An Exercise on the Optimal Use of
Laura Castellucci and Alessio D’Amato†
October 13, 2005
According to the EU water framework directive 2000/60, water tariffs should be
based on the full cost recovery principle, including scarcity and external effects. To
disregard these two aspects is not only conceptually misleading, as we try to show,
but also leads to determine a wrong, distorted tariff. Our tentative application to
the italian case shows, for example, that water tariffs should be up to three times
higher than the actual ones, revealing a significant distortion.
JEL classification: D6, Q3, Q58
As we all know ”water” is a necessity for life, it enters into every con-
sumption function and into many industrial processes (as an input and
as a waste disposal device); it is largely used in the agricultural sector
for irrigation, it affects health and welfare of society and it is increas-
ingly used for recreational purposes. One would expect water to play
an important role at various levels including government policy. This
is not the case. The following is instead true: 1. water management
∗A previous version of this paper has been presented at the International Confer-
ence on Water Economics, Statistics and Finance, Rethymno, Creete, Greece, 8 - 10
†University of Rome “Tor Vergata”, Department of Economic Studies and Quan-
titative Methods, SEFEMEQ, Via Columbia, 2; 00133, Rome, Italy; tel. +39 06
72595924/27; fax: +39 06 2040219; e-mail: email@example.com, dam-
appears to be of little interest both at a theoretical and at a practi-
cal level. It suffices to consider how few papers are published, how
restricted is the relevance of the subject either as a teaching topic, as
a theme of political discussion or as a simple concern by the general
public; 2. no use of economic incentives is in general at work to im-
prove water management; on the contrary distortionary subsidies are
very often in place. Water-related policies being our general concern,
we focus here on groundwater, leaving surface water aside.
A widespread belief among economists is that with no government
intervention the groundwater resource is misallocated1, while getting
the right value of water in its alternative uses, namely agricultural,
residential and industrial, is crucial for an efficient policy to be de-
signed. The literature on water demand is extensive, although most
of the works deal with residential and agricultural water demand2,
leaving the industrial one as the least investigated; several papers also
deal with cost functions estimates with respect to various countries3.
Two aspects seem to be overlooked by the present literature. At
a theoretical level, the optimal use of groundwater is in general ad-
dressed without considering external effects; at an empirical level, little
has been done with respect to Italy. The very limited availability of
empirical studies applied to the italian water sector may have several
reasons, the lacking of data being the most important. The aim of our
paper is therefore twofold. On one hand, we want to investigate the
consequences on the rules for an optimal water use, of considering the
existence of externalities and, on the other hand, we want to provide
empirical estimates concerning the ”true” (or shadow) value of water
in our country. Such empirical investigation is, in our view, instru-
mental to the design and implementation of an efficient water sector
regulation by public authorities, according to the idea that the State
should regulate the services and not provide them.
1See for example  and the literature that followed it.
2To mention just few, for residential demand:  and ; for agricultural demand:
 and .
3Examples may be:  and .
The building blocks of our simple model are the following. We
assume that groundwater is a stock resource which can be consid-
ered nonrenewable, as in ; in other words we consider that the
current withdrawal of groundwater is in fact a reduction in tomorrow
supply4.We then consider two possible scenarios. The first, which is
deemed myopic behaviour, coincides with the hypothesis of short run
net benefits maximization. The second implies instead the maximiza-
tion of social welfare by a benevolent social planner. We first show
the theoretical outcomes, which are different in the two cases, as one
might expect, and then we draw some lessons for our country.
The State of the Art
Optimal rules for the use of natural resources, whether renewable or
exhaustible5, are well established in the economic literature. Take the
harvesting rate equal to the rate of reproduction while maximizing the
present value of profits from the resource, is the optimal rule for re-
newable resources and deplete the resource at a rate such that its price
grows at the discount rate, is the optimal rule for an exhaustible one.
The last rule, known as the Hotelling rule6, is the common reference
for exhaustible resource studies.
The problem of the possible shortage of nonrenewable resources has
received intermittent attention by the economists. The ”Coal Ques-
tion” by Jevons (1865) has been one of the remotest contributions, just
preceded by Ricardo’s lack of fertile land as a constraint to growth.
