Cumulative Average Formulation

Cumulative average formulation, or cumulative average theory, (CAT) is commonly associated with T. P. Wright, who initiated an important discussion of this method in 1936.⁷³ The theory is that, as the total quantity of units produced doubles, the cumulative average cost decreases by a constant percentage. This approach uses the same functional form as unit formulation, but it is interpreted differently:

Ῡ = AX^b, where

Ῡ = the cumulative average cost of X units,

A = the first unit (T1) cost,

X = the cumulative number of units, and

b = the constant slope coefficient of the learning curve (where slope equals 2b).

In cumulative average theory, if the average cost of the first 10 units is $100 and the slope is 90 percent, the average cost of the first 20 units is $90, the average cost of the first 40 units is $81, and so on.

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73. Wright, T.P., “Factors Affecting the Cost of Airplanes,” Journal of Aeronautical Science 3:4 (1936): 122-28; reprinted in International Library of Critical Writings in Economics 128:3 (2001): 75-81.↩︎