The Value of Flexibility in the Italian Water Service Sector: A Real Option Analysis


The Value of Flexibility in the Italian Water Service Sector:

 

A Real Option Analysis

 

Chiara D’Alpaos and Michele Moretto

2004

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The Value of Flexibility in the

Italian Water Service Sector:

A Real Option Analysis

 

Chiara D’Alpaos and Michele Moretto

NOTA DI LAVORO 140.2004

NOVEMBER 2004

NRM – Natural Resources Management

Chiara D’Alpaos and Michele Moretto,

Department of Economics, University of Brescia

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The Value of Flexibility in the Italian Water Service Sector:

A Real Option Analysis

Summary

We analyze the optimal investment strategy of a monopolist which has subscribed a

concession contract to provide a public utility, i.e. water service. We present a strategic

model in which a monopolist chooses both the timing of the investment and the

capacity. We focus not only on the value of the immediate investment, but rather on the

value of the investment opportunity. We then extend the model to two interdependent

projects, where investing in the first project provides the opportunity to acquire the

benefits of the new investment by making a new outlay. We show that flexibility to

defer an investment may generate, ceteris paribus, additional profits which may induce

positive effects in terms of policy and consumers surplus.

Keywords:

 

Irreversible investment, Flexibility to defer, Capacity expansion choice

JEL Classification:

 

D81, G31, L95

This study was carried out under the 2004-5 two-year research project “Measurement

of the value of flexibility in integrated water services via simulation techniques and

numerical methods” financed by the University of Brescia. The authors want to thank

Gilberto Muraro, Cesare Dosi, Paola Valbonesi and the participants to the “9th Joint

Conference on Food, Agriculture and the Environment (Conegliano, Italy, August 28-

31)” for their helpful comments and suggestions. They also want to thank ATO

Bacchiglione and its director Vanni Carraro, Studio Bonollo and Guido Zanovello of

Studio Altieri for the information provided. Usual caveats apply

 

.

Address for correspondence

 

:

Michele Moretto

Department of Economics

University of Brescia

Via S. Faustino, 74b

25122 Brescia

Italy

Phone: +39 030 2988830

Fax: +39 030 2988837

E-mail: moretto@eco.unibs.it

1 Introduction

In recent years water sector reforms have concentrated on involving the pri-

vate sector in the operation and management of water utilities. In Italy

following the promulgation of Law 36/94, known as Legge Galli, an attempt

has been made to open up the water service sector to competition in order

to guarantee e¢ ciency in production and management of the resource (de-

clared to be scarce).

 

1

The increase in the opportunity cost of investments

devoted to the provision of public services has induced the Government to

promote the involvement of private .rms in the production of water ser-

vices. The aim is to capture new .nancial resources and reduce the ine¢ –

ciency which has characterized the public production of water services up to

now (Dosi and Muraro, 2003). Unlike what has happened in telecommuni-

cations where technological innovations eroding some monopolistic aspects

have introduced competition into the sector, the structural and technical

characteristics of the water sector constrain the legislator to promote e¢ –

ciency through .competition for the market.(Muraro and Rebba, 2003).

 

2 3

In other words the private .rms interested in provision of the water service

compete to be entitled to a contract which gives them the right to pro-

duce, operate and manage the water utilities for a certain period of time.

Under Law n

 



36/94 the legislator establishes a separation between water

resource planning and the operation of water utilities. The resource plan-

ning is assigned to the local water authority (ATO)

 

4

which, in turn, assigns

the operation to a private provider which will be selected via an auction

1

 

See Muraro (2003).

2

 

It is not reasonable to construct parallel pipelines to distribute drinking water and

collect wastewater. An exception is represented by common carriage competition in Great

Britain (Webb and Ehrhardt, 1998), where several water utilities compete for customers

using a single set of pipes. This solution might be adopted for providing the service to big

industrial users but it is di¢ cult to implement for domestic users because of the existence

of strong economies of scale and scope (Dosi and Muraro, 2003).

3

 

The water sector is characterized by some constraints related to the nature of the

resource itself and to technological and physical features of the infrastructures (i.e. water

.ows by gravity in the network). These put some limitations on network interconnections

and provision of the service on a large scale.

4

 

The Galli Law establishes new local water authorities (ATOs), whose borders are set

by the Italian Regions. As an example of their jurisdiction consider that in Veneto Region

there are 8 local water authorities. The ATO are now taking over control functions which

were previously state-run (decentralization). Generally speaking the term ATO refers to

both the water authority and the area where the authority operates. When the reform is

accomplished, only one private .rm will operate in each ATO.

2

mechanism. The ATO sets the price (tari¤)

 

5

cap for the water utilities

(including aqueduct systems, sewerage systems and treatment plants). Fur-

thermore, the ATO draws up the .Piano d.Ambito.(a 30 year plan) which

includes the timing and level of infrastructure investments, and ensures that

the provider ful.lls the contract requirements.

In this speci.c case, the .Piano d.Ambito. sets out the typology and

timing of the investments the provider has to make, ruling out any manage-

rial .exibility. Designers and planners choose among di¤erent alternative

technical solutions (e.g. ground water vs. river basin abstraction, branch-

ing pipe systems vs. interconnected pipe systems, etc.) and make capital

budgeting decisions according to the Net Present Value (

 

NPV

) rule.

Nevertheless, a wide range of feasible alternative technical solutions ex-

ists from which designers and planners can choose as regards operation and

management of the infrastructures making up the system. Technological

innovations lead to the construction of more complex systems characterized

by a high operational .exibility. It is quite common today to design .in-

tegrated. aqueduct systems (namely vertical integrated systems with sev-

eral interconnections between the network infrastructures) which can be

expanded by sequential or modularized investments (Zanovello, 1977). Such

systems can easily be modi.ed over time in order to meet the requirements

of facing and adapting to changes in the state variables (e.g. average day

demand, number of users, input costs, adoption of new technologies, etc.).

Moreover the interconnection and integration between supply sources en-

ables the system to handle crisis in the provision of the service caused, for

example, by pollution emergencies or peaks in day demand curves.

This .exibility, arising from technical aspects, has an economic value,

which is strongly related to the provider.s .ability.to decide whether and

when it is optimal to invest. That is, a .rm which has the possibility to

decide whether and when it is optimal to invest is holding something like a

.nancial (call) option. By deciding to exploit this .opportunity., the .rm

exercises its (real) option and consequently pays an opportunity cost which

becomes part of the investment costs.

In recent years, following early papers by Brennan and Schwartz (1985),

McDonald and Siegel (1985, 1986), Majd and Pindyck (1987) and Paddock

 

et

al.

 

(1988), there has been an increasing production of literature concerning

5

 

The Law n

36/94 de.nes a new pricing mechanism. The tari¤determined on the basis

of .Metodo Tari¤ario Normalizzato. (ex. Lege: .Decreto del Ministero dell.Ambiente e

del Territorio I

 



agosto 1996.) introduces a price cap regulation which guarantees at the

same time ex-post full recovery of the service costs and an .adequate. capital rate of

return (Moretto and Valbonesi, 2003).

3

applications of the real option approach to investment decisions in varied

industrial sectors.

 

6 Teisberg (1993) and Saphores et al.

(2004) apply the

real option approach to regulated .rms in the energy sector, while Teisberg

(1994), Trigeorgis (1996) and Childs and Triantis (1999) are among the few

interested in the analysis of multi-stage investments in R&D. Nevertheless,

these contributions do not refer to interdependent projects concerned with

di¤erent capacity levels to be realized by regulated .rms.

 

7

This paper is a .rst attempt to apply real option results to capital bud-

geting in the water service as a regulated sector. We present a simple model

to value the .exibility of aqueduct systems. The aqueduct systems are char-

acterized by a high degree of technological and operational .exibility and,

among the water utility infrastructures, are the ones which require higher

irreversible sunk costs.

 

8

In particular our aim is to show that managerial

and technical .exibility might turn out to be economically relevant in the

case the .Piano d.Ambito.gives to the provider the option to strategically

decide when to invest.

 

9

We also correct the option value to take into account

that the length of concession contracts is generally shorter than plants.use-

ful life. Finally we investigate the e¤ects of .exibility on consumer surplus

and tari¤ reduction.

The paper is organized as follows. The next section presents a simpli.ed

model to value the .exibility to defer investments. Section 3 deals with

investment decisions in capacity expansion (i.e. a water abstraction plant)

and investigates the pro.tability of devising interdependent projects to face

uncertain future demand. Section 4 illustrates the concluding remarks.

6

 

See also Dixit and Pindyck (1994) and Trigeorgis (1996) for a systematic treatment

of the real option approach.

7

 

Interdependent projects di¤er from multi-stage projects because in order to generate

a stream of pro.ts they do not require an earlier investment-installment cost to acquire

a subsequent option to continue operating the project until the next installment becomes

due (see Trigeorgis, 1996, Chapter 4).

8

 

61% of the total turnover of the water service sector industry is represented by pro.ts

coming from the production and distribution of water (in 1999 it was equal to 3

 

.

85 billion

Euros). The 2002 report to the Italian Parliament on the state of the art of the water

sector and accomplishment of the reform laid down by the Galli Law points out the need

for huge investments (15.78 Euros per year per capita) in the aqueduct system in order

to improve the e¢ ciency of existing infrastructures, search for new catchment areas and

springs and construct new plants.

9

 

However the supply of the service is obligatory.

4

2 The model

The aim of this section is to show how .exibility can be valued with reference

to plants for the production of drinking water. To emphasize the role of .ex-

ibility embedded in water production plants, we introduce some simplifying

assumptions in order to obtain a close form solution for the investment.s

value.

 

10

Conventional capital budgeting techniques and in particular the

 

NPV

rule fail to capture the strategic impact of projects and the additional value

deriving from the opportunity to delay an investment decision. The

 

NPV

rule gives a measure of an investment.s pro.tability according to a now-or-

never proposition, that is if the investor does not make the investment now,

he will lose the opportunity forever. A project whose

 

NPV

is negative or

equal to zero, though, might have a positive

 

NPV

in the future. Similarly

a project whose

 

NPV is positive might have an even greater NPV

in the

future. Therefore the

 

NPV

rule does not take into consideration the oppor-

tunity cost to delay the investment. By deciding to make an expenditure for

an irreversible investment the investor gives up the possibility of waiting for

new information that might a¤ect the desirability or the timing of the in-

vestment itself should market conditions change adversely. This opportunity

cost might be relevant in the water service sector where only a private .rm

has the right to make the investment. The ability to defer an irreversible

investment expenditure might profoundly a¤ect the decision to invest.

