We analyze the optimal accumulation of renewable energy (backstop) generating capacity in a capital-energy economy with exhaustible fossil fuels. The analysis rests upon graphical illustrations of optimal control considerations. Due to the exhaustibility of fossil fuels the relative profitability of backstop capacity vs. capital investments increases in time. Furthermore, it turns out that the optimal economic evolution and, therefore, the steady-state levels of capital, backstop capacity, and consumption crucially depend on the capital endowment. In particular, a sufficiently large endowment gives rise to the accumulation of an excess capacity. Furthermore, a high capital endowment allows to use the full production potential of the steady-state capital stock, so that there is no mark-up on backstop costs in the steady-state. In contrast, a low capital endowment may render capacity investments non-optimal, so that the conomy is in a poverty trap. Both cases are based on an intertemporal consumption trade-off. The lower the time preference rate the more benficial the trade-off and , therefore, the lower the critical capital endowment values.