What would have happened to the rate of growth England reached
with the industrial revolution as the coal deposits would have become
4If one prefers can consider that groundwater is indeed rechargeable although with
a recharge rate that is very small relative to the capacity of the groundwater aquifer.
Our extreme hypothesis is equivalent to the assumption of an extraction rate greater
than the rate of natural recharge, as it is usually the case in reality.
5To be precise only renewable resources can be used while the exhaustible ones
6See the seminal Hotelling 1931 paper, in 
exhausted, was the forward looking concern of Jevons7. And Ricardo
had already warned that the capitalist economy would have stoppd
growing when land, due to less and less fertility, would have been
exhausted. During the XX century, sort of unconstrained optimism
made the problem of natural resource availability forgettable and only
around the 70s both the first oil price shock and the publication of
a book, namely The Limits to Growth, marked the comeback of NR
into the economic theory of growth. The Hotelling rule, demonstrated
in 1931, eventually gained momentum.
But it is only in 1987 and thanks to the publication of Brundtland
report, that ”sustainable development” became the target and the
aim, at least in principle, of the economic policies of OECD countries.
Attention was called on the possible overexploitation of both types of
NR8and the problem of ”equity” among generations on the use of NR
At present, controversies are going on about precise definition, con-
tent, ways of measuring and pursuing sustainable development, etc.,
but despite the multiplicity of voices, the debate can reduce to two po-
sitions, one optimistic and the other pessimistic . For the first group,
thanks to the market incentives to generate ”discovery and substitu-
tion”, there are no limits to growth. No such a threat exists as far
as substitution among capital resources (natural or human-made) is
possible and as far as technical progress will continue to develop as it
did in the past. On the contrary, for the second group, with no govern-
ment intervention, mismanagement and scarcity will prevail because
externalities are present and NR are in general public and/or common
goods. That is to say , market signals are quite often wrong and in
several cases even missing.
Actually, as standard economics teaches, a growing demand for a
good will generate difficulties when its supply is inelastic and/or there
7Not a real concern for a modern economic approach based on an unconstrained
confidence in a technological progress capable of meeting human being needs.
8Declining fish population in the ocean being a straightforward example of mis-
are no substitutes. The starting point of Hotelling investigation into
the efficiency of non renewable NR utilization, is in fact the assump-
tion of a ”finite” availability of them. Quantities consumed today are
no longer available tomorrow: here is an opportunity cost to be consid-
ered9. Several studies have been produced with the aim of empirically
testing Hotelling rule implications and although for the most part they
appear not to be consistent with prices and in situ value10, the reason
seems to rely on the existence of several ”mitigating factors” (such
as new discoveries and technical progress) that have delayed the im-
minence of nonrenewable resource exhaustion rather than on flaws in
the theory. The question is therefore whether, and for how long, the
mitigating factors will continue to produce their positive effects in the
future, notwithstanding the growing demand of NR by a growing world
population. The basic problem remains because NR, which provide
life support services, are in general open access and public goods. ”
Market interventions are necessary to prevent inefficient use of these
resources. Because of this, the attention focused on the environmen-
tal impacts of non renewable resource use will continue to increase
with increased emphasis on the details of ecological interactions and
management of global public assets.”11.
The case of water is probably the most interesting and complicated
in the field of NR studies given its importance and peculiarities. First,
it may be a renewable resource, although at an unknown rate, when
we deal with surface water, or a non renewable one, when dealing with
ground water pumped at a rate greater than its rate of recharge. Sec-
ond , water is a NR which is fundamental to life and has no substitute
. Third , its market ”signal”, i.e. its selling price, is in general wrong
in the sense that market does not, of course, capture either all the
externalities produced by the water use or the user cost12of present
9Call it user cost or royalty or in situ value, see footnote 12.
10See [10, p. 2066]. This paper is a very interesting review of the main issues on
the subject in recent time.
11[10, p. 2103]. Italics are ours.
12’User cost’ has the same meaning of ’royalty’. The point is that when an ex-
haustible resource is used its stock depletes. The price of the resource for the actual