The real option approach, .rst proposed by Myers (1977), Kester (1984)

and McDonald and Siegel (1986)

 

11

, establishes a theoretical framework which

permits introduction into the valuation model of the .exibility to postpone

investments, whose value is not captured by

 

NPV

. In other words the real

option approach provides the decision-maker with a tool to address the issues

of irreversibility, uncertainty and timing, drawing the valuation procedures

from the body of knowledge developed for .nancial options during the past

decades.

The investor with an opportunity to invest is holding something like a

.nancial call option where the investment project is the underlying asset, the

10

 

We believe that the adoption of more sophisticated models which can be solved only

by means of numerical methods would not give any additional value to the analysis and

would not make any improvment in the quality of the results, owing to the quality of

information the ATOs and the providers have at their disposal while awaiting the reform

(Law 36/94) to be accomplished soon.

11

 

To learn about the theory of the real option approach and for an overview of recent

developments, see Dixit and Pindyck (1994) and Trigeorgis (1996).

5

investment costs represent the strike price and the expiry of the concession

contract is the upper bound of the call option.s maturity time.

2.1 An investment in capacity expansion

We use a simpli.ed version of the model proposed by McDonald and Siegel

(1986). In particular:

1. The investment project

 

A is a large

scale project which generates, once

installed, an instantaneous pro.t .ow equal to:

 

 

A

t

 

= t(XA

)

where

 

XA is the project.s dimension (expressed in m3

).

2. The project lifetime is

 

Tu, i.e. at Tu

the salvage value is zero.

3.

 

t

evolves over time according to a geometric Brownian motion with

instantaneous expected return

 

  0 and instantaneous volatility

 >

0

d

 

A

t

 

= 

A

t

 

dt + 

A

t

 

dzt with

A

0

 

=A

(1)

where

 

dzt

is the increment of a standard Brownian process with mean

zero and variance

 

dt (i.e. E(dzt) = 0 and E(dz

2

t

 

) = dt

). From (1) we

get

 

E(

A

t

 

j A) = Aet, therefore 

represents the expected cash

.ow growth rate.

4. Investment in project

 

A entails a sunk capital cost IA

:

5. The investment exercise time is

 



.

Since the investment project we are analyzing (aqueduct system) is not

traded in limited supply for investment purposes by many investors it is not

considered a traded asset. Therefore its expected rate of return

 



falls below

the equilibrium total expected rate of return, say

 

^

, required in the market

by investors from an equivalent-risk traded .nancial security. The result-

ing rate of return shortfall

 

  ^ 􀀀  > 0

(i.e. the di¤erence between the

equilibrium expected return on a similar traded .nancial security and the

actual project drift,

 



, on the non-traded asset) represents the opportunity

cost (in annuity terms) to invest at time zero, i.e. it is analogous to a con-

stant .dividend.yield.

 

12

Furthermore, since the equivalent traded .nancial

12

 

In complete markets we can hypotesize the existence of a traded asset that maintains

the same price as

 

A while it pays a constant dividend yield , with b 􀀀  = 

(see

McDonald and Siegel, 1984; Cox, Ingersoll and Ross, 1985).

6

security must satisfy the asset price equilibrium relationship

 

^ = r +

RP;

where

 

r is the risk-free rate and RP

is the risk premium, we can write the

expected risk-adjusted rate of return of the project as

 

􀀀RP = r􀀀

where

r

 

􀀀 

will be referred to hereafter as the cost of carry.

This is the basis of the risk-neutral valuation approach proposed by Cox

and Ross (1976) and Harrison and Kreps (1979), in which the actual growth

rate

 

 is replaced with a risk-neutral equivalent drift r 􀀀 

. That is, the

adjustment is analogous to discounting certainty-equivalent cash .ows at

the risk-free rate, so that we can rewrite (1) in the following form:

d

 

A

t

 

= (r 􀀀 )

A

t

 

dt + 

A

t

 

dz

t A

0

 

= A

(2)

Hence, given the current value of

 

A

t

 

;

the market value of the project can

be evaluated as the expected present value of discounted cash .ows using

equivalent risk-neutral probabilities and the risk-free interest rate (Cox and

Ross, 1976; Harrison and Kreps, 1979):

V

 

A(A) = E

t

Z

 

T

u

0

e

 

􀀀

rtA

t

 

dt





 

 

A(XA

)



(1

 

􀀀 e􀀀Tu)

(3)

where

 

E

denotes the expectation operator under the risk neutral probability

measure. Since

 

V A is a multiple of A

it is also driven by a geometric

Brownian motion with the same parameters

 

r 􀀀  and 

, i.e.:

dV

 

A

t

 

= (r 􀀀 )V

A

t

 

dt + V

A

t

 

dzt; V

A

0

 

= V A

(4)

This means that the analysis could be replicated using the present value

as the state variable. Hereinafter we may take

 

V

A

t

 

as the primitive exogenous

state variable for the regulatory process. The above assumptions make the

project.s value of the opportunity to invest (Extended Net Present Value)

analogous to a European call option on a constant dividend-paying asset

(the plant), i.e.:

F

 

A(V

A

t

 

; t) = E

t

n

e

 

􀀀r(􀀀t)

max

􀀀

V

 

A



 

􀀀 IA;

0

o

where

 

 is the expiration date and V

A



 

is the project value at time 

.

Imposing a non-arbitrage condition, the extended net present value

 

FA(Vt; t

)

can be obtained as the solution of the following second order di¤erential

equation (Black and Scholes, 1973; Merton, 1973):

1

2



 

2(V A)2F

A

V V

 

+ (r 􀀀 )(V A)F

A

V

 

􀀀 rFA 􀀀 F

A

t

 

= 0

(5)

7

subject to the terminal condition:

F

 

A(V

A



 

;  ) = max[(V

A



 

􀀀 IA)+; 0]

(6)

and to the boundary conditions:

F

 

A(0; t) = 0 and

lim

V

 

A

!1

F

 

A(V

A

t

 

; t)=V

A

t

 

= 1

(7)

The solution of (5) is given by the well-known formula derived by Black

and Scholes (1973):

F

 

A(V

A

t

 

; t) = e􀀀(􀀀t)(d1)V

A

t

 

􀀀 e􀀀r(􀀀t)(d2)IA

(8)

where:

d

 

1(V

A

t

 

) =

ln(

 

V

A

t

 

=IA) + (r 􀀀  + 2=2)( 􀀀 t

)



 

p 􀀀

t

; d

 

2(V

A

t

 

) = d1(V

A

t

 

) 􀀀 p 􀀀

t

and

 

()

is the cumulative standard normal distribution function.

So far we have implicitly assumed that the .rm can exploit the pro.ts

generated by the project for its entire lifetime, once it is realized. However,

concession contracts have a limited length, around 30 years, generally shorter

than the project lifetime. Therefore it is necessary to add, at least, two more

assumptions to take into account the limited contract life. In particular:

7. The concession contract lasts for

 

Tc years, so that   Tc < Tu

.

8. The salvage value is given by:

S

 

= IAe􀀀(Tc􀀀)

=

Then, by assumption 7 in order to calculate the asset value we must

consider the operating life (i.e. economic life) of the project instead of its

useful life (i.e. technical life). Consequently whenever the provider decides

to defer the investment, he reduces the time over which he can gain pro.ts

by running the plant. Assumption 8, simply assume a salvage value as a %

of the replacement cost. This % depreciates at rate

 



over the remaining

years to the end of the concession. Therefore if the .rm invests at

 

 = 0

the

salvage value is obviously equal to zero but if the .rm invests close to the

end of the concession,

 

 = Tc

, the salvage value coincides the replacement

cost.

The actual value of the project turns out to be less than (3) and equals

to:

8

V

 

A(A) =

E

Z

 

Tc􀀀



0

e

 

􀀀

rtA

t

 

dt + e􀀀r(Tc􀀀)

S



(9)



 

 

A(XA

)



(1

 

􀀀 e􀀀(Tc􀀀)) + IAe􀀀(r+





 

)(Tc􀀀

)

Since (9) tends to zero when

 

 tends to Tc

, condition (6) has to be

substituted by:

 

13

lim



 

!T

c

F

 

A(V

A



 

; 

) = lim



 

!T

c

max[(

 

V

A



 

􀀀 ^IA)+; 0] = 0

(10)

where

 

^IA = IA(1 􀀀 e􀀀(r+





 

)(Tc􀀀))

:

2.2 Interdependent projects

Interdependent projects can be considered as a portfolio of growth options.

We extend the above benchmark case of a single indivisible project assum-

ing that the provider has the possibility of choosing between two alternative

projects

 

A and B

of di¤erent scales. With respect to the assumptions pre-

viously introduced we add:

1. Project

 

A

is equal to the one described in the previous section, while

project

 

B

is larger in scale and generates, once installed, an instanta-

neous pro.t .ow equal to

 

B

t

 

(XB) with XB > XA

.

2. The cash .ow is simpli.ed into a linear function as:

 

 

B

t

 

(XB) = tX

B A

t

 

(XA) = tX

A

where

 

t is the instantaneous pro.t per cubic meter (m3)

equal for

both the projects and described by the following geometric Brownian

motion:

d

 

t = (r 􀀀 )tdt + tdzt 0 =



where

 

r 􀀀   0

is the instantaneous risk-adjusted expected rate of

return and

 

 > 0

is the instantaneous volatility.

13

 

Brennan and Schwartz (1985) introduce a similar boundary condition. Their analysis,

though, do not take into account the reduction in the asset value, because in their case

the contract lease does not provide for any limitations on the number of years for which

the resource can be exploited.

9

3. Investment in projects

 

A and B entails sunk capital costs IA and I

B

respectively, with

 

IB > IB

:

4. The investor can operate only one project at a time and the investment

is constrained to be sequential, with investment

 

A occurring before B

.

5. Finally, for the sake of simplicity, we assume that for both projects

the expiration time is in.nite.

The last two assumptions require some further comments. Firstly, since

the investment is sequential, the private .rm can always invest in the smaller

scale project and subsequently invest in the bigger scale one, incorporating

the former into the latter by paying an additional cost. Moreover, an in.nite

expiration time appears to be non-restrictive referring to aqueduct systems

whose lifetime is very long. This implies that we can assume

 

Tc = Tu = T

.

