A model of firm exit under inefficiency and uncertainty

Analyzing the dynamics of structural change of an industry is a fundamental but challenging issue in economics. Accordingly, many attempts have been made to rationalize entry and exit decisions of firms, which, in total, appear as structural change of a sector. Among the most often hypothesized determinants of entry and exit behavior are (in)efficiency and uncertainty in conjunction with sunk costs of irreversible investments. According to the efficient market hypothesis competitive superiority discriminates among firms (Demsetz 1973). In the long run inefficient firms should be driven out of the market. In fact, inefficiency seems to increase the probability of exit. Among others, Wheelock and Wilson (2000) have shown that there exists a correlation between inefficiency and exit. However,many firms that are found inefficient persist in the market (Emvalomatis, Stefanou, and Lansink 2011). Another relevant strand of literature is the real options approach. Uncertainty and irreversibility generate a value of waiting which, in turn, leads to (dis)investment reluctance and economic inertia (Dixit and Pindyck 1994). Empirical evidence of the presence of real options effects has been provided, for example by Hinrichs, Musshoff, and Odening (2008). Both aforementioned explanations of firm’s entry and exit behavior have received extensive attention in the literature, but only separately. A joint treatment of these two aspects is the topic of this paper. We derive a model of firm exit under output price risk allowing for inefficiency of firms. To the best of our knowledge the interaction of inefficiency and uncertainty has not been analyzed so far in the framework of dynamic firm models. The consideration of inefficiency into the real options approach requires to introduce a production function. We do not impose a priori specific functional forms on the production function. We derive the properties inherited to the instantaneous profit function from the original production function by using a dual Legendre transformation. This allows deriving flexibly the substitution properties of the production function among multiple inputs and multiple outputs in a general setting. We derive two classes of profit functions imposing structure on the primal technology. The difference among the classes depends on how the inefficiency is considered. In the first class, inefficiency is considered separately from inputs and outputs, and acts as a shifter. In the second case inefficiency modifies the production function, directly interacting with inputs and outputs. Specific calculations to simulate the exit trigger prices are carried out on the particular case of a Cobb-Douglas production function. In both the separable and the non-separable classes inefficiency causes firms to exit from the market earlier compared with more efficient firms. Higher volatility of output price makes more reluctant the firms to decide to exit irreversibly the market. Higher unit costs, as well as a higher salvage value, decrease the reluctance to exit the market. Calculations are done for different hypothetical returns to scale cases, a higher and a lower one without qualitative difference in the findings. But these results show that, for the same price, it is possible to have a range of firms of different levels of efficiency and different returns to scale present in the market. Our model results generate a rich set of hypothesis that can be empirically tested, for example, in the case of German dairy sector.