Análisis de las tipografías aplicadas a los packs

Figure (2.4) shows optimal abatement rates for Scenario I for the bonding and liability policies compared to the no bankruptcy case from Chapter 1. Recall that for the solvent firm, the bond and liability policies give identical results. The figure is plotted for p =$2 and full reserves at time zero. We observe that optimal abatement rates increase with the waste stock for all three cases. As the level of waste gets closer to its maximum level, the firm must abate at a higher rate in order to maintain production capacity. The firm’s abatement rates converge as the landfill capacity constraint binds. However, there is an obvious gap between such rates with the solvent firm having the highest abatement rates, followed by the bonding policy and then the strict liability rule under Scenario I. Recalling from Chapter 1, the marginal rule for abatement under each policy is given by

− C0a(a∗) = ∂V

∂w − 1b=true θ(w) ⇒ (

0 ≤ a∗ ≤ ¯a if w < ¯w

φ¯q ≤ a∗ ≤ ¯a if w = ¯w. (2.19)

0 500 1000 1500 2000 2500 0 20 40 60 80 100 120 Waste Pile Abatement rate

Optimal abatement at p₀=2, Scenario I deterioration rate

Liability, k 0= 0.1

Bond, k 0= 0.1 Bond & liability,

k

0= 0 (solvent firm)

Figure 2.4: Optimal abatement rates in Scenario I under the bonding and liability policies, at time zero, p0 = $2, and s0= 1173 million pounds.

rule does not include the full restoration costs of waste generated by extraction as future clean-up costs may be avoided through bankruptcy. Consequently, the firm’s marginal cost of environmental deterioration, ∂V_∂w − 1b=true θ(w), is higher under the bond than the

liability, leading to higher abatement efforts with bonding requirements. This result is in contrast with equal abatement rates that we have observed in Chapter 1 for the solvent firm.

We have discussed in Chapter 1 that dV_dw for a solvent firm operating under the liability rule reflects the cost of using up capacity in the landfill as well as adding to future clean-up costs. Under the bond, because the clean-up cost is paid immediately, this term for the solvent firm reflects the cost of using up capacity net of the marginal clean-up benefit and any interest paid. It follows that the solvent firm exercises the same abatement under both policies. When bankruptcy is possible, dV_dw reflects the cost of using up capacity in the landfill as well as the impacts of bankruptcy on the eventual clean-up cost/benefit under each policy. The value of having spare capacity in the landfill is reduced as the firm might go bankrupt and be unable to use this capacity. It follows that abatement is less valuable

0 500 1000 1500 2000 2500 0 20 40 60 80 100 120 Waste Pile Abatement rate Optimal abatement at p 0=2, Scenario II deterioration rate Liability, k₂= 1.5x10−4 Bond, k₂= 1.5x10−4

Bond & liability, solvent firm

Figure 2.5: Optimal abatement rates in Scenario II under the bonding and liability policies, at time zero, p0 = $2, and s0 = 1173 million pounds.

to the firm, and optimal abatement rates are reduced compared to a solvent firm. The lowest abatement rates are for the strict liability rule, because under bankruptcy the firm would avoid its eventual clean-up costs altogether.

Another way to interpret the optimal abatement decisions when bankruptcy is possible is to observe that the hazard rate, λ(·), increases the effective discount rate in Equa- tion (2.15). This implies that the firm cares less about future benefits and costs. Under both policies, the firm generates more waste today as it puts less weight on the future impact of the loss in landfill capacity. For the liability case, it also puts less weight on the future clean-up costs triggered by project termination.

Optimal abatement under Scenario II for the bond and liability policies compared to the solvent firm are shown in Figure (2.5). The most obvious difference of Scenario II with Scenario I and with the solvent firm is that the optimal abatement levels first decline and then increase with the waste stock. In addition, at low waste levels, the optimal abatement rates are initially higher than for the solvent firm, but then drop below the solvent firm at higher waste levels below full capacity of ¯w.

For intuition we can identify two effects that account for the shape of the optimal abatement curve, depending on which effect dominates. First, the optimal abatement rate will tend to rise with the waste stock in order to maintain capacity in the landfill for future production. This effect explains why optimal abatement rises with the waste stock for the solvent firm, as well as for the Scenario I cases. In Scenario II, there is a second effect to consider in that the firm is able to reduce the probability of bankruptcy through abatement. In this case, the impact on optimal abatement choices depends on the level of waste stock. At low levels of waste, the value of the project is relatively high (under both the bond and liability cases) so it is beneficial for the firm to reduce bankruptcy risk. However, this benefit declines with waste accumulation as the effective discount rate increases with λ(·), meaning the firm is less concerned with value from future production. At low levels of waste, this second effect dominates. Thus, we see optimal abatement rates for the bond and liability cases decline as w increases, but are higher than for the solvent firm. However at some point, the first effect starts to dominate and optimal abatement increases with w and falls below the optimal rates for the solvent firm. Finally at the maximum ¯w, if the firm chooses to produce copper, the abatement level must be equal to the deterioration rate. As a result, the abatement choices of the three cases converge at w = ¯w. Similar to Scenario I, the optimal abatement rate for the liability case is always lower than for the bond since bankruptcy allows the firm to escape clean-up costs under the strict liability rule.

Note that a higher λ(·) due to a higher k0 in Equation (2.5) and a higher k2 in Equa-

tion (2.6) further reduces the optimal abatement rates, under both policies. These results are shown in AppendixB.2 using a sensitivity analysis on these parameters.

The decreasing pattern of optimal abatement under the bond in Scenario II depends on the parameters of the clean-up cost function. As the restoration becomes costlier at all levels of waste – i.e., a higher β in Table2.2, bankruptcy hurts the firm more than the base-case parameters. Consequently, the firm abates progressively as waste builds up to post a lower bond. Creating a smaller quantity of waste reduces the risk of bankruptcy through λ(p, w) so that with a higher probability the firm will receive the clean-up benefit. Therefore, for a sizable restoration cost, the optimal abatement path has an increasing pattern at all levels of waste in Scenario II. This case is shown in Appendix B.3 using a

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