234 DIDÁCTICA DE LAS CIENCIAS SOCIALES

I begin by assuming that the regulator knows: (a) the field level abatement costs, (b) the relation between abatement actions and reduced emissions , and (c) the true form of the ambient abatement action .13 The cost minimization problem faced by a regulator seeking to

minimize the overall abatement costs to meet the expected ambient reductions by choosing field- level abatement actions is:

∑ , , . . (3)

where shows that true field level abatement costs are used in solving the cost minimization problem. Next, consider the discrete change in the total abatement, / given that abatement action is adopted by the field defined as:

, ∆ (4)

where, ∆ is used to show the discrete nature of the set of abatement actions, and accounts for the fact that the abatement actions on other farms affect the impact of farm (Braden et. al. 1989;Lintner and Weersink 1999; Khanna et al. 2003). The first term of the right-hand side of equation (2) , , , captures the nonseparability and is associated with endogenous transfer or delivery coefficients (Khanna et al., 2003). The presence of nonseparability is what makes a trading program difficult to implement. Next, nonlinearity refers to the fact that impact depends on the abatement action, ∆ ( i.e. not being constant in ) (Shortle and Horan 2013).

The solution vector ∗ to the problem defined by equation (3) identifies for each field ∗, the least-cost abatement action assignment and thus implies an optimal amount of edge of field pollution ∗ ∗ , ∀ 1, … , farms and ∀ 1, … , available abatement actions. The total cost is given by ∗ _∑ ∗_{, , . An “*” is used to indicate that this is the least-cost} solution.

The first-best solution is achieved when the regulator has the ability to solve the problem defined by equation (3) in the presence of complete cost information. Additionally, I assume he has the ability to implement a command and control policy where he can mandate the abatement action ∗ ; however, it is unlikely for the regulator to have complete cost information.

The cost asymmetry can be overcome by pursuing incentive based policies that shift the burden of optimization from the regulator to private farmers such as PS and trading. The implementation of any of the incentive based policies requires a functional form for the

abatement function ) and for the relation between field level abatement actions ( ) and the expected edge-of-field abated emissions ( ).

Next, I consider how these different policies perform relative to the first-best by considering two different assumptions for the abatement function. First, I assume that the abatement function is defined as an exact combination of edge-of-field reduced emissions and a set of fixed and exogenously determined delivery coefficients. Next, I assume the abatement function is non-linear and non-separable in the individual field-level reduced emissions, but policies are implemented using an approximation that is a linear combination of individual edge- of-field reduced, and delivery coefficients where the delivery coefficients are fixed.

3.2.2. A linear and separable water quality production function ( ∑ )

First best, complete cost information, CAC and incentive-based policies

Suppose that a regulator seeks to achieve a given level of total ambient emissions reductions, ̅, and ambient function is exactly a linear combination of the individual edge-of- field reductions and a set of delivery coefficients. The delivery coefficients determine how much of the edge-of-field reductions contribute to the total abatement level. Moreover, it is assumed that the delivery coefficients are exogenously determined. According to earlier studies on air and water pollution, the abatement function can be expressed as an exact combination of delivery coefficients and site specific emissions (Montgomery, 1972). Assuming perfect cost information (the regulator and the farmers have the same cost information), this solution can be replicated

with the same outcomes in any number of ways: a command-and-control, a performance standard, and a permit trading setting.

Under command-and-control, each farm is mandated to adopt, ∗_{. Alternatively, the} environmental agency could require that each farm meets an individualized performance

standard ∗ ∗ ∗ _{. In this case, the farmer can choose the abatement action that minimizes} the abatement cost at field level:

, , . ∗ ₍₅₎ Another alternative is to rely on private optimizing behavior and to allow trading among farmers such that a total ambient emissions cap is met. As Montgomery (1972) demonstrated, an “ambient based permit system” where each firm is faced with an ambient cap such that the total ambient emissions reduction target is met can achieve the least-cost allocation.

In short, under perfect information on costs and farm-level emissions, and a linear and separable water quality production function, the three above mentioned regulatory approaches can be employed to achieve the least-cost solution. Another alternative is to rely on private optimizing behavior and to allow trading among farmers such that a total ambient emissions cap is met.

