A model of firm exit under inefficiency and uncertainty

This paper examines the impact of technical efficiency on the optimal exit timing of firms in a stochastic dynamic framework. While an extensive literature deals with exit behavior under output price uncertainty and efficiency of firms separately, the interplay of these two aspects has not yet been examined. Starting from a standard real options approach, we incorporate technical efficiency via a production function and derive an optimal price trigger at which firms irreversibly exit a market. The profit function in the optimization problem inherits properties from the production function by means of a dual Legendre transform. We consider two types of production technologies which differ in the way efficiency interacts with the primal technology. Assuming separability of efficiency on the primal technology, we show that higher efficiency and higher returns to scale make the firm more reluctant to irreversibly exit the market. We then extend this model to a case where efficiency is not separable from other inputs and derive explicit results from a Cobb-Douglas production function. Unexpectedly, we find that higher efficiency does not always increase the reluctance to exit if firms exhibit low returns to scale.