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A simple model of discontinuous firm’s growth

D'Elia, Enrico (2011): A simple model of discontinuous firm’s growth.

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Typically, firms change their size through a row of discrete leaps over time. Sunk costs, regulatory, financial and organizational constraints, talent distribution and other factors may explain this fact. However, firms tend to grow or fall discontinuously even if those inertial factors were removed. For instance, a very essential model of discontinuous growth can be based on a couple of assumptions concerning only technology and entrepreneurs’ strategy, that is: (a) in the short run, the firm’s equipment and organization provide the maximum profit only for a given production level, and diverging form it is costly; and (b) in the long run, the firm adjusts its size as if the current equipment had to be exploited until overall profit exceeds the profit expected from the new desired plant at the current production level. Combining the latter two hypotheses entails a number of testable consequences, usually regarded as nuisance facts within the traditional theoretical framework. First of all, an upper bound constraints both investment and disinvestment. Secondly, the profitability is not a continuous function of the firms’ size, but exhibits a number of peaks, each corresponding to a locally optimal size. Thirdly, firms tend to invest when profit approaches a local minimum, corresponding to the lowest profit claimed by the entrepreneur. Therefore, firm’s level data would prove only weak statistical relationships among profitability, output and investment. Finally, the distribution of firms by growth rate is multimodal since, within each sector, every firm typically adjusts its size through the same sequence of leaps. There are a number of analogies between the firm’s growth process predicted by the model and some physical phenomena explained by the quantum theory.

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