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 country experiencing a cost reduction can actually be worse off. This holds true for a variety of quantity and price-based emission policies. Under price-based policies, a country with lower abatement costs might engage 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 by 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 benefits energy importers because the value of fossil fuels is reduced. The opposite holds for a shock to CCS which benefits energy exporters. The channels identified in the theoretical model can be confirmed in a more complex global computable general equilibrium model. Some regions are indeed worse off from a shock that lowers their abatement costs.