is lower than the true cost of

the CES production function.

13

capital, the investment in railroad right-of-way is substantially suppressed. Since the elasticity of
substitution among inputs is high in the Cobb-Douglas production function case, the regulatory shift
to PC regulation corrects this distortion in the input mix, i.e., it increases the investment in railroad
right-of-way and decreases that in non-capital input. Thus, when the elasticity of substitution among
inputs is higher, railroad right-of-way is increased and operating costs are decreased, compared with
the Leontief production function case.

4-3 Modified PC Regulation

To remove the adverse effect on congestion from PC regulation, we consider modifications of
PC regulation. First, we focus on quality-contingent PC regulation, the form of which is

tcap + t ( q) = tcap − 0.722 q −4.52 ≥ t .

bg

Since v q = −0.722q −4.52 , as we show in Appendix 2, this form of quality-contingent PC regulation

always satisfies t ′( q ) = v ′( q ) and then all input choices are socially optimal. We consider two cases:
one is the case in which tcap is set at the break-even level of the railway business (Cases 1-3-1(Leontief) and 2-3-1 (Cobb-Douglas)), and the other is the case in which tcap is set at the first-best
price level (Cases 1-3-2 (Leontief) and 2-3-2 (Cobb-Douglas)). The results are in Table 5.
Table 5 is here.
This quality-contingent PC regulation alleviates congestion without damaging the cost-reducing
efforts. As a result, it can attain almost the same social welfare as the first-best optimum. This result
holds regardless of the elasticity of substitution among inputs.
Next, we analyse investment-contingent PC regulation, the form of which is
tcap + k1 ( L − LROR ) + k2 ( Z − Z ROR ) ≥ t ,where LROR and Z ROR are the values of railroad right-of-way, L , and non-capital input, Z ,respectively, under the present ROR regulation. The formula shows that investment in excess of thepresent ROR level is compensated by an increase in the allowed price. The parameters k1 and k2 are14

set so that the investment costs of L and Z are fully recovered through the increase in the ceiling
price, i.e., no distortions exist regarding the choice of L and Z . The level of tcap is set in the same
way as in the analyses of quality-contingent PC regulation, i.e., at the break-even level of the railway
business (Cases 1-4-1 (Leontief) and 2-4-1 (Cobb-Douglas)), and at the first-best price level (Cases
1-4-2 (Leontief) and 2-4-2 (Cobb-Douglas)). The results are presented in Table 6.
Table 6 is here.
We first look at the results in the case of the Leontief production function (Cases 1-4-1 and1-4-2). The results show that investment-contingent PC regulation can ease congestion in a fair way.
However, cost-reducing efforts are 0.674 – 0.703, which is about only one fifth of that under
quality-contingent PC regulation. These low effort levels result in higher operating costs and lower
incremental social welfare than under quality-contingent PC regulation.
In reality, the elasticity of substitution among inputs is probably low, and consequently, theabove results in the case of Leontief production function would hold. However, if the elasticity of
substitution were high, another result would hold. The results in the case of the Cobb-Douglas
production function (Cases 2-4-1 and 2-4-2) show that the high elasticity of substitution among inputs
mitigates the distortion brought about by low cost-reducing efforts under investment-contingent PC
regulation. The problem of investment-contingent PC regulation is no return for cost-reducing
efforts; if the railway firm invests in railroad right-of-way and non-capital input, it can raise the price,
but if it invests in cost-reducing efforts, it cannot raise the price. Thus, if the elasticity of substitution
is high, the railway firm substitutes other inputs for cost-reducing efforts and consequently, thedistortion brought by low cost-reducing efforts is lessened.

This result suggests thatinvestment-contingent PC regulation approaches quality-contingent PC regulation when the elasticity
of substitution is higher.
Finally, we consider a regulatory method in which the regulator contracts with the regulated firm
for its investments in advance, and costs of investment are added onto the ceiling price. This
regulation is equivalent to PC regulation with a direct designation of investment levels. Office of the15