First-best, cost asymmetries, CAC and incentive-based policies

In reality, it is likely that while the farmer knows the true cost of their abatement actions, the environmental authority does not. Thus, the environmental authority is unable to identify the abatement actions cost efficient allocation. However, the regulator is likely to have some limited information on the distribution of costs, such as the mean of the abatement costs. I assume that

the regulator knows the vector of average costs for each abatement action. In this case, the regulator solves the following problem:14

∑ _, , ̅ . . ∑ , (6)

where, denotes that the regulator uses his best estimates of costs (i.e. average estimates of the costs) and the total cap is set at the ∑ ̅. The solution to this problem, denoted by “ ”, will generally differ from that obtained in solving equation (4), and the assignment of abatement practices, , will not necessarily coincide with the least-cost solution, ∗. Likewise, the edge-of-field emissions reductions, ̂ ̂ , will be different from the first-best, ∗

∗ ∗ _{. The total estimated cost of the regulator is given by: ∑ , , ̅ .}

Under a command-and-control policy approach, the solution imposed by the authority, ”, may not reflect the least cost allocation of abatement actions since individual farmers may have much lower or higher costs than the average cost estimates, which, if known by the regulator, could be used to more cost-effectively assign practices to fields. Nonetheless, the overall

abatement target, ̅, is met. The total cost of a command and control can be lower or higher than the regulator estimated costs:

∑ , , ∑ , , ̅ (7) In this case, the authority can potentially increase social welfare relative to a command- and-control assignment of conservation actions, by allowing firms to meet a performance standard, ̂ , set at a similar level as in CAC. Since farmers know their true costs, they may

14 _{In the case of abatement costs being nonlinear in , a smart regulator would want to minimize}

the expected costs by taking into account the distribution of the farmers’ type. However, given that I consider that enters in a linear way, minimizing the sum of total costs evaluated at the average farm leads to the same interpretation.

be able to meet the standard allocated to them with less total costs by choosing a different

abatement action. In the presence of a performance standard program, farmers face the following optimization problem:

, , . ̂ (8) Farmers minimize the abatement costs given the field level abatement costs, subject to a performance standard based on average estimates of true costs. The solution is given by

, and the corresponding costs, ∑ , , . Again, a clear

comparison with: ∑ , , ̅ , the regulator estimated costs, cannot be made, however, there are cost savings relative to ∑ , , , the total costs under a command-and- control.

Additional cost savings are potentially achievable if the environmental authority makes the performance standard tradable. The farmer minimizes the abatement costs by choosing an abatement practice and the number of permits to trade, such that the total reductions measured at the edge-of-field level are less than the amount allowed by the number of permits held after trading. Let be the th farm’s abatement permit requirement. Then, a farmer solves:

, , , . (9) and the permit price is determined in a market equilibrium where ∑ 0. Indeed, when the performance standard is fully tradable, the least-cost solution would be achievable, as this would be equivalent to implementing Montgomery’s (1972) ambient-based permit system. Since by construction, ∑ ̅, unfettered trading between firms who each know their own true costs will achieve the least-cost solution and the ambient environmental goal is satisfied.

When the regulator has limited information on the abatement costs and the water quality production function is characterized linear and separable, his optimal solution,

, , … , , does not coincide with the solution under performance standard or permit trading. However, the water quality goal will be achieved under any of the regulatory

approaches. Total costs across the three policy approaches will be lowest under a trading setting. The total costs of the regulator’s solution evaluated at the true abatement costs can be higher or lower than the total costs of the three approaches. The magnitude of the divergences is an empirical question.

First-best, no cost information, CAC and incentive based policies

In this case the regulator has no cost information but he has the ability to identify the combinations of abatement actions that achieves the water quality goal. Let the vector of

abatement actions by identified as a satisficing solution ; with ̅. Obviously the cost of implementing this solution via a command-and-control is likely to be very high. However, under a linear and separable production function with fixed and exogenously determined delivery coefficients, trading has the ability to achieve the first-best solution, with both the water quality target met and the abatement costs minimized.