Lueck miceli individuals can realize economies of enforcing exclusive rights to the asset. Equation (2.2) mplies that waste can be reduced simply by restricting access to the asset A contracting model can illustrate how common property can limit waste from the rule of capture.Contracting to form common property effectively creates a group that has exclu only to the group's size and the joint effort to exclude outsiders. In this setting, individuals ns rights to the resource. We assume that(contractual)agreement among group members pertains acting together can realize economies of enforcing exclusive rights to the asset, so we also assume the costs of excluding(or policing) non-members can be represented as p(n), where p'(n) <0andp"(m)>0. a simple and customary method of allocating use of common property is a rule that grants equal access to all members of the group(Ostrom 1990). Equal sharing of the asset avoids the explicit costs of measuring and enforcing individual effort(or use) but still creates an incentive for over use.Effort is not explicitly part of the common property contract'so each member chooses his own effort(xi) as he captures his share of the assets output(Y=f(xv again)in competition with other group members. The size of the group is chosen to maximize the wealth of the group subject to the constraint of aggregate effort(X )by members operating in a common property regime, and in recognition of the costs of excluding outsiders. Optimal group size is a tradeoff between increased resource use with a larger group and increased enforcement costs associated with a smaller group. Formally the problem is maxR=/∑mx(n)-∑m(wx(m)-p(m, where x f is the individuals solution to the problem in equation(2. 1). The optimal group size, no determines total effort and must satisfy the first-order necessary condition B0-∑((∑x)-)∠ dnp(n)=0 Equation (2.5)states that the gain from an additional member in terms of a marginal reduction in policing costs must equal the marginal reduction in aggregate rent from overuse of the resource The net present value of the common property resource is thus V=L R(x, ne"dt>0,where vs>y>v=0. While the value of an asset governed by common property is less than its first-best value, it could have greater value than private property depending on the magnitude of the policing cost and overuse effects The model is based on Lueck(1994). Also see Caputo and lueck(1994)and wagner(1995). Others us evolutionary game theory models(e.g. Sethi and Somanathan 1996) Common property might also be viewed as an output sharing contract with moral hazard. In this framework group members shirk as in a principal-agent model(see Lueck 1994). Evidence of both types of common property asset sharing(e. g, share access to a pasture)and output sharing(e.g share the cheese produced from cattle on the common pasture)-are found in the empirical literature Total effort is given by X =xneLueck & Miceli – Property Law 9 individuals can realize economies of enforcing exclusive rights to the asset. Equation (2.2) implies that waste can be reduced simply by restricting access to the asset. A contracting model can illustrate how common property can limit waste from the rule of capture.32 Contracting to form common property effectively creates a group that has exclusive rights to the resource. We assume that (contractual) agreement among group members pertains only to the group's size and the joint effort to exclude outsiders. In this setting, individuals acting together can realize economies of enforcing exclusive rights to the asset, so we also assume the costs of excluding (or policing) non-members can be represented as p(n), where p'(n) < 0 and p''(n) > 0. A simple and customary method of allocating use of common property is a rule that grants equal access to all members of the group (Ostrom 1990). Equal sharing of the asset avoids the explicit costs of measuring and enforcing individual effort (or use) but still creates an incentive for over use.33 Effort is not explicitly part of the common property ‘contract’ so each member chooses his own effort (xi) as he captures his share of the asset’s output (Y = f(Σxi) again) in competition with other group members. The size of the group is chosen to maximize the wealth of the group subject to the constraint of aggregate effort (Xc ) by members operating in a common property regime, and in recognition of the costs of excluding outsiders. Optimal group size is a tradeoff between increased resource use with a larger group and increased enforcement costs associated with a smaller group. Formally the problem is 1 1 max ( ( )) ( ( )) ( ) c n n c i i n i i i R f x n wx n p n = = =−− ∑ ∑ , (2.4) where c i x is the individual’s solution to the problem in equation (2.1). The optimal group size, nc determines total effort34 and must satisfy the first-order necessary condition 1 1 ( ( ) ) ' '( ) 0. c n n i i i i i R dx f x w pn n dn = = ∂ ⎡ ⎤ = − −= ∂ ∑ ∑ ⎢ ⎥ ⎣ ⎦ (2.5) Equation (2.5) states that the gain from an additional member in terms of a marginal reduction in policing costs must equal the marginal reduction in aggregate rent from overuse of the resource. The net present value of the common property resource is thus 0 ( , ) 0, c c rt V R x t e dt ∞ − = > ∫ where V* > Vc > Voa = 0. While the value of an asset governed by common property is less than its first-best value, it could have greater value than private property depending on the magnitude of the policing cost and overuse effects. 32 The model is based on Lueck (1994). Also see Caputo and Lueck (1994) and Wagner (1995). Others use evolutionary game theory models (e.g. Sethi and Somanathan 1996). 33 Common property might also be viewed as an output sharing contract with moral hazard. In this framework group members shirk as in a principal-agent model (see Lueck 1994). Evidence of both types of common property – asset sharing (e.g., share access to a pasture) and output sharing (e.g. share the cheese produced from cattle on the common pasture) – are found in the empirical literature. 34 Total effort is given by 1 c n c c i i X x = = ∑