Rail Regulator (2000) proposes such a regulatory method as an appropriate regulation for Railtrack.
We call this method price-cap regulation with cost pass-through (PCCP). Price-cap regulation withcost pass-through is a version of investment-contingent PC regulation in that the regulator uses
information on investments. Denoting the designated levels of railroad right-of-way and non-capitalby L∗ and Z ∗ , respectively, price-cap regulation with cost pass-through can be written as
tcap ≥ t , L = L∗ , and Z = Z ∗ .
We set L∗ and Z ∗ at the first-best levels of railroad right-of-way and non-capital. The level of tcap
is set at the break-even level of the railway business (Cases 1-5-1 (Leontief) and 2-5-1(Cobb-Douglas)), and at the first-best price level (Cases 1-5-2 (Leontief) and 2-5-2 (Cobb-Douglas)).
The results are presented in Table 7.
Table 7 is here.
The results in Table 7 suggest that price-cap regulation with cost pass-through approaches
investment-contingent PC regulation when the elasticity of substitution among inputs is large, while
it approaches quality-contingent PC regulation when the elasticity of substitution is small. In the
Leontief production function, in which the elasticity of substitution is zero, investments in railroad
right-of-way and non-capital input determine the level of cost-reducing efforts. Thus, if L∗ and Z ∗are set at their first-best levels in price-cap regulation with cost pass-through, cost-reducing efforts
are also at their first-best level. Since congestion is relieved without damaging cost-reducing efforts,
price-cap regulation with cost pass-through in this case has the same effects as quality-contingent PC
regulation. On the other hand, in the Cobb-Douglas production function, in which the elasticity of
substitution is one, the designation of railroad right-of-way and non-capital by price-cap regulation
with cost pass-through decreases cost-reducing efforts through the substitution of inputs. In this case,the results in price-cap regulation with cost pass-through approach those in investment-contingent PC
regulation.
In real urban railways in Japan, railroad right-of-way is a bottleneck input, and consequently, theLeontief production function would approximate reality. Thus, price-cap regulation with cost16

pass-through would closely resemble quality-contingent PC regulation. To implement price-cap
regulation with cost pass-through, the regulator has to know the desirable investment levels. If theregulator can obtain information on desirable investment levels more easily than a commuter’s
marginal benefit of transportation quality, price-cap regulation with cost pass-through is a desirable
candidate as a regulatory tool for relief congestion.

5 Conclusion
Our analysis stated above shows that (pure) PC regulation would not be suitable for Japanese
urban railways that are extremely congested because it has adverse effects on congestion throughdecrease in investments although it removes the distortion in the input mix. In modified PC
regulations, quality-contingent PC regulation is consistent with the relief of congestion and is free ofdistortions in its cost-reducing efforts. Although investment-contingent PC regulation also alleviates
congestion and is easier to implement, it distorts incentives for cost-reduction. When the elasticity of
substitution among inputs is small, which would be the case for Japanese urban railways, price-cap
regulation with cost pass-through yields almost the same result as quality-contingent PC regulation,and thus is a strong candidate as a regulation method for relieving congestion.
Before concluding our analysis, we consider dynamic incentives of each method of regulation,
which we have not focused on so far8. In the present ROR regulation for Japanese urban railways,
there exists no dynamic incentive for cost-reduction. The current procedure is as follows9. First, therailway firm files for a rise in fares when it wants to, and next, the regulator approves it after
inspecting its costs and claimed fare levels. Periodical review is not built in. That is, in the regulatory
system for Japanese urban railways, railway firms have the initiative in raising fares. Since railway
firms can almost freely file for a rise in fares, they have no dynamic incentive to reduce their costs. If

8For dynamic incentives of ROR and PC regulations, see Baumol and Klevorick (1970), Cabral and Riordan (1989), and Armstrong etal. (1995).
9

See Moriya (1996) for a detailed analysis on the process of the revision of fares in Japan.

17periodical review is introduced, coupled with the regulatory shift to PC regulation, dynamic
cost-reducing incentives emerge, because railway firms can obtain profits entirely by cost-reducing
efforts until the next review. This dynamic cost-reducing incentive caused by periodical review
works equally for PC regulation and its variants, such as quality-contingent PC regulation,
investment-contingent PC regulation, and PC regulation with cost pass-through. Taking a periodical
review system into account, our analysis would underestimate the cost-reducing effects of PC-type
regulation, and consequently, the merits of the regulatory shift to PC-type regulation would be muchlarger.

