Based on the R＆D model, this paper presents a model with exhaustible energy, environment threshold and abatement spending input. The method of optimal control is employed to obtain the balance growth solutions. Further, the characteristics of the prerequisites to sustainable development are discussed according to these solutions, that is, what dynamic relations must be satisfied between economic growth and the rate of energy exhausting, the proportion of investment in abatement. These relations supply an altemative theoretical criterion when assessing the effects of various energy policies