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Recently there has been increased interest in accelerated depreciation as a policy tool that could induce firms to invest more and so lead to faster growth rates of productivity and output. These issues have been discussed at various times in the past with some ambiguous conclusions, but with the consensus being that the goal of increased investment (at least) would likely follow its introduction. In this paper, it is shown that in the context of a neo‐classical production model of the firm, accelerated depreciation schemes will not necessarily lead to increased investment, which is the general result of the analysis. The technique used shows how sufficient conditions may be obtained for accelerated depreciation to result in increased investment. The models that are used are relatively uncomplicated. In the first part of the paper it is assumed that the time horizon of the firm is only one period, although final capital stock is explicitly included, and in the second part of the paper the model is extended to a two period horizon. To extend the planning period of the firm further, perhaps to infinity or some general period, “T”, would simply require an increased use of symbols and an increase in the complexity of the process. It would not change the basic result of this paper, which shows that increased investment does not necessarily follow from accelerated depreciation, ceteris paribus.