18

Case 1-0
(Status-quo: Case 1-1 Case 1-2-0 Case 1-2-1 Case 1-2-2 Case 1-2-3 Case 1-3-1 Case 1-3-2
ROR)

QPC withPC
IPC with thePC withthe Profits QPC withwithout
PC withPC withProfits ofFirst Bestthe Firstof Railway the First
Changing
Lower Fare Lower Fare
Railway BusinessBest FareBusiness Best Farethe FareBreak-even
Break-even

Regualtory
Shift to …

Production
Function

Case 1-4-1

Leontief

Leontief

Leontief

Leontief

Leontief

Leontief

Leontief

Leontief

Leontief

Case 1-4-2

IPC with theFirst Best Fare

Leontief

Case 1-5-1Case 1-5-2

PCCP with
the Profits of PCCP with
Railway the First BestBusiness
Fare
Break-even
Leontief

Leontief

tcap =8.82,
tcap =7.94,
ROR=228,000, L=228,000, tcap =7.91, tcap =11.3,
L
tcap =8.13 tcap =8.13
ρ =0.068 <ROR
ROR=1,290,000, Z=1,290,000, L * =351,000, L * =351,000,
α 1 +α 2 =1 tcap =8.13 tcap =11.3
tcap =10.6 tcap =13.8 Z
×0.8
×0.6
r =0.073-5
k 1 =2.45×10 , k 1 =2.46×10-5, Z * =545,000 Z * =545,000
ROR

FeatureCase 2-0(Status-quo: Case 2-1 Case 2-2-0 Case 2-2-1 Case 2-2-2 Case 2-2-3 Case 2-3-1 Case 2-3-2
ROR)

Regualtory
Shift to …

Production
Function

CobbDouglas

k 2 =5.49×10-6

k 2 =5.51×10-6

Case 2-4-1

Case 2-4-2

QPC withPC
IPC with thePC withthe Profits QPC withwithout
PC withPC withProfits ofFirst Bestthe Firstof Railway the First
Changing
Lower Fare Lower Fare
Railway BusinessBest FareBusiness Best Farethe FareBreak-even
Break-even

IPC with theFirst Best Fare

CobbDouglas

Cobb-Douglas

CobbDouglas

CobbDouglas

CobbDouglas

CobbDouglas

CobbDouglas

CobbDouglas

Cobb-Douglas

Case 2-5-2

PCCP with
the Profits of PCCP with
Railway the First BestBusiness
Fare
Break-even
CobbDouglas

CobbDouglastcap =11.4,
tcap =7.36,
ROR=237,000, L=237,000, tcap =6.54, tcap =11.3,
L
tcap =7.62 tcap =7.62
ρ =0.068 <ROR
ROR=1,170,000, Z=1,170,000, L * =423,000, L * =423,000,
α 1 +α 2 =1 tcap =7.62 tcap =11.3
tcap =9.51 tcap =13.7 Z
×0.8
×0.6
r =0.073
k 1 =2.44×10-5, k 1 =2.49×10-5, Z * =183,000 Z * =183,000
ROR

FeatureCase 2-5-1

k 2 =5.46×10-6

Table1: Cases in the simulation19

k 2 =5.56×10-6

Annual fare per commuter(= t )

Tokyu To-Yoko Line(peak time)(1993)

Case 1-0(Leontief)

Case 2-0(Cobb-Douglas)(10,000yen)

6.61

8.13

7.62

(%)

197

197

199

(m2)

227,000

228,000

237,000(10,000yen/m2)

56.6

56.5

56.5

(billion yen)

24.7

21.1

26.3

(billion yen)

13.8

12.9

11.7

176,000

177,000

177,000

/

0.169

0.152

Congestion rate (= 100/q )Railroad right of way (= L )Average land price (= V /r )Rate BaseOperating costs(= Z )Number of commuters (=N)
Effort (= e )Annual profits of railway
business(billion yen)

3.31

-0.111-0.136

Annual profits of sidebusinesses(billion yen)

3.63

3.56

3.56

(billion yen)

6.94

3.45

3.42

Annual total profit

Table 2: Actual data and the present ROR regulation

20

Case 1-1
(First Best, Leontief)

Case 2-1(First Best, Cobb-Douglas)(10,000yen)

11.3

11.3

(%)

132

131

(m2)

351,000

423,000(10,000yen/m2)

