Unilaterally optimal climate policy and the green paradox

Consider a Hotelling model with exploration investments, a backstop technology and two groups of countries, a climate coalition and a free-riding fringe.
If the coalition is price taker in the fossil fuel market, a higher marginal climate damage leads to a reduction of the coalition’s cumulative fuel consumption, which reduces the fuel price and, thus, induces carbon leakage. If the coalition is sufficiently small or its energy demand is sufficiently price sensitive, both the initial extraction and the cumulative discounted climate damages decrease (no weak/strong green paradox). This also applies if exploration investments are sufficiently productive, so that a lower fuel price leads to a considerably lower total extraction. If the coalition acts strategically in the fossil fuel market, it accounts for terms-of-trade and carbon-leakage effects. Then, a higher marginal climate damage can lead to an increase of the coalition’s cumulative fuel consumption, which prevents a weak green paradox, while a strong green paradox never occurs.
In an empirically calibrated economy, we show that a strong green paradox can occur without a weak green paradox and vice versa with a price-taking coalition. With a strategically acting coalition, a weak green paradox can be part of a unilaterally optimal policy reaction.