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: firstname.lastname@example.org, 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 
 Krautkraemer J.A. (1998), Nonrenewable Resource Scarcity,
Journal of Economic Literature, vol.XXXVI.
 Moore M., Negri D., (1992), A Multicrop Production Model of Ir-
rigated Agriculture, Applied to Water allocation Policy of the Bu-
reau of Reclamation, Journal of Agricutural and Resources Eco-
 Nauges C.,Thomas A., (2000), Privetely-operated Water Utilities,
Municipal Price Negotiation, and Estimation of Residential Water
Demand: the Case of France, Land Economics, 76 (1).
 Provencher B. (1999), Issues in the Conjunctive Use of Surface
Water and Groundwater, in Bromley D.(ed.), Handbook of Envi-
ronmental Economics, Blackwell.
 Spaggiari G.C. (1992), Il Costo ombra delle acque sotterranee in
Romagna (in italian), Consorzio Acque, Ecotec
 Tietenberg, T. H. (2004), Environmental Economics and Policy,
4thedition, Pearson Addison Wesley.
 United Nations Environmental Program (2002), Global Environ-
mental Outlook 3, Earthscan Publications Ltd, London Sterling,
 Varela-Ortega C. ,Sumpsi J., Garrido A, et al., (1998), Water
Pricing Policies, Public Decision Making and Farmers’ Response:
Implication for Water Policy”, Agricultural Economics, 19.
Figure 1: Shadow cost of groundwater (t)
Degree of externality