Hence, the market value of the project

 

B

can be evaluated as the ex-

pected present value of its discounted cash .ows.

V

 

B() =

E

Z

 

T

0

e

 

􀀀

rtB

t

 

dt



=

X

 

B



(1

 

􀀀 e􀀀T )

(11)

Now, contrary to what has been done in the previous section, while de-

termining the market value of project

 

A

we must take into account that once

A

 

is installed, it is optimal to switch to project B

whenever the instanta-

neous pro.t

 

 becomes large enough. In particular, we can express V A(

)

as

V

 

A(

) = max



 



E

(Z

 





0

e

 

􀀀

rtA

t

 

ds + e􀀀r

􀀀

V

 

B() 􀀀 IB



)

(12)

where

 

  is the optimal switching time from A to B

.

It is easy to check that the solution to problem (12) is to switch from

 

A

to

 

B as soon as  exceeds the critical threshold AB (see Appendix A):

14



 

AB

=

 

 

 

􀀀

1



I

 

B

(

 

XB 􀀀 XA)(1 􀀀 e􀀀T

)

(13)

14

 

The switching rule (13) can be rewritten as follows:

V

 

B(AB) 􀀀 A(AB

) =

 

 

 

􀀀

1

I

 

B

where

 

A(AB) = X

A



 

(1􀀀e􀀀T ) represents the value of project A

when there is no option

to switch.

10

where

 




1

2

 

􀀀 r􀀀





 

2

+

q􀀀

 

1

2

 

􀀀 r􀀀





 

2



 

2

+

 

2

r



 

2 > 1

. Moreover, the project.s market

value turns out to be:

V

 

A(

) =

8><

>:

X

 

A



 

(1 􀀀 e􀀀T

) +







 



AB



 


I

 

B

 

 

􀀀1 if   

AB

X

 

B



 

(1 􀀀 e􀀀T ) 􀀀 IB if  > 

AB

(14)

Some comments on (14) are necessary. It is worth pointing out that for



 

2 (0;1) V A()  V B(). The two functions coincide if and only if  = 0

,

while for

 

 2 [AB;1) V A() 􀀀 V B() = 􀀀IB

. In other words the current

value of project

 

B.s expected cash .ows is always greater than A

.s, also

taking into consideration the value of the opportunity to switch, eventually,

from

 

A to B at cost IB

:

In order to determine under which conditions it is optimal to proceed

with sequential investments, let.s consider the opportunity to invest in project

A

 

, which entails the option to switch subsequently to project B

. For each

t

 

 1;

this is equivalent to solving the following problem:

F

 

A(t

) = max



 



E

 

t

n

e

 

􀀀r(􀀀t)

􀀀

V

 

A() 􀀀 IA

o

(15)

By (14) the expression for

 

V A() is nonlinear in 

, therefore there is

a discontinuity in the threshold

 

A

beyond which it is optimal to invest in

project

 

A

. This threshold is given by (see Appendix B):



 

A

=

8><

>:

 

 

 

􀀀1 I

A

X

 

A(1􀀀e􀀀T)

)

if

 

X

B

X

 

A 􀀀 1 < I

B

I

 

A

 

 

 

􀀀1 IB+I

A

X

 

B(1􀀀e􀀀T)

)

if

 

X

B

X

 

A 􀀀 1  I

B

I

 

A

(16)

The .rst expression shows that

 

A < AB

therefore it is optimal to invest

.rst in project

 

A and then to wait until the instantaneous pro.t exceeds 

AB

to invest in project

 

B incorporating A. By analyzing (16), investment in

A

is myopic: it occurs as if the option of ultimately switching to

 

B

were not

present, that is

 

A(A) = AXA(1􀀀e􀀀T)

)



 

=


 

 

􀀀1IA

:

On the contrary when

 

A  AB

it is optimal to invest in both the

projects simultaneously and, therefore, proceed directly with the implemen-

tation of

 

B

.

11

3 The value of .exibility to invest in an aqueduct

system

3.1 The case of a water abstraction plant

With reference to the previous section let.s suppose, as an example, that the

.Piano d.Ambito.plans an investment capacity expansion due to an increase

in water demand (i.e. number of users) or an increase in water supply (i.e.

average day demand per capita). In order to meet the requirements the

provider could choose between two di¤erent alternative projects: a) buy the

volume

 

X

necessary to provide the water service to the new users via another

private .rm (alternative

 

O

), it being allowed by the law; b) construct a new

water abstraction plant (well .eld)

 

15 designed on the basis of volume

X

(alternative

 

A

).

Since the price of trading water among ATO is established by the regu-

lator according to solidarity and fairness criteria, we can form the hypoth-

esis that the expected Net Present Value of this alternative is zero, that is

NPV

 

O = 0

:

Alternative

 

A

consists of: a) well .eld (3 wells); b) pumping station; c)

treatment plant; d) storage system (capacity equal to 10

 

,000 m3

); e) treat-

ment plant; f) electrical system for the equipment installed. The treatment

plant includes a .ltration process on Granular Activated Carbon (GAC) and

the storage system includes disinfection and chlorination procedures.

 

16

In

fact groundwater extraction guarantees the provision of good quality water,

which does not need highly speci.c treatment to meet the regulations for

drinking water standards.

The project.s useful life

 

Tu

is equal to 50 years and the system guarantees

a water provision of about 300 l/s (equivalent to 9,460,800

 

m3=year

) but it is

subject to water losses in the network

 

i ranging from 20 to 30%:

We assume

that the plant.s construction and installment costs are not time-dependent

and amount to about 3,500,000 Euros.

We evaluate the .exibility of waiting to invest in project

 

A

, by treating

the opportunity to defer the investment as a European Call Option. As it

has already been pointed out, the discounted expected cash .ows represent

15

 

A well .eld is the sinking of several moderately sized boreholes, spaced apart in some

pattern, their yields being collected together. This system is used in order to develop a

good yield from an area where a single well could not be expected to guarantee a large

enough yield.

16

 

For a more detailed overview of technical solutions, technologies and design criteria

see Hammer (1993) and Twort

 

et al

. (2000).

12

the current value of the asset and the investment cost

 

IA

represents the

exercise price of the option. Assuming pro.t is a linear function of the

dimension

 

XA, pro.t at time t

can be written as:

 

 

A

t

 

= R

A

t

 

(1 􀀀 i)XA 􀀀 C

A

t

 

XA

(17)

where

 

R

A

t

 

are the revenues per cubic meter at time t; C

A

t

 

are operating

costs (including maintenance costs) per cubic meter0 at time

 

t; XA

is the

plant dimension;

 

i

are the volume losses in the network. We also make the

following simplifying assumptions:

1. Revenues are deterministic and we draw their value using projections

of water price and demand estimated by the ATO on the basis of the

.Metodo Tari¤ario Normalizzato.over the entire concession period.

2. The operating costs

 

17

(sum of production, maintenance and running

costs)

 

18

are a random variable following a geometric Brownian motion

with a growth rate

 

r 􀀀  and volatility 

:

dC

 

t = (r 􀀀 )Ctdt + Ctdz

t

3. The risk-free discount rate

 

r

is known, deterministic and not time-

dependent.

4. Revenues can be discounted at the constant risk-free rate

 

r

, the number

of users (consumers) being certain over time (Brennan and Schwartz,

1985).

5. The discounted value of the project.s future cash .ows is a good ap-

proximation of the present value of the asset.

6. The project.s salvage value at the end of its lifetime is zero.

17

 

Variable costs, in particular the expenditure for chemicals used in water treatment

(chlorination) and energy (pumping plant), are the most relevant ones as regards an

abstraction plant consisting of wells. In this case the expenditure for chemicals is non-

signi.cant when compared with energy costs and can therefore be ignored. The price of

energy is likely to follow an exogenous di¤usive and geometric stochastic process.

18

 

Fixed costs for running the plant are generally estimated as a percentage of operating

costs (20-30%) and vary signi.cantly depending on the management and the organization

of the .rm running the service.

13

Recalling (3), the value of the project is:

 

19

V

 

A =

E

Z

 

T

u

0

(

 

e􀀀rt(1 􀀀 i)R

A

t

 

􀀀 e􀀀rtC

A

t

 

)XA

dt



(18)

=



(1

 

􀀀 i)R

A

r

􀀀

1

 

􀀀 erT

u



􀀀

C

 

A



(1

 

􀀀 e􀀀Tu

)



X

 

A

Estimates of costs, revenues and other variables were derived from discus-

sions with water industry experts. Table 1 shows estimates of the project.s

technical and economic parameters (e.g. dimension, project life, investment

cost, etc.).

X

 

A (m3=s) 0:

300

I

 

A (Euro) 3; 500;

000

T

 

u (years

) 50

C

 

A(Euro=m3) 0:

13

R

 

A (Euro=m3) 0:

30

i

20%

30%



1%

2%

3%

4%

r

 



5%



 



30%

40%

Table 1: Summary information for alternative

 

A.



 

Designers and industry experts interviewed agree on esti-

mating the average operational costs of this type of plant at

19

 

Water service experts use an expected rate of return (WACC) ^

equal to 7%. This

value is the capital rate of return provided for by Law 36/94 and subsequent implemen-

tation decrees. In this case (18) should be written as:

V

 

A =

E

Z

 

T

0

(

 

e􀀀rt(1 􀀀 i)R

A

t

 

􀀀 e􀀀^tC

A

t

 

)XA

dt



where the cost growth rate is

 



. Obviously the two expressions for the project.s value are

equivalent.

14

around 0.13 Euro/

 

m3

. The average has been calculated over a

distribution.



 

Revenues per cubic meter have been determined by a sta-

tistical analysis performed over a distribution whose parameters

have been estimated on the basis of the average tari¤ paid by

users for the provision of drinking water.



 

The risk-free rate is assumed to be equal to the rate of

return of stated-owned bonds.



 

Variance has been estimated considering analogous in-

vestment projects realized in the past, whose operating costs

were known throughout the project life. A scenario analysis was

conducted to prove the consistency of these estimates which can

be considered representative for this kind of plant.

If the private .rm can decide at time

 

 = 3; 5; 10

years to proceed or not

with the investment, the Extended Net Present Value of the projects can

be determined using (8). Tables 2 and 3 display the results. The value of

the .exibility to defer the investment (that is the di¤erence between the Ex-

tended Net Present Value,

 

FA, and the Net Present Value, NPV A

) decreases

for increasing values of

 



and increasing exercise time of the option.

