**1. Introduction**

Groundwater management is an issue which remains a practical matter in many human regions throughout the world [1]. Besides, it is very necessary to clarify that groundwater represents the largest stock of accessible freshwater and accounts for about one-third of freshwater withdrawals globally [2–4]. However, increased rainfall scarcities have resulted in an augmented use of groundwater, in order to satisfy the increasing domestic, agricultural, and environmental-ecosystem preservation for different water.

 Nevertheless, it is necessary to take into account that historically, surface water has been the main source of water for human consumption, as it was easy and cost effective to access. So, it can be expected that during the second half of the twentieth century, groundwater withdrawals will increase. It is also very relevant to reflect that groundwater supply could represent around one third of the world population [5].

 This wide use of groundwater in many parts of the world has resulted in water level decline and groundwater depletion and is mainly related to phenomena such as biodiversity loss, pollution, and seawater intrusion in coastal aquifers.

 An example could be found in the paper by El Moujabber et al. [6], in which the state of groundwater desalination by seawater intrusion in the Lebanese cost is introduced (specifically in the region of Choueifat-Rmeyle, located in the south of Mount-Lebanon). The main consequence that is obtained is related to the fact that groundwater management can behave like relevant backstop technologies and also that substitutes have become a practical concern in many arid and semiarid regions throughout the world [7].

 A fundamental idea that needs to be pointed out is that groundwater is essential for sustaining agriculture production patterns, as well as consumption models and the biodiversity or the resilience of ecosystems. The combination of this fact with the intense scarcity in many parts of the world makes necessary the development of rules for the corrected and efficient allocation of resources among competing uses over time and space.

 This presents an economic question which has been close to groundwater economics since the middle years of the decade of 1950s. It is necessary to point out that the question of how to manage this resource, mainly because groundwater constitutes about 89% of the freshwater on earth (discounting that in the polar ice caps). From this, an important economic concept could be deduced related to water scarcity and which is related to the fact that the world water scarcity is one of the most important hydraulic resources that need to be taken into account.

 It is also necessary to point out that groundwater systems are rather dynamic with groundwater in motion from zones of recharge to areas of discharge and that a great number of years could, hundreds of years, interfere in the passage of water through this subterranean part of the hydrological cycle. Since flow rates regularly do not ordinarily go beyond a small number of meters per day and can be as low as 1 meter per year (these groundwater velocities compare to rates of up to 1 meter per second for river flows) [8].

Groundwater resources provide a primary (or supplemental) source of irrigation water throughout much of the world, yet overpumping and subsequent aquifer depletion may pose "the single largest threat to irrigated agriculture" [9, 10].

 Two main questions need to be indicated in when taking water extractions into account. The first is double: one is water scarcity in local watersheds (or whole basins created by extreme surface and groundwater withdrawals). The other is water degradation from pollution loads leading to many tracts of rivers and whole aquifers being damaged and losing their capacity to sustain ecosystem functioning and human accomplishments.

Following the wide-scale development of groundwater pumping for agriculture in 1950s, some results have been obtained that the open access nature of groundwater implied that farmers were overextracting water, and therefore, it could be exhausted much before than it might be economically optimal.

These conclusions were called into question by Gisser and Sanchez. These authors, mainly in their very influential paper argue that the difference in producer surplus between the open access and optimally managed cases was numerically insignificant for large aquifers subject to inelastic water demand. Perhaps the most interesting point in the work by Gisser and Sánchez is multidisciplinarity. An essential assumption that we need to take into account is that the GSE model is a dynamic model. Besides, we need to take into account that variables in the model are economic, hydrological, and agronomic variables of groundwater use. In this chapter, the demand and supply functions for irrigated water are defined, and these functions are associated with the hydrological characteristics of the aquifer. Then, the path of water allocation through time is calculated under the policy regime and the free-market regime [11].

#### *Groundwater Management Competitive Solutions: The Relevance of the Gisser-Sanchez Model DOI: http://dx.doi.org/10.5772/intechopen.85507*

This effect has remained controversial, and numerous studies have analyzed whether the Gisser and Sanchez Effect (GSE) persists under a variety of specific conditions, such as convex pumping costs [12], shifting (nonconstant) water demand [13], adaptation by crop shifting [14], confined aquifers [15], heterogeneous users [16]; strategic decision-making [17, 18], conjunctive management [19], risk aversion [20], and backstop water sources [21]. These studies generally find support for the GSE, even under all these different conditions.

 Nevertheless, it is necessary to point out that authors, such as Stratton et al. [22], apply the GSE model, although relaxing a very important significant assumption of a fixed irrigation technology. Results indicate that the GSE fails when irrigation technologies with different water use efficiency become available. These results are robust and hold even when maintaining some of the very fundamental statements in the original model (such as constant marginal pumping costs per linear foot of lift). Besides, the gains from optimal groundwater management become even more significant when irrigation technology is not only variable but also endogenous variables. That is, variables whose values the model is designed to explain. In the model, there are also exogenous variables. That is, variables whose values are taken as given from outside the model [23]. The expression "Endogenous Technical Change" implies that higher water costs could induce the development of technologies that might improve water use efficiency [19, 24]. The expression "Endogenous Technical Change" implies that higher water costs could encourage the development of technologies that might improve water use efficiency [24, 25].

 The main objective of this chapter is to re-evaluate the validity of the GSE hypothesis in groundwater management. In this chapter, the conceptual framework within which the elements interacting in the management of groundwater resources is examined. The most important conclusion obtained is that the role of the market is limited with respect to the price of water in an aquifer. This is an important result, because it points to the mechanism that could pull competitive water prices and quality-graded quantity of groundwater, in line with their equilibrium levels. In Section 2, some models of groundwater use and management are introduced, and the most important economic models for groundwater use can be found (joint with the potential of groundwater management control variables in such models). In Chapter 3, some relationships between the Gisser and Sanchez effect and the difficulties to establish clear groundwater property rights are discussed. In Section 4, the robustness of GSE under a private if property rights regime is discussed, both in quantity and in quality terms. In Section 5, a discussion section is introduced. Finally, some conclusions are provided.
