In management, models of the learning curve effect and the closely related experience curve effect express the relationship between equation and efficiency or between efficiency gains and investment in the effort.Examples In management, models of the learning curve effect and the closely related experience curve effect express the relationship between equation and efficiency or between efficiency gains and investment in the effort. 'Learning curves' were first described qualitatively in 1885 by the German psychologist Hermann Ebbinghaus, who was investigating the difficulty of memorizing varying numbers of verbal stimuli. Subsequent findings about the complex processes of learning are discussed in the Learning curve article. Experience shows that the more times a task has been performed, the less time is required on each subsequent iteration. This relationship was probably first quantified in 1936 by an engineer at Curtiss-Wright in the United States, where it was determined that every time total aircraft production doubled, the required labour time decreased by 20 percent. Subsequent empirical studies from other industries have yielded different values ranging from only a couple of percentages up to 30%, but in most cases it is a constant percentage: It did not vary at different scales of operation. The Learning Curve model posits that for each doubling of the total quantity of items produced, costs decrease by a fixed proportion. Empirical research has validated the following mathematical form for the unit cost, Px, producing unit number x starting with P1 for a wide variety of different products and services: where (1-b) is the proportion reduction in the unit cost with each doubling in the cumulative production. To see this, note the following: Of course, this is only a statistical average and will rarely if ever exactly predict the unit cost of producing any future product. However, it has been found to be useful in many contexts with b ranging from 0.75 to 0.9 in different industries (so 1-b ranges from 0.1 to 0.25, as noted elsewhere in this article).