Let.s consider .rst the case where

 

 = 30%, i = 20% and  = 2%

.

Project

 

A whose NPV A is negative (NPV A = 􀀀700

thousands of Euros)

might have a positive

 

NPV A in the future (e.g. FA

=1.100 thousands of

Euros when

 

 = 10)

. Therefore, the optimal strategy is to delay the invest-

ment. On the contrary, everything else being equal and assuming

 

i = 30%

,

project

 

A has such a highly negative NPV A

that is never pro.table either

to invest or wait to invest.

Let.s now consider the case where

 

 = 30% and  = 3%

. Assuming

i

 

= 20%, FA is less than the corresponding NPV A

, therefore there is no

advantage in deferring the investment and the provider should start con-

struction immediately. On the contrary, assuming

 

i = 30%, FA

is greater

than the corresponding

 

NPV A

and consequently it is expedient to delay the

investment.

In all other cases (i.e.

 

 = 4% and i = 20􀀀30%

) the option value is not

high enough to suggest waiting to invest, therefore the optimal investment

strategy is to start construction immediately.

Finally, comparing Table 2 and Table 3 it is easily demonstrated that

for increasing values of

 



the Extended Net Present Value of the project

15

increases and consequently the option value of deferring the investment in-

creases.



NPV

 

F

A

0 3 5 10

i=20% i=30% i=20% i=30% i=20% i=30% i=20% i=30%

2% -700 -5,900 400 – 600 – 900 –



 

3% 6,300 1,100 6,000 1,500 5,800 1,600 5,300 1,800

4% 11,600 6,400 10,400 5,800 9,600 5,400 8,100 4,700

Table 2:

 

NPV A and FA for  = 30%

and di¤erent expiration times of the

option.



NPV

 

A F

A

0 3 5 10

i=20% i=30% i=20% i=30% i=20% i=30% i=20% i=30%

2% -700 -5,900 600 – 800 – 1,100 –



 

3% 6,300 1,100 6,100 1,700 5,900 1,900 5,500 2,000

4% 11,600 6,400 10,500 5,900 9,700 5,600 8,300 5,000

Table 3:

 

NPV A and FA for  = 40%

and di¤erent expiration times of the

option.

As already mentioned in section 2.1, the literature on the estimate of

Extended Net Present Value in regulated industrial sectors does not consider

that in general the length of concession is shorter than the project lifetime.

This results in an over-estimation of the current value of the asset and a

consequent distortion in the option value.

For example, in the above case we assumed that the private .rm has

the possibility of making pro.ts throughout the useful life of the project,

but usually concession contracts last for about 30 years. Therefore in de-

termining the asset.s present value we have to take into consideration the

plant.s operating life (economic life,

 

Tc = 30

years) instead of its useful life

(technical life,

 

Tu = 50

years). Consequently, by exercising the option to

defer the investment, the private .rm reduces the period of time over which

it can make pro.ts from running the plant and then it reduces the expected

16

revenue cash .ow. In the light of these considerations the present value of

the project should be given by (9) including a salvage value.

Nevertheless, since the Galli Law does not make an explicit reference to

the procedures to be used to guarantee the .rm an amount of money corre-

sponding to the asset.s salvage value and the formula adopted to determine

the water tari¤ (.Metodo Tari¤ario Normalizzato.) already includes some

form of the depreciation allowances, we maintain here the assumption of

salvage value equal to zero.

 

20

The present value of the project is now:

V

 

A =

E

Z

 

Tc􀀀



0

e

 

􀀀rt[(1 􀀀 i)R

A

t

 

􀀀 C

A

t

 

]XA

dt



=

=



(1

 

􀀀 i)R

A

r



1

 

􀀀 er(Tc􀀀

)



􀀀

C

 

A



(1

 

􀀀 e􀀀(Tc􀀀)

)



X

 

A

while the formula for evaluating its Extended Net Present Value (8) does

not vary.

Analyzing the results obtained assuming

 

 = 30% and 40% and i

= 20%

(illustrated in Figure 1 and 2 respectively) we .nd that, everything else

being equal, the value of .exibility increases as

 



increases but, as it has

been previously shown, it decreases when

 



increases. It is also worth noting

that when

 

 is equal to zero the Extended Net Present Value, FA

, and the

conventional Net Present Value,

 

NPV A, coincide. In particular when 

is

equal to 30 years (i.e. when the concession contract ceases) the Extended

Net Present Value of the asset is zero. The option value to delay represents

the opportunity cost of waiting to invest (Figure 3 and 4).

Let.s consider, as an example, the scenario characterized by

 

 = 30%

,



 

= 2%. In this case the Net Present Value of the project is NPV A

=

4

 

; 000; 000 Euros. The extended NPV has a maximum for  = 9

and it is

about

 

FA = 4; 970; 000

Euros (Figure 1). Therefore the .rm.s opportunity

cost to invest by waiting 9 years is approximately

 

970; 000

Euros or, put

di¤erently, the Net Present Value of investing today is

 

NPV A 􀀀 FA

=

4

 

; 000; 000 􀀀 4; 970; 000 = 􀀀970; 000; i.e. the NPV

of investing today which

includes the opportunity cost is negative.

20

 

This assumption seems to be non-restrictive at least for one more reason. The capital

depreciation functions are generally of hyperbolic type (Mauer and Ott, 1995) with an

estimated rate of depreciation

 



substantially high. Nevertheless, introducing a salvage

value in the valuation model would not substantially modify the results obtained as regards

the NPV and the Extended Net Present Value. Under the hypothesis of the salvage value

being equal to zero we obtain a cautious estimate of the .exibility value.

17

Figure 1:

F

 

A assuming  = 30% and i = 20%

(in thousands of Euros).

Figure 2:

F

 

A assuming  = 40% and i = 20%

(in thousands of Euros).

Figure 3:

Opportunity cost to defer the investment assuming

 

 = 30% and i

= 20%

(in thousands of Euros).

Figure 4:

Opportunity cost to defer the investment assuming

 

 = 40% and i

= 20%

(in thousands of Euros).

The analysis of .exibility could have interesting e¤ects in terms of pol-

icy and consumer surplus (i.e. tari¤ reduction). The possibility of delaying

investment decisions may induce the .rm to bid more aggressively in order

to win the concession race (Muraro, 2002). For example assuming water

losses in the network equal to 20% and

 

 = 30%

, the value of .exibility has

a maximum for

 

 = 15 and  = 9 years for  = 1% and  = 2%

respec-

tively (Figure 1). For these reference cases the potential tari¤ reductions

are displayed in Table 5.

 

21



 

pmax FA 

R



 

= 1%

15 years 28%



 

= 2%

9 years 4%

Table 5: Maximum tari¤ reduction assuming

 

 = 30%

:

3.2 The case of interdependent projects

Most of the investments occurring in the water service sector and in partic-

ular investments in aqueduct systems o¤er a wide range of choice between

alternative technical solutions. In fact the planners can combine the single

plants and elements making up the system in several di¤erent ways in or-

der to guarantee greater operational .exibility (D.Alpaos, 2003). It is quite

common today to design complex aqueduct systems which can be expanded

by sequential or modularized investments. Such systems can easily be mod-

i.ed over time in order to meet the requirements of facing and adapting to

changes in the state variables (e.g. future demand, number of users, input

cost increments, adoption of new technologies, etc.). This .exibility arising

from technical aspects has an economic value.

21

 

Assuming  = 1% the NPV A

is negative, therefore we determined the tari¤ reduction

assuming a Net Present Value equal to zero as the benchmark.

18

As an example let.s consider a .rm.s need to invest in capacity expansion

in order to face uncertain future growth in demand and suppose it has the

opportunity of proceeding with sequential investments, whose characteristics

are analogous to those of alternative

 

A

described in section 4.1. Assuming

that the .rm can switch from a smaller scale project to a bigger scale one

by paying an additional cost. The costs related to di¤erent discharge values

are displayed in Table 4.

Discharge (

 

l/s

)

300 900 1,200 1,500 2,100

I

 

(Euro 10 3

) 3,500 7,100 9,400 12,200 15,000

Table 4: Plant costs depending on di¤erent discharge values.

By using (13) and (16) we can obtain the thresholds on the basis of

which we evaluate the pro.tability of proceeding or not with a sequential

investment, with the investment in

 

A occurring before B

. The results of the

simulations we performed for di¤erent discharge values assuming

 

i

= 20%

and

 

 = 30%

are shown in Table 5 and 6.

The results clearly show the importance of scale economies in investment

decisions related to capacity expansion.

 

22

When the dimension of project

A

 

is equal to 300 l=s and the dimension of B is equal to 900 l=s

, assuming



 

= 2% and  = 4%

, the optimal investment strategy consists in investing

.rst in

 

A and then switching to B as soon as the instantaneous pro.t



becomes greater than the threshold

 

AB

. Everything else being equal, when

the dimension of project

 

B is equal to or greater than 1200 l=s

it is always

optimal to invest in the bigger scale project, i.e. the condition

 

AB

>



 

A is satis.ed. Assuming that project A

is designed for a discharge value

greater than or equal to 900 l/s the optimal strategy consists in undertaking

sequential investments.

Moreover, since the condition

 

0 = 0:8  0:3 􀀀 0:13 < A

always obtains,

whenever it is optimal to invest in sequential investments, it is more prof-

itable to start constructing

 

A (there is no time lag on A

) and wait to invest

in project

 

B

(Table 5 and 6).

22

 

Generally, in fact, the section of the supply network and distribution network are sized

on the basis of the average day demand thanks to the possibility of constructing reservoirs.

Construction costs, furthermore, depend on the length of the pipes according to a virtually

linear law. In this regard, see the study carried out by Venturi

 

et al.

(1970) on estimate

of the construction cost functions in parametric form for various types of plant.

19

Analogous considerations can be made taking into account the results

shown in Tables 7 and 8 assuming

 

 = 40%, i = 20% and value losses of



equal to 2% and 4% respectively. Everything else being equal, the trigger



 

AB increases when 

increases.

