**4. The robustness of GSE under a private property rights regime**

The solution which is commonly proposed for the inefficiencies arising in common property resource extraction is central-optimal control by a regulator, who uses taxes or quotas to obtain the efficient allocation of resources over time.

In the background of groundwater depletion, a solution has been commonly suggested which is based on a tradable permit scheme [37, 38]. In the framework of groundwater reduction, a number of authors have recommended a similar institutional arrangement in which firms are arranged and endowment of tradable permits to the in situ groundwater stock, which they control over time. Each firm's bundle of permits represents its private stock of groundwater.

This private stock is worsening due to groundwater pumping and intensifications to reflect the firm share of periodic recharge. It also changes in response to the activity of the firm in the market for groundwater stock permits, increasing when permits are purchased and decreasing when permits are sold. The market price for permits serves to allocate groundwater over time.

It is necessary to point out that this particular regime is inefficient, mainly because both the pumping cost externality and the risk externality persist after the allocation of permits. Moreover, this regime is time inconsistent. However, different efforts to quantify the value of groundwater resource under both optimal control and the private property rights regime indicate that groundwater privatization recovers most of the potential gain from management. In particular, a programming model for Madera County, in California (USA), can be found in [37]. This regime recovered 95% of the potential gain from management.

#### **4.1 The GSE in models of conjunctive use of surface and groundwater**

A tributary aquifer is characterized by a groundwater stock that is hydrologically connected to a body of surface water. In this aquifer, surface water may recharge the underground aquifer, or groundwater may supplement surface flows depending upon hydrological conditions.

In papers such as [38], results can be found in which an analytical economic model is developed and is focused primarily on the hydrologic link between surface and groundwater, by modeling the instantaneous rate of aquifer recharge caused by groundwater pumping, through river effects. In this chapter, some externalities river effects can be found, which reinforced groundwater overpumping present due to the usual common property effects. Results of this chapter indicate that optimal policy requires compensation to be paid for both river effects and aquifer depletion net of river effects. This work points to an externality created by groundwater overpumping provoked mainly by the common property effects.

From this, the main conclusion which needs to be pointed out is that optimal policy requires a recompense to be paid for both river effects and aquifer depletion *Groundwater Management Competitive Solutions: The Relevance of the Gisser-Sanchez Model DOI: http://dx.doi.org/10.5772/intechopen.85507* 

net of river effects [39]. It is necessary to highlight that these effects indicate the existence of some externalities which could be related to groundwater pumping, which might be adjusted with the precise management. The main consequence probably could be that GSE might be very likely removed by the improvement in management benefits.

Unfortunately, no empirical results exist of these results focusing primarily on the hydrologic link between ground and surface water, and at the same time acknowledging the stochastic nature of surface water supplies. Instead, the main literature that incorporates stochastic surface supplies into a groundwater model in which surface water and groundwater are modeled as substitute goods, aquifers are not connected with surface water, and they only benefit from substantial natural recharge.

## **5. Discussions**

Regarding the GSE model, it needs a number of important assumptions. One of the most significant has to do with the disregard for aquatic ecosystems linked and dependent on aquifer systems.

In the GSE model, a very special point needs to be pointed out, which is that the aquifer is presented as a "bath-tub", unconfined aquifer, with infinite hydraulic conductivity [40]. A bath-tub approach to modeling an aquifer assumes that it responds uniformly and instantly to groundwater extraction [41, 46, 47]. From this, the spatial distribution of the users of the resource is not so relevant, and the evolution of the spatial profile of drawdown does not affect current and future extraction choices. Gisser-Sánchez assumes a deterministic and constant recharge, constant return flow and average rainfall, independence of surface water and groundwater systems, and a bottom-less aquifer. Since their competitive steady state presents a positive water stock, their estimation of welfare gains from optimal management excludes stock externality [42].

 Another important assumption which is discussed in this chapter is the appropriateness of the stock effect assumption. This hypothesis reflects the dependence of extraction costs and the eventual benefits on the stock of the resource. From this, it could be established the way these assumptions might affect the time variation of the shadow price of groundwater externality. In this chapter, the main result is that this could lead to a declining value of in situ resource over time. Therefore, the addition on nonmarginal extraction costs could be close to inappreciable, which could imply the validation of the Gisser-Sanchez effect, which also presents the remarkable hypothesis that groundwater markets have the benefit of allowing more flexible movement of water to serve changing conditions and demands.

 Finally, a main conclusion could be derived from the paper introduced which is that a very relevant model such as [4, 5] is a very appropriate work to analyze groundwater management, mainly because it states the conditions under which welfare improvements from policy interventions could be significant in aquifer administration. This result could be compared with nonregulation or free market solutions in groundwater management.

### **6. Conclusion**

The main conclusion of this chapter has to do with the GSE effect and points mainly to the different effects related to welfare improvements and aquifer management. In this work, an optimal policy requires a compensation to be paid for both river effects and aquifer depletion, which points to an additional externality created by groundwater pumping. This externality could be corrected with an appropriate management of the groundwater, which could eventually eliminate the GSE effect and even increase management benefits.

No empirical results have been obtained in order to test these results, which have to do mainly with the eventual links between ground and surface water. These results could be pertinent in order to improve groundwater management, because from this, the stochastic nature of surface water flows could be acknowledged.

Nevertheless, probably the most significant result in this chapter is that different effects related to welfare improvements and aquifer management and the relevance of the GSE effect exists. Besides, it is necessary to indicate that an optimal aquifer management policy requires a compensation to be paid for both the existing river effects and aquifer depletion. These conclusions stem from the fact that externalities exist, which are linked to groundwater pumping. This externality could also be corrected with a suitable management of the groundwater. This result is quite relevant because it could potentially remove the GSE effect, and therefore, even increase management benefits.

It is similarly essential to take into account the appropriateness of some of the assumptions in the model, since some of them (like the linear relationship between pumping costs for nonconsumptive benefits), and which are an essential tool in groundwater management.

Environmental uses of groundwater water and the way markets work present a significant impact on users and the environment. An interesting conclusion is provided by [48], in his paper for the journal *Resources* (from Resources for the Future), which is that there is rapid depletion of aquifers in the United States, and this presents significant impacts on users and the environment, requiring stakeholders across the country to look for creative and effective policy solutions. So, there is an interesting conclusion that groundwater markets can be applied broadly in groundwater management in order to protect one the most relevant freshwater environmental resource.
