Appendix 1
A formal analysis of the moral hazard problem (Latacz-Lohmann, 1998)
The decision to violate conservation agreements fits naturally into the framework of choice under risk. Risk arises because the probability of being caught in violation often is less than one. Therefore, an individual who violates an agreement stands either a chance of succeeding with the violation, and hence having increased wealth, or a chance of being caught and punished. In the exposition below, ? is a vector of variables describing agricultural technology. The management prescriptions involved in a conservation agreement are modelled as a quantity constraint, 
, imposed on certain aspects of agricultural technology. may include, for example, an upper limit on fertiliser or pesticide usage, a stocking rate limitation, or a provision to leave field margins uncultivated.
Define a contract violation as 
and assume that violations are detected with probability p. Next assume that the sanction imposed in case of detected violations, S( ?v), depends on the degree of the violation, with S' > 0. Finally, assume that a conservation grant, G, is paid on the understanding that 
during the period of the agreement and that G must be fully repaid in case of detected violation.
Imposing risk-neutrality, the farmer's decision problem can be modelled as discrete choice among the following three options, which provide distinct levels of expected income.
Option 1: 'Compliance'
(1) 
Option 2: 'Non-compliance gamble'
(2) 
Option 3: 'No participation'
(3) 
(which represents the farmer's reservation income)
?(·) denotes profits from farming (excluding the conservation grant); Y is total farm income (including the conservation grant); E is the expectation operator; ? * represents the features of the optimal, unconstrained, farming technology in the absence of a conservation agreement; and the indices C, NC and 0 indicate compliance, non-compliance and no participation, respectively. It is assumed that ?( ?*) = ?( ?v*) > ? ( ). Equality of ?(?*) and ?( ?v*) implies full violation of the contract, while inequality implies partial violation. Note also that the expected non-compliance income in expression (2) is evaluated at the optimal degree of violation, ? v*. This is the degree of non-compliance that maximises expression (2). In the remainder of this exposition, we will refer to 
as 'compliance costs', and to 
as 'violation benefits'.
Figure 1 is a graphical illustration of expressions (1) to (3). At payment levels below G1 in Figure 1, the farmer has no incentive to participate because unconstrained farming yields a higher income than participation. The segment [ G1, G2] pictures a range of payment levels in which a non-compliance gamble yields a higher expected income than both compliance and non-participation. Finally, compliance is likely to occur at payment levels beyond G2. Underlying Figure 1, as it is drawn, is the assumption that the probability of detection and the level of sanction are sufficiently low such that 
where G = 0. This inequality is required for the range labelled 'non-compliance gamble' to exist. It is obvious that this need not be the case. Higher levels of sanction and/or detection probability would remove the above inequality, thus eliminating incentives for non-compliance.
Figure 1: A geometrical illustration of the moral hazard problem
It follows, using the above model, that the regulator can manipulate four contract variables in order to prevent farmers from cheating. These are:
1. The probability of detection p, as just explained. Variations of the detection probability affect the slope of the E(Y NC) function in Figure 1.
2. The level of sanction S( ?v). Variations in S( ?v) will lead to parallel shifts of the E(Y NC) function.
3. The stringency of the management prescriptions . Changes in this characteristic will lead to parallel shifts of the Y C function in Figure 1.
4. The payment rate G. Since detected violations will, by assumption, involve the full grant being repaid, increases in G will act as an additional deterrent to non-compliance.
The critical levels of each of these contract variables can be determined by equating expressions (1) and (2) and solving for the variable of interest. This simple exercise (which is left to the reader) will show that the probability of detection, the size of sanction and the level of payment are perfect substitutes with respect to reducing non-compliance. A reduction in one of the variables can be compensated for by an increase in the other.