Discharge (

 

l/s

)

900 1200 1500 2100

300

 

AB = 0:

111



 

A = 0:

108



 

AB = 0:

097



 

A = 0:

100



 

AB = 0:

094



 

A = 0:

097



 

AB = 0:

077



 

A = 0:

082

900

 

AB = 0:

290



 

A = 0:

072



 

AB = 0:

188



 

A = 0:

072



 

AB = 0:

116



 

A = 0:

072

1200

 

AB = 0:

377



 

A = 0:

073



 

AB = 0:

155



 

A = 0:

073

1500

 

AB = 0:

272



 

A = 0:

075

Table 5: Optimal trigger assuming

 

 = 2% and  = 30%

:

Discharge (

 

l/s

)

900 1200 1500 2100

300

 

AB = 0:

079



 

A = 0:

078



 

AB = 0:

070



 

A = 0:

072



 

AB = 0:

068



 

A = 0:

070



 

AB = 0:

056



 

A = 0:

059

900

 

AB = 0:

210



 

A = 0:

053



 

AB = 0:

136



 

A = 0:

053



 

AB = 0:

084



 

A = 0:

053

1200

 

AB = 0:

377



 

A = 0:

052



 

AB = 0:

155



 

A = 0:

052

1500

 

AB = 0:

167



 

A = 0:

054

Table 6: Optimal trigger assuming

 

 = 4% and  = 30%

:

Discharge (

 

l/s

)

900 1200 1500 2100

300

 

AB = 0:

149



 

A = 0:

147



 

AB = 0:

131



 

A = 0:

135



 

AB = 0:

128



 

A = 0:

131



 

AB = 0:

105



 

A = 0:

111

900

 

AB = 0:

394



 

A = 0:

099



 

AB = 0:

255



 

A = 0:

099



 

AB = 0:

157



 

A = 0:

099

1200

 

AB = 0:

517



 

A = 0:

098



 

AB = 0:

209



 

A = 0:

098

1500

 

AB = 0:

314



 

A = 0:

102

20

Table 7: Optimal trigger assuming

 

 = 2% and  = 40%

.

Discharge (

 

l/s

)

900 1200 1500 2100

300

 

AB = 0:

106



 

A = 0:

104



 

AB = 0:

093



 

A = 0:

096



 

AB = 0:

091



 

A = 0:

093



 

AB = 0:

074



 

A = 0:

079

900

 

AB = 0:

280



 

A = 0:

070



 

AB = 0:

181



 

A = 0:

070



 

AB = 0:

112



 

A = 0:

070

1200

 

AB = 0:

363



 

A = 0:

070



 

AB = 0:

149



 

A = 0:

070

1500

 

AB = 0:

233



 

A = 0:

073

Table 8: Optimal trigger assuming

 

 = 4% and  = 40%

.

4 Final remarks

In this paper we propose an option approach to evaluate the strategic value

of .exibility to defer investment decisions in the Italian water service sector.

We show how some technical .exibility might turn into managerial .exibility

which has a substantial economic value.

The value of .exibility might be bene.cial for the consumers. In fact if

the provider can choose whether and when it is optimal to invest, he might

bid more aggressively o¤ering a lower tari¤.

21

A Appendix

Within the range of

 



where it is non-optimal to invest in the larger scale

project, the value of alternative

 

A

can be obtained as the solution of the

following second order di¤erential equation (Dixit and Pindyck, 1994):

1

2



 

2 2V

A



 

+ (r 􀀀 )V

A



 

􀀀 rV A + A = 0

(19)

subject to the following boundary conditions (

 

value matching condition

and

smooth pasting condition

 

):

V

 

A(AB) = V B(AB) 􀀀 IB and V

A



 

(AB) = V

B



 

(AB);

(20)

The optimal timing to switch from

 

A to B

turns out to be:



 

AB = min(t  0 j V A(AB) = V B(AB) 􀀀 IB):

(21)

The general solution of equation (19) can be written as:

V

 

A() = K1
+ K2 + vA()

(22a)

where

 

1 <
< r=
(r 􀀀 ); < 0

are respectively the positive and negative

root of the characteristic equation

 

(x) =

1

2

 

2x(x 􀀀 1) + (r 􀀀 )x 􀀀 r = 0

;

and

 

K1; K2

are two constants to be determined. The .rst two terms in

(22a) represent the solution of the homogeneous equation, while the third

term represents a particular solution. As particular solution we take the

expected discounted value

 

vA() of the bene.ts that project A

generates in

the absence of the option to switch to project

 

B

(Harrison 1985, page 44):

v

 

A() =

E

Z

 

T

0

e

 

􀀀

rtA

t

 

dt



=

 

 

A



(1

 

􀀀 e􀀀T )

(23)

To make sure

 

vA() is positive we assume  > 0:

Finally, in order to

have a .nite value for

 

V A() when  gets very small, we set K2 = 0

(i.e.

lim

 

!0 V A() = 0

). Therefore the general solution can be re-written in the

following form:

V

 

A() = K1

+

 

 

A



(1

 

􀀀 e􀀀T )

(24)

Finally, since

 

K1

represents the correction we have to impose on the

value of project

 

A by the option to switch to B

in the future, the constant

K

 

1 must necessarily be positive. We obtain K1 and AB

by imposing the

boundary conditions (20).

22

B Appendix

Unlike what happens when dealing with the European Call Option, to eval-

uate a perpetual option we use a di¤erential equation which is not time-

dependent.

Considering project

 

A

, the solution of (15) can be obtained by solving

the following second order di¤erential equation (McDonald and Siegel 1986;

Dixit and Pindyck, 1994):

1

2



 

2 2F

A



 

+ (r 􀀀 )F

A



 

􀀀 rFA = 0

(25)

imposing the usual boundary conditions:

F

 

A(A) = V A(A) 􀀀 IA and F

A



 

(A) = V

A



 

(A);

(26)

Nevertheless, when analyzing (14) (or 24) we notice that the expression

referring to the value of project

 

A

reveals two di¤erent forms depending on

 < 

 

AB or vice versa  > AB

. Therefore we have two di¤erent boundary

conditions (26) depending on

 

A > AB or A < AB

. In particular we get:



 

A

=

8><

>:

 

 

 

􀀀1 I

A

X

 

A(1􀀀e􀀀T)

)

if

 

X

B

X

 

A 􀀀 1 < I

B

I

 

A

 

 

 

􀀀1 IB+I

A

X

 

B(1􀀀e􀀀T)

)

if

 

X

B

X

 

A 􀀀 1  I

B

I

 

A

(27)

23

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24

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26

-1000

1000

3000

5000

7000

9000

11000

0 10 20 30

 

t

F

A

A

d=1%

d=2%

d=3%

d=4%

Figure 1

-1000

1000

3000

5000

7000

9000

11000

0 10 20 30

 

t

F

A

d=1%

d=2%

d=3%

d=4%

Figure 2

27

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

12000

0 3 6 9 12 15 18 21 24 27 30

t

NPV

A-FA

A-FA

d=1%

d=2%

d=3%

d=4%

Figure 3

-6000

-4000

-2000

0

2000

4000

6000

8000

10000

12000

0 3 6 9 12 15 18 21 24 27 30

 

t

NPV

A-FA

A-FA

d=1%

d=2%

d=3%

d=4%

Figure 4

28

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CLIM 83.2003

 

Giuseppe DI VITA

: Is the Discount Rate Relevant in Explaining the Environmental Kuznets Curve?

CLIM 84.2003

 

Reyer GERLAGH and Wietze LISE

: Induced Technological Change Under Carbon Taxes

NRM 85.2003

 

Rinaldo BRAU, Alessandro LANZA and Francesco PIGLIARU

: How Fast are the Tourism Countries Growing?

The cross-country evidence

KNOW 86.2003

 

Elena BELLINI, Gianmarco I.P. OTTAVIANO and Dino PINELLI:

The ICT Revolution: opportunities and risks

for the Mezzogiorno

SIEV 87.2003

 

Lucas BRETSCGHER and Sjak SMULDERS:

Sustainability and Substitution of Exhaustible Natural Resources.

How resource prices affect long-term R&D investments

CLIM 88.2003

 

Johan EYCKMANS and Michael FINUS:

New Roads to International Environmental Agreements: The Case of

Global Warming

CLIM 89.2003

 

Marzio GALEOTTI:

Economic Development and Environmental Protection

CLIM 90.2003

 

Marzio GALEOTTI

: Environment and Economic Growth: Is Technical Change the Key to Decoupling?

CLIM 91.2003

 

Marzio GALEOTTI and Barbara BUCHNER

: Climate Policy and Economic Growth in Developing Countries

IEM 92.2003

 

A. MARKANDYA, A. GOLUB and E. STRUKOVA

: The Influence of Climate Change Considerations on Energy

Policy: The Case of Russia

ETA 93.2003

 

Andrea BELTRATTI

: Socially Responsible Investment in General Equilibrium

CTN 94.2003

 

Parkash CHANDER: The γ

-Core and Coalition Formation

IEM 95.2003

 

Matteo MANERA and Angelo MARZULLO

: Modelling the Load Curve of Aggregate Electricity Consumption

Using Principal Components

IEM 96.2003

 

Alessandro LANZA, Matteo MANERA, Margherita GRASSO and Massimo GIOVANNINI:

Long-run Models of

Oil Stock Prices

CTN 97.2003

 

Steven J. BRAMS, Michael A. JONES, and D. Marc KILGOUR:

Forming Stable Coalitions: The Process

Matters

KNOW 98.2003

 

John CROWLEY, Marie-Cecile NAVES

(lxiii): Anti-Racist Policies in France. From Ideological and Historical

Schemes to Socio-Political Realities

KNOW 99.2003

 

Richard THOMPSON FORD (lxiii)

: Cultural Rights and Civic Virtue

KNOW 100.2003

 

Alaknanda PATEL

(lxiii): Cultural Diversity and Conflict in Multicultural Cities

KNOW 101.2003

 

David MAY

(lxiii): The Struggle of Becoming Established in a Deprived Inner-City Neighbourhood

KNOW 102.2003

 

Sébastien ARCAND, Danielle JUTEAU, Sirma BILGE, and Francine LEMIRE

(lxiii) : Municipal Reform on the

Island of Montreal: Tensions Between Two Majority Groups in a Multicultural City

CLIM 103.2003

 

Barbara BUCHNER and Carlo CARRARO:

China and the Evolution of the Present Climate Regime

CLIM 104.2003

 

Barbara BUCHNER and Carlo CARRARO

: Emissions Trading Regimes and Incentives to Participate in

International Climate Agreements

CLIM 105.2003

 

