1. Managing Biodiversity as an Insurance against Crop Failures: Nature as a Preventive and Insurance Tool Ernst-August Nuppenau University of Giessen, Germany

2. Content Introduction Outline of method Modelling of farm behaviour, risk andan Ecological Main Structure (EMS) A framework for farmers‘ participation in biodiversity and interest functions Farmers‘ behaviour in field margin provision for an EMS Tragedy of the common in public risk management Bargain Equilibriumfor public risk management Bargain Equilibrium Application Risk reduction, payments, insurance alternatives and institutions Summary and Outlook

3. Motivation and Key Issues The loss of biodiversity in the countryside has attracted ecologist who portray this as a public concern. Farmers argue that actions to preserve biodiversity will reduce their competitiveness and income. We argue that institutional problems have been overlooked and biodiversity is a public good for risk reduction. Cultural landscapes have been created deliberately to serve farmers as natural pest control over centuries. Biological risk reduction in communities competes with purchases of pesticides and land for production; instead of land allocated to an Ecological Main Structure (EMS) farmer maximise land occupation.

4. Objectives and Methods The paper applies a political economy model of social bargaining to the provision of an ecological main structure by farmers. The paper shows how a tragedy of the commons problem can be overcome, if the provision of an EMS is organized by a collective management of field margin provision. A politically partial manager of a public good "natural risk elements for reduction" is entitled to procure land for the EMS. The theory of achieving a bargaining solution is presented and in this framework we can discuss institutional amendments such as payments.

5. Diagram 1: Framing interest functions and provision of land for environmental services in an EMS Diagram 1: Settlement Structure and Nature Provision Example: 40 ha of an EMS have to be proportionally (2%) accrued for a main structure from 20 small farmers, having 50 ha, and 10 big farmers, having approximately 100ha:  Each small farmer has to provide 2 ha and a big farmer has to provide 4 ha.

6. Framing biology, risk and land allocation in an EMS A matrix  ”converts” a vector of habitats ”b” on field margins into a vector of species ”s”. The size of the main structure B has an impact on species appearance and hence biodiversit D. s =  1 b +  B and D = s ln(s)  s (1+s) as Shannon Wiener Index The matrix ”  ” and the vector ”  ” can be thought as a probability function, both depicted as a Markov process or cellular automate. Species diversity is translated into risk of crop failure  =  oj +  1j Das stochastic variable Since, species need support by multiple habitats b, or field margins, a linear combination  guarantees a composition of habitats that supports ”s”, whereas s'= [s 1,s 2,...,s i,...,s 1n ] is a vector of species appearance). In terms of interest of residents as members of the community, diversity ”D” is a public good, being non-rival and -exclusive. A broad range of nature elements such as oak trees, etc. should be included.

7. Farmers and voluntary field margin provision for an EMS The objective function of a representative farmer in field margin provision corresponds to a constrained optimization: Profit= (-) (+) (-) (-) (+) where: increase: ”  ” and decrease ”  ” : p j = gross margins per hectare, (profit  ) l ij = size of the field i on farm j, area cropped, (profit  ) C(.)= cost function on quantity of q ij at field l ij b j = field margins, individual cost reducing effect by biological activity (cost  =>profit  )  = crop risk level or reduction due to community’s EMS and (cost  =>profit  ): stochastic r ij = pesticide costs (profit  ) The profit function can be easily altered to an expected profit.

8. Introducing the ecological constraint ”  ” profits on an individual farm can be expressed as dependent on individual allocation ”b j ” of field margins and communal achievement B: Will a community of farmers may decide on B. Will individual optimization behavior go for the b j ’s. We look at the optimization by setting the first derivatives 0: Also, purchases of pesticides are contingent on B.

9. Diagram 2: Farmers‘ individual willingness to contribute

10. Complete bargaining equilibrium The model of the bargaining centers around Harsanyi‘s multiple agent model. Diagram 3: Bargain structure

11. A interior solution, to be derived, is similar to the one prescribed by Rausser and Zusman (1992), resulting in a weighted objective function (logarithmic presentation). The weights w 1,..., w j..., w m correspond to the ratio of achievements in the bargaining process (optimal interest function in the bargaining process). Weights can also be expressed as the first derivative of the strength or power in bargaining, that is acquired from the threat strategy not to co-operate). Optimization provides the vector b, land allocation: EMS, in the community. Habitats, biodiversity and risk of crop failure are related phenomena.

12. Diagram 4: Bargaining solution and modified willingness to contibute after bargaining

13. Summary and Outlook A common property management of biodiversity can be a substitute for market transactions in risk reduction as associated with crop failure. Reduced Risk from biodiversity reduces expenditure for pesticides. We outlined a spatial framework for investigating collective decision making in a community of farmers to reduce crop failure by promoting biodiversity through an EMS. We analysed how the tragedy of the commons may prevail in the indivi du- al calculations of farmers and preferences for purchase of pesticides. Farmers have the alternative of accepting higher costs due to purchase of pesticides or contribute to set-aside land to an EMS. We sketched how a social optimum of field margin provision can be reached by multilateral bargaining with a common property manager. In pursuing the idea of a public good manager for risk, he may be entitled to charge individual contributions to beneficiaries and guarantee compensation payments for providers of nature. In the given solution farmers’ risk and manager’s interests are considered simultaneously. The manager receives informal gifts.