First-best

Table 10.2 Test results. The values refer to the points of time at which the first-best solution was found, the total effort to terminate was nearly the same (5 10 nodes). Times are in seconds, initial quantities of S0 are in tons, objective values (mspan) are in time units and the overproduction (op) is measured in tons.

A (red), 2SA (green) and lOA (purple), while naphthalene represents a unique group which has only the first best volume , equal to the total hydrophobic volume, and zero for the second and third ones. 

This chapter assesses the combination of maximum acceptable concentrations (MACs) and product-specific bans (PSBs) used by regulators. First, it analyses whether this approach is near optimal , in the sense of approximating the ideal first best , in which a social planner has full knowledge of aU aspects of the problem, and in particular the damages associated with chemical use. ft then analyses the opportunities... 

The first step is to define the ideal mentioned above. This will be taken as the choices of a social plaimer who is fully informed about aU aspects of the problem. This includes the benefits derived by society from the use of agricultural chemicals, the cost of their production, and the dynamics of environmental degradation, for both present and future generations. The critical piece of information for the analysis, however, is the social damage done by chemical use, or, equivalently, the social utility derived from an uncontaminated environment. The first best social plaimer (which will be denoted as FB) knows social damages from chemical use and incorporates them fully into her choices. 

The social planner maximises the discounted sum over time of social utility from chemical use. Utility is defined as the total surplus (area under the inverse demand curve) minus production costs from a good (in this case, agricultural chemical). In the first best, surplus is derived from two factors - use of the chemical, and the stock of environmental quality. Hence [/FB = [/fb(q 5) where Uis the social utility function, Q is total chemical use, and S is the amount of environmental quality. The inclusion of S in the... 

Fig. 8.1. Sales ofthe polluting chemical by the first best and ignorant regulator case 1.

Consider now the second question how does use of the first chemical in IR s policy compare to the first best Again, the answer to the question depends on how the MAC level S compares to the extent of first best environmental preservation S . Figure 8.1 plots sales of the polluting chemical x t) on the vertical axis against time on the horizontal axis for both FB andIR. (The formeris labelled x (t), the latter x (r).) Itshows the case where S = S , so that T" < T . The area under the x(t) schedule and above the line y must equal the total polluted resource stock Because T and = x (P ), it must be that the sales sched-... 

The methods require the use of a fit algorithm (first, best, or worst fit, as described in Section IV.D) initial allocation of space will require time while an appropriately sized area of free space is located. 

Before we conclude this section, it is also worthwhile to introduce and summarize the terminology we will be using in the remainder of this chapter. A compensation system is said to induce or implement an action if that action represents the agent s optimal choice. Such action is called incentive compatible. A pair that consists of a compensation system and an action is called a contract. Such a contract is feasible if the prescribed action is incentive compatible and if the compensation system satisfies the participation constraint. The optimal contract is the pair (not necessarily unique) of a compensation system and incentive compatible action that maximizes the principal s expected payoff and satisfies the participation constraint. The action prescribed in the optimal contract is called second-best as opposed to the so-called first-best action that is optimal when the agent s action is observable by the principal. 

To explore the effect of information asymmetry on service level, we can compare the second-best service intensity a, which is optimal when the agent s actions are not observable, to the first-best intensity, that maximizes the principal s objective when the agent s actions are observable the first-best service strategy delivers the same service level, the so-called first-best level, in each period and state. The first-best service level is obtained by maximizing the principal s payoff per customer when the cost of service is the actual cost g a) and not the induced cost J [s a) ph cl)s a) PD (i)s a)] used... 

In addition, the first-best service level coincides with the second-best one either when r = 0, or when a = 1. In both cases, the tension between incentives and... 

The rest of the chapter is organized as follows. In the next section, we provide a survey of the relevant literature. Section 3 outlines the notation and modeling assumptions. In Section 4, all three models are presented and in Section 5, we show that none of the channel coordination mechanisms described in the literature can achieve a first-best solution. Optimal coordinating contracts are also proposed in this section. Section 6 contains numerical experiments, and in Section 7 we wrapup the chapter with a discussion of managerial insights and conclusions. 

The first and most natural response to some emergency is a moment of panic, particularly if you fear that your own safety is in jeopardy. So, the first, best response is simply to recognize that moment of panic, take a deep breath to calm down (a bit), and then decide how to respond. 

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