Anil MARKANDYA and Dirk T.G. RÜBBELKE:

Ancillary Benefits of Climate Policy

NRM 106.2003

 

Anne Sophie CRÉPIN (lxiv):

Management Challenges for Multiple-Species Boreal Forests

NRM 107.2003

 

Anne Sophie CRÉPIN (lxiv):

Threshold Effects in Coral Reef Fisheries

SIEV 108.2003

 

Sara ANIYAR (

lxiv): Estimating the Value of Oil Capital in a Small Open Economy: The Venezuela’s Example

SIEV 109.2003

 

Kenneth ARROW, Partha DASGUPTA and Karl-Göran MÄLER(lxiv):

Evaluating Projects and Assessing

Sustainable Development in Imperfect Economies

NRM 110.2003

 

Anastasios XEPAPADEAS and Catarina ROSETA-PALMA(lxiv):

Instabilities and Robust Control in Fisheries

NRM 111.2003

 

Charles PERRINGS and Brian WALKER

(lxiv): Conservation and Optimal Use of Rangelands

ETA 112.2003

 

Jack GOODY

(lxiv): Globalisation, Population and Ecology

CTN 113.2003

 

Carlo CARRARO, Carmen MARCHIORI and Sonia OREFFICE

: Endogenous Minimum Participation in

International Environmental Treaties

CTN 114.2003

 

Guillaume HAERINGER and Myrna WOODERS

: Decentralized Job Matching

CTN 115.2003

 

Hideo KONISHI and M. Utku UNVER

: Credible Group Stability in Multi-Partner Matching Problems

CTN 116.2003

 

Somdeb LAHIRI

: Stable Matchings for the Room-Mates Problem

CTN 117.2003

 

Somdeb LAHIRI

: Stable Matchings for a Generalized Marriage Problem

CTN 118.2003

 

Marita LAUKKANEN

: Transboundary Fisheries Management under Implementation Uncertainty

CTN 119.2003

 

Edward CARTWRIGHT and Myrna WOODERS

: Social Conformity and Bounded Rationality in Arbitrary

Games with Incomplete Information: Some First Results

CTN 120.2003

 

Gianluigi VERNASCA

: Dynamic Price Competition with Price Adjustment Costs and Product Differentiation

CTN 121.2003

 

Myrna WOODERS, Edward CARTWRIGHT and Reinhard SELTEN

: Social Conformity in Games with Many

Players

CTN 122.2003

 

Edward CARTWRIGHT and Myrna WOODERS

: On Equilibrium in Pure Strategies in Games with Many Players

CTN 123.2003

 

Edward CARTWRIGHT and Myrna WOODERS

: Conformity and Bounded Rationality in Games with Many

Players

1000 Carlo CARRARO, Alessandro LANZA and Valeria PAPPONETTI: One Thousand Working Papers

NOTE DI LAVORO PUBLISHED IN 2004

IEM 1.2004

 

Anil MARKANDYA, Suzette PEDROSO and Alexander GOLUB

: Empirical Analysis of National Income and

So2 Emissions in Selected European Countries

ETA 2.2004

 

Masahisa FUJITA and Shlomo WEBER:

Strategic Immigration Policies and Welfare in Heterogeneous Countries

PRA 3.2004

 

Adolfo DI CARLUCCIO, Giovanni FERRI, Cecilia FRALE and Ottavio RICCHI:

Do Privatizations Boost

Household Shareholding? Evidence from Italy

ETA 4.2004

 

Victor GINSBURGH and Shlomo WEBER:

Languages Disenfranchisement in the European Union

ETA 5.2004

 

Romano PIRAS:

Growth, Congestion of Public Goods, and Second-Best Optimal Policy

CCMP 6.2004

 

Herman R.J. VOLLEBERGH:

Lessons from the Polder: Is Dutch CO2-Taxation Optimal

PRA 7.2004

 

Sandro BRUSCO, Giuseppe LOPOMO and S. VISWANATHAN

(lxv): Merger Mechanisms

PRA 8.2004

 

Wolfgang AUSSENEGG, Pegaret PICHLER and Alex STOMPER

(lxv): IPO Pricing with Bookbuilding, and a

When-Issued Market

PRA 9.2004

 

Pegaret PICHLER and Alex STOMPER

(lxv): Primary Market Design: Direct Mechanisms and Markets

PRA 10.2004

 

Florian ENGLMAIER, Pablo GUILLEN, Loreto LLORENTE, Sander ONDERSTAL and Rupert SAUSGRUBER

(lxv): The Chopstick Auction: A Study of the Exposure Problem in Multi-Unit Auctions

PRA 11.2004

 

Bjarne BRENDSTRUP and Harry J. PAARSCH

(lxv): Nonparametric Identification and Estimation of Multi-

Unit, Sequential, Oral, Ascending-Price Auctions With Asymmetric Bidders

PRA 12.2004

 

Ohad KADAN

(lxv): Equilibrium in the Two Player, k-Double Auction with Affiliated Private Values

PRA 13.2004

 

Maarten C.W. JANSSEN

(lxv): Auctions as Coordination Devices

PRA 14.2004

 

Gadi FIBICH, Arieh GAVIOUS and Aner SELA

(lxv): All-Pay Auctions with Weakly Risk-Averse Buyers

PRA 15.2004

 

Orly SADE, Charles SCHNITZLEIN and Jaime F. ZENDER

(lxv): Competition and Cooperation in Divisible

Good Auctions: An Experimental Examination

PRA 16.2004

 

Marta STRYSZOWSKA

(lxv): Late and Multiple Bidding in Competing Second Price Internet Auctions

CCMP 17.2004

 

Slim Ben YOUSSEF:

R&D in Cleaner Technology and International Trade

NRM 18.2004

 

Angelo ANTOCI, Simone BORGHESI and Paolo RUSSU

(lxvi): Biodiversity and Economic Growth:

Stabilization Versus Preservation of the Ecological Dynamics

SIEV 19.2004

 

Anna ALBERINI, Paolo ROSATO, Alberto LONGO and Valentina ZANATTA:

Information and Willingness to

Pay in a Contingent Valuation Study: The Value of S. Erasmo in the Lagoon of Venice

NRM 20.2004

 

Guido CANDELA and Roberto CELLINI

(lxvii): Investment in Tourism Market: A Dynamic Model of

Differentiated Oligopoly

NRM 21.2004

 

Jacqueline M. HAMILTON

(lxvii): Climate and the Destination Choice of German Tourists

NRM 22.2004

 

Javier Rey-MAQUIEIRA PALMER, Javier LOZANO IBÁÑEZ and Carlos Mario GÓMEZ GÓMEZ

(lxvii):

Land, Environmental Externalities and Tourism Development

NRM 23.2004

 

Pius ODUNGA and Henk FOLMER

(lxvii): Profiling Tourists for Balanced Utilization of Tourism-Based

Resources in Kenya

NRM 24.2004

 

Jean-Jacques NOWAK, Mondher SAHLI and Pasquale M. SGRO

(lxvii):Tourism, Trade and Domestic Welfare

NRM 25.2004

 

Riaz SHAREEF

(lxvii): Country Risk Ratings of Small Island Tourism Economies

NRM 26.2004

 

Juan Luis EUGENIO-MARTÍN, Noelia MARTÍN MORALES and Riccardo SCARPA

(lxvii): Tourism and

Economic Growth in Latin American Countries: A Panel Data Approach

NRM 27.2004

 

Raúl Hernández MARTÍN

(lxvii): Impact of Tourism Consumption on GDP. The Role of Imports

CSRM 28.2004

 

Nicoletta FERRO:

Cross-Country Ethical Dilemmas in Business: A Descriptive Framework

NRM 29.2004

 

Marian WEBER

(lxvi): Assessing the Effectiveness of Tradable Landuse Rights for Biodiversity Conservation:

an Application to Canada’s Boreal Mixedwood Forest

NRM 30.2004

 

Trond BJORNDAL, Phoebe KOUNDOURI and Sean PASCOE

(lxvi): Output Substitution in Multi-Species

Trawl Fisheries: Implications for Quota Setting

CCMP 31.2004

 

Marzio GALEOTTI, Alessandra GORIA, Paolo MOMBRINI and Evi SPANTIDAKI:

Weather Impacts on

Natural, Social and Economic Systems (WISE) Part I: Sectoral Analysis of Climate Impacts in Italy

CCMP 32.2004

 

Marzio GALEOTTI, Alessandra GORIA ,Paolo MOMBRINI and Evi SPANTIDAKI:

Weather Impacts on

Natural, Social and Economic Systems (WISE) Part II: Individual Perception of Climate Extremes in Italy

CTN 33.2004

 

Wilson PEREZ:

Divide and Conquer: Noisy Communication in Networks, Power, and Wealth Distribution

KTHC 34.2004

 

Gianmarco I.P. OTTAVIANO and Giovanni PERI

(lxviii): The Economic Value of Cultural Diversity: Evidence

from US Cities

KTHC 35.2004

 

Linda CHAIB

(lxviii): Immigration and Local Urban Participatory Democracy: A Boston-Paris Comparison

KTHC 36.2004

 

Franca ECKERT COEN and Claudio ROSSI

(lxviii): Foreigners, Immigrants, Host Cities: The Policies of

Multi-Ethnicity in Rome. Reading Governance in a Local Context

KTHC 37.2004

 

Kristine CRANE

(lxviii): Governing Migration: Immigrant Groups’ Strategies in Three Italian Cities – Rome,

Naples and Bari

KTHC 38.2004

 

Kiflemariam HAMDE

(lxviii): Mind in Africa, Body in Europe: The Struggle for Maintaining and Transforming

Cultural Identity – A Note from the Experience of Eritrean Immigrants in Stockholm

ETA 39.2004

 

Alberto CAVALIERE:

Price Competition with Information Disparities in a Vertically Differentiated Duopoly

PRA 40.2004

 

Andrea BIGANO and Stef PROOST:

The Opening of the European Electricity Market and Environmental

Policy: Does the Degree of Competition Matter?