58.8

58.8

(billion yen)

5.50

1.83

182,000

181,000

3.24

1.70

Annual fare per commuter
Congestion rate
Railroad right of way
Average land priceOperating costs
Number of commuters
EffortAnnual profits of railway
business(billion yen)

6.06

7.92

Annual profits of sidebusinesses(billion yen)

472

472

(billion yen)

478

480

(billion yen)

24.1

26.4

Annual total profit
Annual incremental social
welfareTable 3: First best21

Case 1-2-2 Case 1-2-3
Case 1-2-0 Case 1-2-1(tcap =8.13 (tcap =8.13(tcap =8.13) (tcap =11.3)
×0.8)
×0.6)
Annual fare per commuter(10,000yen)

8.13

11.3

6.50

4.87

(%)

261

246

270

282

(m2)

149,000

164,000

139,000

127,000(10,000yen/m2)

48.5

50.4

46.9

44.8

(billion yen)

3.01

3.22

2.87

2.69

153,000

159,000

148,000

141,000

2.29

2.38

2.22

2.14

Congestion rate
Railroad right of way
Average land priceOperating costs
Number of commuters
EffortAnnual profits of railway
business(billion yen)

9.83

14.5

7.53

5.35

Annual profits of sidebusinesses(billion yen)

3.05

3.17

2.95

2.82

(billion yen)

12.9

17.7

10.5

8.17

(billion yen)

-54.7

-34.8

-69.5

-89.2

Annual total profit
Annual incremental social
welfareTable 4-1: Price-cap regulation: Leontief

22

Case 2-2-2 Case 2-2-3
Case 2-2-0 Case 2-2-1(tcap =7.62 (tcap =7.62(tcap =7.62) (tcap =11.3)
×0.8)
×0.6)
Annual fare per commuter(10,000yen)

7.62

11.3

6.10

4.57

(%)

262

245

272

283

(m2)

187,000

208,000

177,000

141,000(10,000yen/m2)

48.3

50.5

46.8

44.8

(billion yen)

0.661

0.773

0.600

0.531

152,000

158,000

147,000

141,000

0.879

0.978

0.823

0.755

Congestion rate
Railroad right of way
Average land priceOperating costs
Number of commuters
EffortAnnual profits of railway
business(billion yen)

10.8

16.2

8.70

6.66

Annual profits of sidebusinesses(billion yen)

3.04

3.18

2.94

2.82

(billion yen)

13.9

19.4

11.6

9.48

(billion yen)

-55.0

-31.9

-69.2

-87.5

Annual total profit
Annual incremental social
welfareTable 4-2: Price-cap regulation: Cobb-Douglas23

Case 1-3-1 Case 1-3-2 Case 2-3-1 Case 2-3-2(tcap =10.6) (tcap =13.8) (tcap =9.51) (tcap =13.7)
Annual fare per commuter(10,000yen)

8.06

11.3

7.06

11.3

(%)

132

132

131

131

(m2)

355,000

351,000

432,000

425,000(10,000yen/m2)

59.5

58.8

59.7

58.8

(billion yen)

5.55

5.50

1.83

1.81

184,000

182,000

183,000

181,000

3.26

3.24

1.70

1.68

Congestion rate
Railroad right of way
Average land priceOperating costs
Number of commuters
EffortAnnual profits of railway
business(billion yen)

0

6.06

0

7.87

Annual profits of sidebusinesses(billion yen)

3.75

3.70

3.76

3.70

(billion yen)

3.75

9.76

3.76

11.6

(billion yen)

24.1

24.1

26.3

26.4

Annual total profit
Annual incremental social
welfareTable 5: Quality-contingent price-cap regulation

24

Case 1-4-1 Case 1-4-2 Case 2-4-1 Case 2-4-2(tcap =7.94) (tcap =8.82) (tcap =7.36) (tcap =11.4)
Annual fare per commuter(10,000yen)

10.6

11.3

6.98

11.3

(%)

140

140

139

134

(m2)

331,000

330,000

430,000

448,000(10,000yen/m2)

58.7

58.6

59.6

58.7

(billion yen)

13.1

12.9

2.34

1.99

182,000

182,000

183,000

180,000

0.674

0.703

0.06950.118

Congestion rate
Railroad right of way
Average land priceOperating costs
Number of commuters
EffortAnnual profits of railway
business(billion yen)

