As A. Alchian points out, competition guarantees only that the efficient firm is more efficient than its rival, not that it achieves optimum conditions. Computer science and economics have strikingly different approaches to optimization problems. In computer science problems are characterized by the difficulty of computing a solution. Computer science recognizes a vast variation in the difficulty in solving optimization problems and the occasional impossiblity of arriving at an efficient solution. F. Knight realized this intuitively, and his ideas have since been made consistent with Bayesian statistics.
Businessmen frequently face very difficult problems.
One example is scheduling, which, in the most general case, is an NP problem. If we blithely assume that firms instantaneously optimize without cost, we cannot study the problem of innovation. For example, we have assumed away innovations in terms of better approximations to scheduling problems. As has been pointed out by H. Simon, the new microeconomics should examine business processes so that attention can be focused on innovation. If we assume that firms instantaneously optimize without cost, we cannot study the problem of innovation in the sense of finding better approximations to optimal conditions.