CCMP 41.2004

 

Micheal FINUS

(lxix): International Cooperation to Resolve International Pollution Problems

KTHC 42.2004

 

Francesco CRESPI:

Notes on the Determinants of Innovation: A Multi-Perspective Analysis

CTN 43.2004

 

Sergio CURRARINI and Marco MARINI:

Coalition Formation in Games without Synergies

CTN 44.2004

 

Marc ESCRIHUELA-VILLAR:

Cartel Sustainability and Cartel Stability

NRM 45.2004

 

Sebastian BERVOETS and Nicolas GRAVEL

(lxvi): Appraising Diversity with an Ordinal Notion of Similarity:

An Axiomatic Approach

NRM 46.2004

 

Signe ANTHON and Bo JELLESMARK THORSEN

(lxvi): Optimal Afforestation Contracts with Asymmetric

Information on Private Environmental Benefits

NRM 47.2004

 

John MBURU (lxvi):

Wildlife Conservation and Management in Kenya: Towards a Co-management Approach

NRM 48.2004

 

Ekin BIROL, Ágnes GYOVAI and Melinda SMALE (lxvi):

Using a Choice Experiment to Value Agricultural

Biodiversity on Hungarian Small Farms: Agri-Environmental Policies in a Transition al Economy

CCMP 49.2004

 

Gernot KLEPPER and Sonja PETERSON:

The EU Emissions Trading Scheme. Allowance Prices, Trade Flows,

Competitiveness Effects

GG 50.2004

 

Scott BARRETT and Michael HOEL:

Optimal Disease Eradication

CTN 51.2004

 

Dinko DIMITROV, Peter BORM, Ruud HENDRICKX and Shao CHIN SUNG:

Simple Priorities and Core

Stability in Hedonic Games

SIEV 52.2004

 

Francesco RICCI

: Channels of Transmission of Environmental Policy to Economic Growth: A Survey of the

Theory

SIEV 53.2004

 

Anna ALBERINI, Maureen CROPPER, Alan KRUPNICK and Nathalie B. SIMON:

Willingness to Pay for

Mortality Risk Reductions: Does Latency Matter?

NRM 54.2004

 

Ingo BRÄUER and Rainer MARGGRAF

(lxvi): Valuation of Ecosystem Services Provided by Biodiversity

Conservation: An Integrated Hydrological and Economic Model to Value the Enhanced Nitrogen Retention in

Renaturated Streams

NRM 55.2004

 

Timo GOESCHL and Tun LIN

(lxvi): Biodiversity Conservation on Private Lands: Information Problems and

Regulatory Choices

NRM 56.2004

 

Tom DEDEURWAERDERE

(lxvi): Bioprospection: From the Economics of Contracts to Reflexive Governance

CCMP 57.2004

 

Katrin REHDANZ and David MADDISON:

The Amenity Value of Climate to German Households

CCMP 58.2004

 

Koen SMEKENS and Bob VAN DER ZWAAN:

Environmental Externalities of Geological Carbon Sequestration

Effects on Energy Scenarios

NRM 59.2004

 

Valentina BOSETTI, Mariaester CASSINELLI and Alessandro LANZA

(lxvii): Using Data Envelopment

Analysis to Evaluate Environmentally Conscious Tourism Management

NRM 60.2004

 

Timo GOESCHL and Danilo CAMARGO IGLIORI

(lxvi):Property Rights Conservation and Development: An

Analysis of Extractive Reserves in the Brazilian Amazon

CCMP 61.2004

 

Barbara BUCHNER and Carlo CARRARO

: Economic and Environmental Effectiveness of a

Technology-based Climate Protocol

NRM 62.2004

 

Elissaios PAPYRAKIS and Reyer GERLAGH

: Resource-Abundance and Economic Growth in the U.S.

NRM 63.2004

 

Györgyi BELA, György PATAKI, Melinda SMALE and Mariann HAJDÚ

(lxvi): Conserving Crop Genetic

Resources on Smallholder Farms in Hungary: Institutional Analysis

NRM 64.2004

 

E.C.M. RUIJGROK and E.E.M. NILLESEN

(lxvi): The Socio-Economic Value of Natural Riverbanks in the

Netherlands

NRM 65.2004

 

E.C.M. RUIJGROK

(lxvi): Reducing Acidification: The Benefits of Increased Nature Quality. Investigating the

Possibilities of the Contingent Valuation Method

ETA 66.2004

 

Giannis VARDAS and Anastasios XEPAPADEAS

: Uncertainty Aversion, Robust Control and Asset Holdings

GG 67.2004

 

Anastasios XEPAPADEAS and Constadina PASSA

: Participation in and Compliance with Public Voluntary

Environmental Programs: An Evolutionary Approach

GG 68.2004

 

Michael FINUS

: Modesty Pays: Sometimes!

NRM 69.2004

 

Trond BJØRNDAL and Ana BRASÃO

: The Northern Atlantic Bluefin Tuna Fisheries: Management and Policy

Implications

CTN 70.2004

 

Alejandro CAPARRÓS, Abdelhakim HAMMOUDI and Tarik TAZDAÏT

: On Coalition Formation with

Heterogeneous Agents

IEM 71.2004

 

Massimo GIOVANNINI, Margherita GRASSO, Alessandro LANZA and Matteo MANERA

: Conditional

Correlations in the Returns on Oil Companies Stock Prices and Their Determinants

IEM 72.2004

 

Alessandro LANZA, Matteo MANERA and Michael MCALEER

: Modelling Dynamic Conditional Correlations

in WTI Oil Forward and Futures Returns

SIEV 73.2004

 

Margarita GENIUS and Elisabetta STRAZZERA

: The Copula Approach to Sample Selection Modelling:

An Application to the Recreational Value of Forests

CCMP 74.2004

 

Rob DELLINK and Ekko van IERLAND

: Pollution Abatement in the Netherlands: A Dynamic Applied General

Equilibrium Assessment

ETA 75.2004

 

Rosella LEVAGGI and Michele MORETTO

: Investment in Hospital Care Technology under Different

Purchasing Rules: A Real Option Approach

CTN 76.2004

 

Salvador BARBERÀ and Matthew O. JACKSON

(lxx): On the Weights of Nations: Assigning Voting Weights in

a Heterogeneous Union

CTN 77.2004

 

Àlex ARENAS, Antonio CABRALES, Albert DÍAZ-GUILERA, Roger GUIMERÀ and Fernando VEGAREDONDO

(lxx): Optimal Information Transmission in Organizations: Search and Congestion

CTN 78.2004

 

Francis BLOCH and Armando GOMES

(lxx): Contracting with Externalities and Outside Options

CTN 79.2004

 

Rabah AMIR, Effrosyni DIAMANTOUDI and Licun XUE

(lxx): Merger Performance under Uncertain Efficiency

Gains

CTN 80.2004

 

Francis BLOCH and Matthew O. JACKSON

(lxx): The Formation of Networks with Transfers among Players

CTN 81.2004

 

Daniel DIERMEIER, Hülya ERASLAN and Antonio MERLO

(lxx): Bicameralism and Government Formation

CTN 82.2004

 

Rod GARRATT, James E. PARCO, Cheng-ZHONG QIN and Amnon RAPOPORT

(lxx): Potential Maximization

and Coalition Government Formation

CTN 83.2004

 

Kfir ELIAZ, Debraj RAY and Ronny RAZIN

(lxx): Group Decision-Making in the Shadow of Disagreement

CTN 84.2004

 

Sanjeev GOYAL, Marco van der LEIJ and José Luis MORAGA-GONZÁLEZ

(lxx): Economics: An Emerging

Small World?

CTN 85.2004

 

Edward CARTWRIGHT

(lxx): Learning to Play Approximate Nash Equilibria in Games with Many Players

IEM 86.2004

 

Finn R. FØRSUND and Michael HOEL

: Properties of a Non-Competitive Electricity Market Dominated by

Hydroelectric Power

KTHC 87.2004

 

Elissaios PAPYRAKIS and Reyer GERLAGH

: Natural Resources, Investment and Long-Term Income

CCMP 88.2004

 

Marzio GALEOTTI and Claudia KEMFERT

: Interactions between Climate and Trade Policies: A Survey

IEM 89.2004

 

A. MARKANDYA, S. PEDROSO and D. STREIMIKIENE

: Energy Efficiency in Transition Economies: Is There

Convergence Towards the EU Average?

GG 90.2004

 

Rolf GOLOMBEK and Michael HOEL

: Climate Agreements and Technology Policy

PRA 91.2004

 

Sergei IZMALKOV

(lxv): Multi-Unit Open Ascending Price Efficient Auction

KTHC 92.2004

 

Gianmarco I.P. OTTAVIANO and Giovanni PERI

: Cities and Cultures

KTHC 93.2004

 

Massimo DEL GATTO:

Agglomeration, Integration, and Territorial Authority Scale in a System of Trading

Cities. Centralisation versus devolution

CCMP 94.2004

 

Pierre-André JOUVET, Philippe MICHEL and Gilles ROTILLON

: Equilibrium with a Market of Permits

CCMP 95.2004

 

Bob van der ZWAAN and Reyer GERLAGH

: Climate Uncertainty and the Necessity to Transform Global

Energy Supply

CCMP 96.2004

 

Francesco BOSELLO, Marco LAZZARIN, Roberto ROSON and Richard S.J. TOL

: Economy-Wide Estimates of

the Implications of Climate Change: Sea Level Rise

CTN 97.2004

 

Gustavo BERGANTIÑOS and Juan J. VIDAL-PUGA

: Defining Rules in Cost Spanning Tree Problems Through

the Canonical Form

CTN 98.2004

 

Siddhartha BANDYOPADHYAY and Mandar OAK

: Party Formation and Coalitional Bargaining in a Model of

Proportional Representation

GG 99.2004

 

Hans-Peter WEIKARD, Michael FINUS and Juan-Carlos ALTAMIRANO-CABRERA

: The Impact of Surplus

Sharing on the Stability of International Climate Agreements

SIEV 100.2004

 

Chiara M. TRAVISI and Peter NIJKAMP

: Willingness to Pay for Agricultural Environmental Safety: Evidence

from a Survey of Milan, Italy, Residents

SIEV 101.2004

 

Chiara M. TRAVISI, Raymond J. G. M. FLORAX and Peter NIJKAMP

: A Meta-Analysis of the Willingness to

Pay for Reductions in Pesticide Risk Exposure

NRM 102.2004

 

Valentina BOSETTI and David TOMBERLIN:

Real Options Analysis of Fishing Fleet Dynamics: A Test

CCMP 103.2004

 

Alessandra GORIA e Gretel GAMBARELLI:

Economic Evaluation of Climate Change Impacts and Adaptability

in Italy

PRA 104.2004

 

Massimo FLORIO and Mara GRASSENI

: The Missing Shock: The Macroeconomic Impact of British

Privatisation

PRA 105.2004

 

John BENNETT, Saul ESTRIN, James MAW and Giovanni URGA:

Privatisation Methods and Economic Growth

in Transition Economies

PRA 106.2004

 

Kira BÖRNER

: The Political Economy of Privatization: Why Do Governments Want Reforms?