0

1.58

0

7.32

Annual profits of sidebusinesses(billion yen)

3.70

3.67

3.75

3.70

(billion yen)

3.70

5.26

3.75

11.0

(billion yen)

17.9

18.2

25.0

25.3

Annual total profit
Annual incremental social
welfareTable 6: Investment-contingent price-cap regulation25

Case 1-5-1 Case 1-5-2 Case 2-5-1 Case 2-5-2(tcap =7.91) (tcap =11.3) (tcap =6.54) (tcap =11.3)
Annual fare per commuter(10,000yen)

7.91

11.3

6.54

11.3

(%)

133

132

145

141

(m2)

351,000

351,000

423,000

423,000(10,000yen/m2)

59.5

58.8

59.5

58.6

(billion yen)

5.50

5.50

1.83

1.83

184,000

182,000

183,000

180,000

3.24

3.24

0.07416

0.156

Congestion rate
Railroad right of way
Average land priceOperating costs
Number of commuters
EffortAnnual profits of railway
business(billion yen)

0

6.06

0

8.45

Annual profits of sidebusinesses(billion yen)

3.75

3.70

3.75

3.69

(billion yen)

3.75

9.76

3.75

12.14

(billion yen)

24.1

24.1

24.7

25.2

Annual total profit
Annual incremental social
welfareTable 7: Price-cap regulation with cost pass-through26

Appendix 1: Derivation of the Bid Rent Function and the Transport Demand
Function
Maximizing the utility function, U ( z , h, q ) = z + u( h ) + v ( q ) , under the budget constraint,z + Rh + t = w , yields u′( h ) = R . Inverting this function yields the demand function for land:h = h( R ) ≡ u′ −1 ( R ) .
Following the usual procedure in the urban economics literature, we derive the bid rent function,
which gives the maximum possible rent, providing utility level u . The bid rent function isR( y − t , q) = max{z ,h}{where y ( ≡ w − u ) is real income.

Rq =w−t − z: z + u(h ) + v( q) ≥ u } ,hThis function satisfies RI =1
1
> 0 , Rt = − < 0 , andhhv ′( q )> 0 , where I ≡ y − t .
hSubstituting the bid rent function into the demand function for land yields a lot size function

from which we eliminate the land rent, R ,h( I , q ) = h( R( I , q )) .
h v ′( q )hhThis function satisfies hI = R < 0 , ht = − R > 0 , and hq = R
<0.
h
h
h
We assume that the railway firm uses L as railroad right-of-way within the city area H . (Weignore railroad right-of-way used outside of the city area.) The residential area left for housing is thus
H − L . We assume that railroad right-of-way can be converted without cost into residential land andvice versa. Given u , the equilibrium number of residents is then defined as
N (t , q, L) =

H −L
.
ˆ
h( y − t, q)

To the railway firm, N ( t , q, L ) is synonymous with the equilibrium transport demand function given
u . The transport demand function satisfies N t =NhR
Nh v ′( q )1< 0 , Nq = − R 2> 0 , and N L = − < 0 .
2
h
h
h
27

Appendix 2: The Bases of Parameters
Rate of return: ρ = 0.068 , interest rate: r = 0.073

Since the allowed rate of return, ρ , as of 1993 is 0.068, we use that value. Taking into
consideration the argument in Kanemoto and Kiyono (1993, 1995) that an allowed rate of return
below the true cost of capital resulted in under-investment in railway capacity, we make the interest
rate, r , a little higher than the allowed rate of return. The interest rate is then 0.073.

