On the statistical origins of the learning curve

This paper presents a statistical rationale for the existence of the learning curve phenomenon. We consider a firm which allocates a fixed amount of input into several activities under uncertainty concerning the values of the parameters of the production function. It is shown, under fairly reasonable assumptions, that if the firm learns about the parameters of the production function from previous observations of allocations and outputs, then a learning curve phenomenon will emerge. This result occurs since the estimates of the parameters become more precise over time, and thus the allocation of the production factor into the various activities becomes more efficient (i.e. closer to the optimum allocation that would have been determined if the parameters were known with certainty). Output, therefore, increases and inputs per unit of output decrease as a function of time (and cumulative output), and a learning curve emerges. 'Plateauing' of the learning curve is discussed, as are the conditions sufficient for the existence of this phenomenon, for which the model presented herein is offered as a possible explanation.