PRA 107.2004

 

Pehr-Johan NORBÄCK and Lars PERSSON

: Privatization and Restructuring in Concentrated Markets

SIEV 108.2004

 

Angela GRANZOTTO, Fabio PRANOVI, Simone LIBRALATO, Patrizia TORRICELLI and Danilo

MAINARDI

 

: Comparison between Artisanal Fishery and Manila Clam Harvesting in the Venice Lagoon by

Using Ecosystem Indicators: An Ecological Economics Perspective

CTN 109.2004

 

Somdeb LAHIRI

: The Cooperative Theory of Two Sided Matching Problems: A Re-examination of Some

Results

NRM 110.2004

 

Giuseppe DI VITA

: Natural Resources Dynamics: Another Look

SIEV 111.2004

 

Anna ALBERINI, Alistair HUNT and Anil MARKANDYA

: Willingness to Pay to Reduce Mortality Risks:

Evidence from a Three-Country Contingent Valuation Study

KTHC 112.2004

 

Valeria PAPPONETTI and Dino PINELLI

: Scientific Advice to Public Policy-Making

SIEV 113.2004

 

Paulo A.L.D. NUNES and Laura ONOFRI

: The Economics of Warm Glow: A Note on Consumer’s Behavior

and Public Policy Implications

IEM 114.2004

 

Patrick CAYRADE

: Investments in Gas Pipelines and Liquefied Natural Gas Infrastructure What is the Impact

on the Security of Supply?

IEM 115.2004

 

Valeria COSTANTINI and Francesco GRACCEVA:

Oil Security. Short- and Long-Term Policies

IEM 116.2004

 

Valeria COSTANTINI and Francesco GRACCEVA:

Social Costs of Energy Disruptions

IEM 117.2004

 

Christian EGENHOFER, Kyriakos GIALOGLOU, Giacomo LUCIANI, Maroeska BOOTS, Martin SCHEEPERS,

Valeria COSTANTINI, Francesco GRACCEVA, Anil MARKANDYA and Giorgio VICINI

 

: Market-Based Options

for Security of Energy Supply

IEM 118.2004

 

David FISK

: Transport Energy Security. The Unseen Risk?

IEM 119.2004

 

Giacomo LUCIANI

: Security of Supply for Natural Gas Markets. What is it and What is it not?

IEM 120.2004

 

L.J. de VRIES and R.A. HAKVOORT

: The Question of Generation Adequacy in Liberalised Electricity Markets

KTHC 121.2004

 

Alberto PETRUCCI

: Asset Accumulation, Fertility Choice and Nondegenerate Dynamics in a Small Open

Economy

NRM 122.2004

 

Carlo GIUPPONI, Jaroslaw MYSIAK and Anita FASSIO

: An Integrated Assessment Framework for Water

Resources Management: A DSS Tool and a Pilot Study Application

NRM 123.2004

 

Margaretha BREIL, Anita FASSIO, Carlo GIUPPONI and Paolo ROSATO

: Evaluation of Urban Improvement

on the Islands of the Venice Lagoon: A Spatially-Distributed Hedonic-Hierarchical Approach

ETA 124.2004

 

Paul MENSINK

: Instant Efficient Pollution Abatement Under Non-Linear Taxation and Asymmetric

Information: The Differential Tax Revisited

NRM 125.2004

 

Mauro FABIANO, Gabriella CAMARSA, Rosanna DURSI, Roberta IVALDI, Valentina MARIN and Francesca

PALMISANI

 

: Integrated Environmental Study for Beach Management:A Methodological Approach

PRA 126.2004

 

Irena GROSFELD and Iraj HASHI

: The Emergence of Large Shareholders in Mass Privatized Firms: Evidence

from Poland and the Czech Republic

CCMP 127.2004

 

Maria BERRITTELLA, Andrea BIGANO, Roberto ROSON and Richard S.J. TOL

: A General Equilibrium

Analysis of Climate Change Impacts on Tourism

CCMP 128.2004

 

Reyer GERLAGH

: A Climate-Change Policy Induced Shift from Innovations in Energy Production to Energy

Savings

NRM 129.2004

 

Elissaios PAPYRAKIS and Reyer GERLAGH

: Natural Resources, Innovation, and Growth

PRA 130.2004

 

Bernardo BORTOLOTTI and Mara FACCIO

: Reluctant Privatization

SIEV 131.2004

 

Riccardo SCARPA and Mara THIENE

: Destination Choice Models for Rock Climbing in the Northeast Alps: A

Latent-Class Approach Based on Intensity of Participation

SIEV 132.2004

 

Riccardo SCARPA Kenneth G. WILLIS and Melinda ACUTT

: Comparing Individual-Specific Benefit Estimates

for Public Goods: Finite Versus Continuous Mixing in Logit Models

IEM 133.2004

 

Santiago J. RUBIO

: On Capturing Oil Rents with a National Excise Tax Revisited

ETA 134.2004

 

Ascensión ANDINA DÍAZ

: Political Competition when Media Create Candidates’ Charisma

SIEV 135.2004

 

Anna ALBERINI

: Robustness of VSL Values from Contingent Valuation Surveys

CCMP 136.2004

 

Gernot KLEPPER and Sonja PETERSON

: Marginal Abatement Cost Curves in General Equilibrium: The

Influence of World Energy Prices

ETA 137.2004

 

Herbert DAWID, Christophe DEISSENBERG and Pavel ŠEVČIK

: Cheap Talk, Gullibility, and Welfare in an

Environmental Taxation Game

CCMP 138.2004

 

ZhongXiang ZHANG

: The World Bank’s Prototype Carbon Fund and China

CCMP 139.2004

 

Reyer GERLAGH and Marjan W. HOFKES

: Time Profile of Climate Change Stabilization Policy

NRM 140.2004

 

Chiara D’ALPAOS and Michele MORETTO

: The Value of Flexibility in the Italian Water Service Sector: A

Real Option Analysis

(lix) This paper was presented at the ENGIME Workshop on “Mapping Diversity”, Leuven, May 16-

17, 2002

(lx) This paper was presented at the EuroConference on “Auctions and Market Design: Theory,

Evidence and Applications”, organised by the Fondazione Eni Enrico Mattei, Milan, September 26-

28, 2002

(lxi) This paper was presented at the Eighth Meeting of the Coalition Theory Network organised by

the GREQAM, Aix-en-Provence, France, January 24-25, 2003

(lxii) This paper was presented at the ENGIME Workshop on “Communication across Cultures in

Multicultural Cities”, The Hague, November 7-8, 2002

(lxiii) This paper was presented at the ENGIME Workshop on “Social dynamics and conflicts in

multicultural cities”, Milan, March 20-21, 2003

(lxiv) This paper was presented at the International Conference on “Theoretical Topics in Ecological

Economics”, organised by the Abdus Salam International Centre for Theoretical Physics – ICTP, the

Beijer International Institute of Ecological Economics, and Fondazione Eni Enrico Mattei – FEEM

Trieste, February 10-21, 2003

(lxv) This paper was presented at the EuroConference on “Auctions and Market Design: Theory,

Evidence and Applications” organised by Fondazione Eni Enrico Mattei and sponsored by the EU,

Milan, September 25-27, 2003

(lxvi) This paper has been presented at the 4th BioEcon Workshop on “Economic Analysis of

Policies for Biodiversity Conservation” organised on behalf of the BIOECON Network by

Fondazione Eni Enrico Mattei, Venice International University (VIU) and University College

London (UCL) , Venice, August 28-29, 2003

(lxvii) This paper has been presented at the international conference on “Tourism and Sustainable

Economic Development – Macro and Micro Economic Issues” jointly organised by CRENoS

(Università di Cagliari e Sassari, Italy) and Fondazione Eni Enrico Mattei, and supported by the

World Bank, Sardinia, September 19-20, 2003

(lxviii) This paper was presented at the ENGIME Workshop on “Governance and Policies in

Multicultural Cities”, Rome, June 5-6, 2003

(lxix) This paper was presented at the Fourth EEP Plenary Workshop and EEP Conference “The

Future of Climate Policy”, Cagliari, Italy, 27-28 March 2003

(lxx) This paper was presented at the 9

 

th

Coalition Theory Workshop on “Collective Decisions and

Institutional Design” organised by the Universitat Autònoma de Barcelona and held in Barcelona,

Spain, January 30-31, 2004

2003 SERIES

CLIM

 

Climate Change Modelling and Policy

(Editor: Marzio Galeotti )

GG

 

Global Governance

(Editor: Carlo Carraro

)

SIEV

 

Sustainability Indicators and Environmental Valuation

(Editor: Anna Alberini)

NRM

 

Natural Resources Management

(Editor: Carlo Giupponi)

KNOW

 

Knowledge, Technology, Human Capital

(Editor: Gianmarco Ottaviano)

IEM

 

International Energy Markets

(Editor: Anil Markandya)

CSRM

 

Corporate Social Responsibility and Management

(Editor: Sabina Ratti)

PRIV

 

Privatisation, Regulation, Antitrust

(Editor: Bernardo Bortolotti)

ETA

 

Economic Theory and Applications

(Editor: Carlo Carraro)

CTN

 

Coalition Theory Network

2004 SERIES

CCMP

 

Climate Change Modelling and Policy

(Editor: Marzio Galeotti )

GG

 

Global Governance

(Editor: Carlo Carraro

)

SIEV

 

Sustainability Indicators and Environmental Valuation

(Editor: Anna Alberini)

NRM

 

Natural Resources Management

(Editor: Carlo Giupponi)

KTHC

 

Knowledge, Technology, Human Capital

(Editor: Gianmarco Ottaviano)

IEM

 

International Energy Markets

(Editor: Anil Markandya)

CSRM

 

Corporate Social Responsibility and Management

(Editor: Sabina Ratti)

PRA

 

Privatisation, Regulation, Antitrust

(Editor: Bernardo Bortolotti)

ETA

 

Economic Theory and Applications

(Editor: Carlo Carraro)

CTN

 

Coalition Theory Network

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