Utility function: U = z + 256log h − 0.722q −4.52

We select this functional form because of the clear meaning of each parameter. First, thecoefficient of log h shows the housing expenses of a household. The “Publication of Land Price(Chika Koji)” reports that the average land price was 56.6 (10,000 yen/m2) in the Tokyu To-Yoko line
area in 1993. We multiply the figure by the interest rate, 0.073, to obtain the land rent, 3.96 (10,000
yen/m2). Since the area of floor space per dwelling in Tokyo was 62.1 m2 in 1993, which is based on
the “Housing Survey of Japan (Jyutaku Tokei Chosa),” annual housing expenses are then estimated to
be 256 (10,000 yen).
The third term, −0.722q −4.52 , expresses the disutility of congestion. Shida et al. (1989) estimate
the disutility of congestion in the Tokyu To-Yoko line to be −0.019 × ( commuting time) × q −4.52 . We
assume that all residents take local trains in the To-Yoko line, travelling 9.2 km in both the morningand evening peak periods. This assumption is based on the “Urban Transportation Annual Report(Toshi Kotsu Nempo),” in which the average passenger-km per pass user in the Tokyu To-Yoko line
in 1993 was 9.2 km. We assume that the morning peak time and the evening peak time each last threehours. In peak time, it takes about 21 minutes on average to commute 9.2 km using the To-Yoko line.
We suppose that the residents worked 236.4 days in 1993, based on the “Monthly Labour Survey Prefectural Survey - (Maitsuki Kinro Tokei Chosa Chiho Chosa)” in Tokyo. Annual commuting time

28

is

21
× 236.4 × 2 = 165.5 hours. The annual total of labour hours in Tokyo, which was 1,860 hours in
60

1993, is also calculated from the survey. According to the “Family Savings Survey (Chochiku Doko
Chosa Hokoku),” the yearly household income in the Keihin (Tokyo and Kanagawa) industrial area
was 854 (10,000 yen) in 1993. The hourly wage in Tokyo is then854
= 0.459 (10,000 yen) in 1993.
1,860

We assume that the opportunity cost of commuting is half the average wage, as Small (1992) suggests.
As a result, the monetary value of annual commuting time a year is 165.5 ×

0.459= 38.0 (10,000 yen)2

in 1993. The money-metric disutility of congestion is then −0.019 × 38.0 × q −4.52 = −0.722q −4.52 in
1993.

Production function: (Leontief) Q = 0.0592 min {6.65L, (1 + e) Z } ,(Cobb-Douglas) Q = 0.32 L0.91 {(1 + e) Z }0.09

Disutility of efforts: ϕ ( e ) = 20000e2

We assume that the efforts by a railway firm multiplicatively expand the non-capital input. We
also assume that the function of disutility of efforts is quadratic for the sake of simplicity. Although
the Tokyu Corporation has many lines besides the To-Yoko line, we have no data on railroad
right-of-way, operating costs, or profits per line. We allocate railroad right-of-way depending on line
length, and allocate operating costs and profits depending on boardings per line.
Our analysis focuses on railways’ performances in peak time. Since we have no data on
operating costs or profits in peak time, we assume that they account for half of the total values. In thesame way, we assume that user costs of railroad right-of-way (= RL ) in peak time account for half ofthe total value. In actual data on Tokyu To-Yoko line in 1993, railroad right-of-way is 454,000 m2 andland rent is 3.96 (10,000 yen). From these values, user costs of railroad right-of-way in peak time are29

3.96 × 454,000= 899,000 (10,000 yen).
2

Dividing this value by land rent, we obtain

454,000= 227,000 m2, which we regard as railroad right-of-way in peak time.
2

We fix theparameters of the production function and the disutility of efforts so that operating costs, railroad
right-of-way and the congestion rate under the present ROR regulation in our simulation will match
the peak-time values.

Real income: y ≡ w − u = −754

The Tokyu To-Yoko line carried 58,700 passengers per hour during peak time in 1993, based on
the “Urban Transportation Annual Report (Toshi Kotsu Nempo).” Since we assume that the morning
peak time and the evening peak time each lasts three hours and that all residents use the line on their
way to and from work, the number of commuters is estimated at 176,000 in 1993. We fix real income,y , to satisfy this number of commuters under the present ROR regulation.

Size of the residential city: H = 11,200,000

Since the size of the residential city, H , is (the number of commuters) × (the average floor
space) + (the area of railroad right-of-way), we estimate it to be 11,200,000 m2 in 1993.

