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By introducing an exhaustible resource into an AK growth model, we can identify the determinants of the scale of green investment needs and its impact on capital accumulation dynamics. The role of green capital in the transition to a low-carbon economy depends, in particular, on the relative magnitudes of the elasticities of demand for polluting goods and of the substitutability between green capital and natural resources. The impact on the optimal savings rate also depends on the productivity of green capital and on the ability to adapt existing capital.