Global Warming Potential (GWP) is an index used to measure the relative accumulated radiative effect of a tonne of greenhouse gas (GHG) compared to that of a 'reference' gas (CO2). Due to the different lifetimes of the GHGs, the GWPs are often measured over a fixed and long period of time (usually 20, 100, or 500 years). The disadvantage of this time-approach is that the index may give a good indication of the relative average effect of each GHG or total radiative forcing over the chosen time horizon, but it may not describe accurately the marginal contribution of each GHG to the overall climate change at a particular point in time, and conditional on a particular climate change policy scenario which is being considered. In this paper, we propose an alternative approach which measures the relative contribution of each GHG to total radiative forcing more accurately and in accordance with the current policy context being considered. We suggest the use of a marginal global warming potential (MGWP) rather than the existing (total or cumulative) GWP index. The MGWP can be calculated accurately and endogenously within a climate model. This is then linked to the marginal abatement cost (MAC) of the gas, estimated within an economic model linked to the climate model. In this way the balancing of the benefits and costs associated with the reduction of a unit of emission of the GHG can be achieved more accurately. We illustrate the use of the new approach in an illustrative experiment, using a multi-sector multi-gas and multi-regional computable general equilibrium economic model (GTAP-E) coupled with a reduced form climate change model (ICLIPS Climate Model, or ICM). The results show that the new approach can significantly improve on the existing method of measuring the trade-offs between different GHGs in their contribution to a climate change objective.