The proposal responds to challenge 2: productive and sustainable farming and the sustainability of the natural resources. The project focuses on the resources forest, soil and water. It departs from the hypothesis that global changes (demographics, climate, economic, technological progress etc.) lead to increased pressure on these resources. In order to conserve resources in the long term, the project explores management regimes that encourage their sustainable use. The new instruments aim at improving the efficiency of the management regimes. They provide the authorities with new options for the conservation of the resources that are added to the traditional options of implementing technological advances. The main scientific and technical contributions of the project are encompassed in: i) methodological advances in the design and implementation of different patterns of natural resource management and ii) verification and validation of these guidelines through empirical studies.

Regarding the first resource (forests) the proposal determines, within a global change scenario, the optimal management regime taking into account not only the value of timber but also the use of forest biomass for energy and the risk of forest fires. The analysis is based on a size-distributed forest taking into account the effects of climate change, the occurrence, spread and potential damage from a wildfire. It is proposed to realize this analysis using a case study in a region of Catalonia that is based on a dynamic model.

Regarding the second resource (water) the project examines the optimal management of common property resources. It focuses on improving the efficiency of the management of an aquifer based, by nature of the common property, in collective decisions (norms, taxes) that restrict the access and use of the resource. Specifically, we will determine (a) norms for sustainable groundwater management based on cooperative game theory and (b) taxes based on individual water extractions, with the subsequent return of these fees to the user community independent from individual consumption.  Besides theoretical work, the proposal foresees studying the management of two specific aquifers (Chikkaballpur Taluk / India and Aquifers of Castilla-La Mancha).

In connection with soil, the proposal focuses on the conservation of soil fertility and the reduction of soil erosion. The research departs from the observation that tenants have no incentive to invest in soil conservation as the end of the duration of their contract approaches. In the economic literature, this problem is known as holdup. As the leasing of agricultural land is common practice, the holdup problem is not marginal but has a geographic dimension and magnitude of considerable size. The analysis is performed within the framework of a principal-agent model in order to design contracts whose characteristics are defined as a function of time. This makes it possible to eliminate, or at least to mitigate, the holdup problem. This study is based on theoretical and empirical work (Ghana).




GOAL 1: Sustainable Management of Forest Resources

In order to analyze the adaptation of forest resources to global change, considering the wood’s production, the biomass production and the risk of fire, we rely on the developed model by Goetz et al. (2010). Next, there is a brief overview of the chosen approach. The proposed model is a discrete version of the above, in which the work is characterized by incorporating aspects that are important for our study: the effect of global change on biological processes, such as tree growth, tree natural mortality and the effect on the fire’s risk.

To estimate the tree breeding it is possible to use the SIBosC (Forest Information System in Catalonia) as a function of the number of fertile trees, of each diameter and intra-specific competition (eg, basal area). In the case that the optimum number of trees cannot be obtained by natural reproduction, the forest manager may seed additional trees. Therefore, plants are the result of natural reproduction and the subsequent selection and/or planting.

The growth of trees, considering climate change, is determined by the biogeochemical model simulation “GOTILWA” (Growth of Trees is Limited by Water, In particular, we consider three different climate cases to analyze the effects on the optimal management regime. The first scenario does not consider climate change and is denoted by BL. The other two scenarios are called A2 and B2 and consider that, from 2000 to 2100, climate change will increase as a result of emissions of carbon dioxide, moderate and high, respectively. The data created from the series of simulations generate the estimation of growth function. Specifically, we consider the change in the diameter of a tree over time as a function of its current diameter, and other biophysical variables (ie. Basal area of the trunk) and weather variables (eg. CO2).

Finally, we will take into account the rate of natural mortality of trees (depending on biophysical variables) and how it can be influenced by global change. In addition to natural mortality, it is proposed, as a new model, to incorporate the mortality due to wildfires. An important effort will be devoted in this part of the work. A quantitative definition of fire risk includes several components: the probability of occurrence, spreading and damage caused by the fire. Therefore, the risk of fire will take into account these factors.

