This paper adopts pollution tax as governmental environment policy when facing cross-border pollution and pollution abatement technology with spillovers. Assume that the governments cooperate in environmental policy, and the firms consider to cooperate or non-cooperate in pollution emission abatement R&D.
We find that if one of the two firms invests in emission abatement R&D investment, in the regime of non-cooperative R&D, it will always raise its own output, but will raise (reduce) the output of its competitor when technology spillover rate is greater (smaller) than 1/2. If the spillover rate equals to 1/2, the change of emission abatement level by one of the two firms does not affect competitor’s output. In the regime of cooperative R&D, the outputs of both of the two firms will raise.
If the governments lift environmental tax in both of the non-cooperative R&D and cooperative R&D regimes, the outputs and profits of the two firms and the consumer surplus of the two nations will decrease when the R&D investment amount is large enough for the two firms. But the results reverse when the R&D investment amount is relatively small. The level of emission abatement is independent to the amount of R&D investment and always increases.
Considering the reaction of the two nations about the governments to lift environmental tax in both of the non-cooperative R&D and cooperative R&D regimes:
For domestic nation, the social welfare will deteriorate when the pollution damage is relatively small; the impact on social welfare cannot be determined exactly when the pollution damage is intermediate; and the government does not allow the firm in its domain to produce that kind of product when the pollution damage is high enough.
For foreign nation (product supply nation), the impact on social welfare cannot be determined exactly when the pollution damage is relatively small; the social welfare will improve when the pollution damage is intermediate; the government does not allow the firm in its domain to produce that kind of product when the pollution damage is high enough.
For the effects of technology spillover: In the non-cooperative R&D regime, if the spillover rate is relatively small, the two firms will produce more outputs, the market price will lower, and the social welfares of the two nations will improve while spillover rate is increasing. But these results reverse and the social welfares of the two
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nations become ambiguous when the spillover rate is relative high. In addition, the increasing spillover rate will induce the two firms to accrue less amount of emission abatement and earn higher profits. Yet, the profits of the two firms have reached their peaks before the technology is fully spilled over. In the cooperative R&D regime, the increasing spillover rate will induce the two firms to produce more outputs, earn higher profits, accrue more amount of emission abatement, and lower the market price;
The social welfares of the two nations will also improve. In both R&D regimes, we also find that higher pollution diffusing level will affect the social welfares negatively for the two nations while the pollution cross border.
Finally, this paper compares the difference between the two R&D regimes. It is shown that, under the situation of relative small (high) spillover rate, the domestic output, profit, emission abatement level, and social welfares in cooperative R&D regime are smaller (greater) than those in non-cooperative R&D regime. But, the price is greater (smaller) in cooperative R&D regime than that in non-cooperative R&D regime. Furthermore, the differences of domestic output, profit, emission abatement level, and social welfare are enlarged, and the difference of market price is shrunk as spillover rate increases.
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