A simple model is used to illustrate the effects of a reduction in (marginal) abatement cost in a two country setting. It can be shown that a the country experiencing a cost reduction can actually be worse off. This holds true for a variety of quantity and price based emission policies. The most important channel is that a country with lower abatement costs engages in additional abatement effort for which it is not compensated. Under a quantity based policy with a given allocation, a seller of permits can also be negatively affected from a lower carbon price. We also argue that abatement cost shocks to renewable energy and carbon capture and storage (CCS) are different in terms of their effects on international energy markets. A shock to renewable energy reduces fossil fuel rents benefiting energy importers, while the opposite holds for a shock to CCS. The channels obtained in the theoretical model can be confirmed in a more complex global computable general equilibrium model. Some regions are indeed worse off from shock that lowers their abatement costs.