Unit Formulation

Unit formulation (or unit theory) states that as the quantity of units doubles, unit cost is reduced by a constant percentage. It is represented by the formula

Y = AX^b, where

Y = the cost of the X^th unit,

A = the first unit (T1) cost,

X = the unit number, and

b = the slope coefficient of the learning curve, defined as ln slope /ln 2

The rate of learning, b, causes the cost to decrease at a constant rate as the quantity produced doubles.

That is, if the slope is 80 percent, the cost of the second production unit is 80 percent of the cost of the first production unit, the fourth production unit is 80 percent of the cost of the second production unit, and so on. Simply stated, as the quantity doubles, the cost reduces by the learning curve slope. For example, assume the first production unit cost $1,000 and the learning curve is 80 percent:

b = ln slope / ln 2

b = ln 0.8 / ln 2

b = -0.322

Cost of the second production unit

Y = AX^b

Y = ($1,000)(2^-0.322) = $800

Cost of the third production unit

Y = ($1,000)(3^-0.322) = $702

Cost of the fourth production unit

Y = ($1,000)(4^-0.322) = $640