Ratio of railroad right-of-way owned by a railway firm to the entire city: α1 = 0.017
Ratio of residential land owned by a railway firm to the entire city: α 2 = 0.0077

The size of the rate base depends on α 1 . In 1993, the book value of the rate base was 189(billion yen). Allocating it depending on line length and adjusting it for peak time, we obtain the bookvalue of rate base of the To-Yoko line, which is 24.7 (billion yen). We fix α 1 at 0.017, so that the sizeof rate base under the present ROR regulation will match that value.
The α 2 parameter is related to the profits of the side businesses that are complementary to the30railway business. Japanese private railways are well known for their diversified side businesses, suchas housing development, supermarkets, and department stores. Since there is no clear evidence toshow what side businesses are complementary to railway businesses, we use the profits of real estatebusinesses as a proxy for those of all side businesses. In the same way as we allocated the profits of
the railway business, we allocate the profits of the side business depending on boardings per line andassume that half of the profits arise in peak time. As a result, we set α 2 at 0.0077.

31

References
Armstrong, M., S. Cowan, and J. Vickers, (1994), “Regulatory Reform,” The MIT Press.
Armstrong, M., R. Rees, and J. Vickers, (1995), “Optimal Regulatory Lag under Price Cap
Regulation,” Revista Espanola de Economia, “Regulation”, 93-116.
Averch, H. and L. Johnson, (1962), “Behaviour of the Firm Under Regulatory Constraint,” American
Economic Review 52, 1052-1069.
Baumol, W. J. and A. K. Klevorick, (1970), “Input Choices and Rate-of-Return Regulation: An
Overview of the Discussion,” Bell Journal of Economics 1, 162-190.
Booz Allen Report (1999), “Railtrack’s Performance in the Control Period 1995-2001: Final Report,”
Booz Allen & Hamilton Limited, London.
Bös D. (1994), “Pricing and Price Regulation,” North-Holland.
Braeutigam, R. R. and J. C. Panzar, (1993), “Effects of the Change from Rate-of-Return to Price-Cap
Regulation,” American Economic Review 83 (2), 191-198.
Cabral, L. M. B. and M. H. Riordan (1989), “Incentives for Cost Reduction Under Price Cap
Regulation,” Journal of Regulatory Economics 1, 93-102.
Helm, D. and Jenkinson, T., (1998), “Competition in Regulated Industries,” Oxford University Press.
Helm, D. and Thompson, D., (1991), “Privatised Transport Infrastructure and Incentives to Invest,”
Journal Transport Economics and Policy 25, 231-246.
Ieda, H., (1995), “Commuter Railways,” Japan Railway & Transport Review, March, 1995.
Kanemoto, Y., (1980), “Theories of urban externalities,” North-Holland.
Kanemoto, Y. and K. Kiyono, (1993), “Investment, Pricing, and Regulation in Urban Transportationand Spatial Development,” in H. Kohno and P. Nijkamp (eds.) Potentials and Bottlenecks
of Spatial Economics Development, 30-44, Springer-Verlag.
Kanemoto, Y. and K. Kiyono, (1995), “Regulation of Commuter Railways and Spatial
Development,” Regional Science and Urban Economics 25, 377-394.
Kidokoro, Y., (1998), “Rate of Return Regulation and Rate Base Valuation,” Regional Science and32

Urban Economics 28, 629-654.
Kidokoro, Y., (2001), “Rate-of-Return and Price-Cap Regulations for Congested Urban Railways,”
mimeographed.
Liston, C., (1993), “Price-Cap versus Rate-of-Return Regulation,” Journal of Regulatory Economics
5, 25-48.
Mizutani, F., (1994), “Japanese Urban Railways,” Avebury.
Moriya, H., (1996), “Shitetsu Unchin no Kenkyu (Studies on the Fares of Private Railways),” Nihon
Keizai Hyoron Sha (in Japanese).
Office of the Rail Regulator (2000), “The Periodic Review of Railtrack’s Access Charges: Final
Conclusions,” Office of the Rail Regulator.
Shida, K., A. Furukawa, T. Akamatsu, and H. Ieda, (1989), “A Study of Transferability of Parametersof Railway Commuter’s Dis-utility Function,” Doboku Keikakugaku Kenkyu No12,519-525 (in Japanese).
Small, K. A., (1992), “Urban transportation economics,” Harwood Academic Publishers.
Train, K. E., (1991), “Optimal Regulation,” The MIT Press.
Varian, H. R., (1992), “Microeconomic Analysis,” Norton.
Welsby, J. and Nichols, A., (1999), “The Privatisation of Britain’s Railways: An Inside View,”
Journal of Transport Economics and Policy 33, 55-76.

33