At the risk of fire, in addition to the conditions for forest cover, we shall especially take into account the effect of changes in climate variables on risk. In order to incorporate the effects of climate change on the model, we have obtained the meteorological data for the period 2000-2010 on “Meteocat” and historical records of forest fires. With this historical data, it is calculated the drought index (DC), an index commonly used to represent the moisture content of the deep layer of compact organic matter in the forest floor. Then DC index historical data and forest fires historical data are correlated in order to determine their relationship. Then, developments of future weather conditions will be specified, taking into account the variation in temperature and precipitation predicted by climate change scenarios considered. These data will provide an estimate of the risk of fire.

The biophysical functions are incorporated into the economic decision model, integrating both greatly. We assume that the forest owner wants to maximize the profitability of the trunk. This performance is calculated as the sum of discounted profits over the time horizon considered. These benefits are calculated as the net income from the sale of wood, less maintenance costs (cleaning, pruning and shredding of waste) and less costs associated with planting additional trees. The model of Goetz et al. (2010) will be completed including revenues and costs of the use of forest biomass for energy purposes.

Maximizing this profit function is subject to the compliance of the functions described of biological type: reproduction, evolution of the number of trees and their growth. This problem was solved using GAMS (General Algebraic Modelling System), obtained for different stands of SIBosC. Two types of stands are considered: young and mature, in order to observe the effect of different initial distributions on the results of the optimization.

Empirical studies related to this objective, require biophysical data collection, estimation functions (SPSS) and many optimizations with GAMS. Thus, we consider necessary to have a technical specialized on program management.


GOAL 2: Sustainable management of water resources

The analysis of the sustainable management of groundwater is based on a dynamic model of integrated assessment. Part of it has been developed over the past four years with the collaboration of Dr. TS Amjath-Babu, linked to Justus von Liebig of Giessen University. In part, this collaboration has been funded by the Academic Exchange Service of Germany, which has allowed Dr. Goetz visit repeatedly Justus von Liebig University. The model has already been developed and the functions and parameters had been specified using data collected from two locations in farmers Chikkaballpur and Taluk, situated in Arid East Zone (AEZ) of the state of Karnataka (South India). This area is characterized by having a semi-arid climate with some rainfall, and is considered a region with overexploitation of groundwater resources problems. The selection of the study of this area is due to the nearly complete absence of surface water, so that 90% of the irrigation water is extracted from the aquifer. The programming of the model is at an advanced stage and once completed, it is proposed to collect data from an aquifer in Castilla-La Mancha, with the same goals we set in the case of Chikkaballpur Taluk - see section 3. For this application we count on with the support of Dr. Stephen, with a lot of experience in the modelling of these aquifers. Although Dr. Esteban has not been able to incorporate into the project, she has shown its willingness to collaborate.

Unlike most economic studies of groundwater modelling, we try to integrate economic and hydrological aspects. For example, our model takes into account decisions such as crop acreage, crop type (perennial or annual or lie fallow crops, cropping pattern, depth of wells, the area that is dedicated to capturing water, etc. all that influence the evolution of the ground water. The model also considers the dynamic interaction between natural extraction and recharge, and water harvesting option to achieve a balance between abstraction temporary water and groundwater recharge. Finally, try to determine the route of private extraction (myopic) and the path of socially optimal extraction. it is intended to employ innovative numerical routines and analyze the profit loss that occurs if farmers adopt the myopic path and determine the magnitude of the gains that can be achieved in the long term if based on the user community rules are introduced.

A brief description of the model is presented. However, due to space constraints, we do a general synthesis of the same. The dynamic mathematical programming model maximizes the net present value of the benefits flows of different types of agricultural producers planting annual and multiannual crops over a certain time horizon. The considered productive inputs are: groundwater, land (leased or not leased, farmland), fertilizer (mineral and organic), labour (hired, rented, own work), electricity (water extraction), maintenance (wells, tools water extraction), bore (well depth).

The static and dynamic constraints include restrictions of ground balance, work balance, land use and water extraction, evolution of well depth (stock variable, with the investment like an comprehensible variable), evolution of multiannual crops (stock variable) and evolution of the groundwater table (stock variable).

To determine the profit function, it is necessary to determine the production functions, cost and benefit of a farmer type 'j' (landless, small, medium and large) at time 't' defined. For the production function, Baule Mitscherlich-specification is used, because water is a key input that cannot be replaced.

