Extend the model from section 12.4 by assuming that there are J (not necessarily symmetric) domestic and Jf (not necessarily symmetric) foreign firms.

(a) Derive the unilaterally optimal emission tax formula for this case.
Assume that both countries issue tradable permits, and that the permit markets of the two countries are separate.

(b) Set up the equation system that describes the world market equilibrium.

(c) Derive a formula for the optimal quantity of permits to be issued domestically.
Assume now that the pollutant is homogeneous and an international emission trading system is implemented.

(d) Set up the equation system that describes the world market equilibrium.

(e) Derive a formula for the totally optimal quantity of permits to be issued worldwide.

(f) Assume now that the pollutant is homogeneous, but permit markets are separate. Assume again there is only one representative firm in each country. Determine the optimal domestic response when the foreign government relaxes its environmental policy (i.e. if the foreign number of permits increases).

(g) Assume again both countries charge emission taxes. Determine the optimal domestic response to a foreign emission tax increase.

Data from section 12.4

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We now turn our attention to the large open economy case. As noted above, an open economy is large if it is able to affect world market prices by its domestic trade or environmental policy. The channel for this is a domestic output change in response to, for example, a change in an environmental policy instrument, which is large enough to affect the world price. Depending on the structure of environmental policy in the foreign country - i.e. prices or quantities - the domestic environmental policy may also have an indirect effect on foreign emission. As we will see, the choice of optimal unilateral domestic environmental policy therefore depends on how the foreign country manages its emissions. In what follows, we consider two major cases: (a) the foreign country uses an emission tax (with a zero tax rate as a special case); and (b) the foreign country sets an emissions cap.