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Gross Capital Stock and Net Capital Stock: The Simplest Case

The Review of Economics and Statistics 1960 42(1), 94
IN a growing economy, current replacement falls short of depreciation. The implications of this fact were discussed at length in a paper by E. D. Domar.' The nature of the subject did not allow Domar to indicate the relationship between the two magnitudes in explicit form; in their place he had to present numerical illustrations. In the case of the individual firm, we can go one step further. Obviously a firm that buys its equipment first-hand will accumulate depreciation funds ahead of the replacement necessity. If the firm decides to reinvest the depreciation allowance, its gross or operating capital, in terms of performance, will increase for some time, although of course the value of the net capital stock by definition would remain constant. This is so because the performance of adequately maintained equipment declines less in proportion to depreciation. At the same time the average lifetime of the equipment items making up the gross capital stock will change. Since the initially installed equipment has to be replaced at some time, the rise in the gross stock from reinvestment of depreciation allowances will be interrupted discontinuously: the gross stock will suffer an abrupt decline, after which it will rise again. Let us give a simple illustration, the basic premises of which will be specified later on. Suppose a railroad invests at the beginning of I957 $IO million worth of rolling stock of a lifetime of exactly ten years, and applies straightline depreciation, amounting at the beginning to $i million per annum. It reinvests after the end of each year the depreciation allowance which was set aside in the preceding year, in rolling stock of the same kind. Assuming that prices do not change, the stock would grow as follows: Beginning of I957 $IO million I958 i i million I959 I2.I million, etc.