The most important thing, in addition to the precise modelling of agricultural activities, is that the project aims to design and make an analysis of policy instruments based on the irrigation community. It is not a regulatory institution that enforces the rules or puts taxes and fees, because it is the community itself that does it.

The proposal set up the specific formulation of different rules for allocating shortage costs among users in order to induce an optimal and efficient solution from the collective point of view, trying to replicate the optimal path of groundwater extraction in the long run. This part of the work will consists in developing a cooperative game and determining different distribution rules. Once defined theoretically the distribution rules, their efficiency and their effectiveness are measured by the mathematical programming model.

Moreover, the same steps are followed to establish user fees. Theoretically, will be determined a distribution formula that allows to obtain an efficient collectively optimal solution, trying to replicate the optimal path of extraction from the aquifer in the long run. The collection of the user license or user fee will be based on individual water extraction, while redistribution of the collection will be based on factors not related to production. You can think of this quota or license as a water price (one license for water use) and redistribution as a compensation for the license, since the ownership of the resource is shared by all members of the community.


GOAL 3: Soil Conservation

To accomplish goals outlined in the memory in this line of research, we try to analyze the contractual relationship between the owner and tenant of a farm. Specifically, in order to analize it, the principal-agent framework is chosen. It is assumed that the owner maximizes profits by choosing the rental and contract duration. Long-term contracts could minimize the transaction cost for the owner, related to the signing of new contracts. However, a long-term contract could prevent the dissolution of the contractual relationship if external conditions of employment are altered and it becomes advisable to end the contractual relationship (for example, in the case of need to sell the land).

Therefore, the owner has to strike equilibrium between the benefits of a long-term contract and the flexibility of a short-term contract. To improve or maintain soil fertility, farmers must apply not only mineral fertilizers, but also invest in the application of organic fertilizers, such as manure. However, the positive effect of manure is not immediate, since the nutrients are released slowly over time. Similarly, the improvement in the structure of the soil (humus content) is a gradual process in time, which is often not evenly distributed over time.

The previous literature about the holdup problem has considered time explicitly, but only in a stylized way (Che and Sákovics, 2004; Felli and Roberts, 2011). Normally, agents can invest in the first period and benefits can only be obtained in the second period. The standard model assumes that each time period considered is equal in length and doesn’t specify the duration. Moreover, it is usual to make a model where investment is a stock variable instead of a flow variable. However, examples we can see in reality life, show that periods of investment and profit are often interrelated and that dynamics of the investment behavior and the realization of benefits is more complex than that described by the standard model.

 From this observation, our starting point is that the investment behavior of agents depends on the length of period of time or on the duration of the contract, particularly if the investment is not a one-time event, but a process continuous while the contract remains in force. Therefore, this proposal focuses on the description of the dynamics of the optimal investment behavior in order to determine the optimal duration of the contract in the presence of a holdup problem.

The objective is to determine the optimal length of contracts. The contract duration “T” is finite and endogenous. In general, we show a simple version of the model.


The principal chooses at each time t the optimal value of T and rent R (t) that maximizes the profit function that is obtained as the difference between the rent R (t) and the function V (T). This profit function includes transaction costs arising from the contract renewal and the possible loss of a long-term contract that make not possible adapting to new situations. Obviously, these expenses and losses depend on the duration of contracts. The short-term contracts involve high transaction costs and long-term contracts prevent the adjustment of the contract to the changes of the context. Therefore, we assume that the function V (T) initially decreases with T but increases again when T increases. Thus, the function V (T) is U-shaped with a single minimum.


The agent determines the input m(t) and the investment n(t) that maximize the profit function, which depends on the quality of the soil (individual rationality). Soil quality depends on the intensity of production and investment in soil conservation. The investment has a delayed effect that can be described by a distribution function in time. The benefit of the agent has to be greater than the benefit obtained without participating (participation constraint).

One member of the team (Awudu Abdulai) will do surveys in Ghana that allow specifying and estimating parameters of the model functions. Then the principal-agent model with GAMS will be implemented, which in turn will allow to assess the extent of the holdup problem and see if different contracts are able to remove or mitigate the holdup problem.