Learning curve model

The learning curve model is the empirical observation that the cost (or labour-hours) per unit drops by a constant percentage every time cumulative production doubles. Make twice as many units and the per-unit cost falls to $s$ times what it was, where $s$ (the learning rate) sits between 0 and 1.

Wright’s learning-curve model at an 85% learning rate: $T_n=T_1{n}^{{\log }_{2}0.85}$.

The standard formula for the $u$-th unit’s cost:

$Z_u=K\cdot u^{{\log }_{2}s}$

where $K$ is the cost (or hours) of the first unit, $u$ is which unit you’re estimating, and $s$ is the learning rate. (Equivalently, ${\log }_{2}s=\log s/\log 2$.) An 80% learning curve has $s=0.8$: every doubling of cumulative output, the per-unit cost drops to 80% of its previous level. So unit 2 costs $0.8K$; unit 4 costs $0.64K$; unit 8 costs $0.512K$.

The learning curve was first observed for aircraft manufacturing in the 1930s (T. P. Wright, 1936). The original Wright’s law was an 80% curve for airframe labour-hours. The empirical observation has since been extended across many industries: semiconductors, solar panels, ships, ball bearings, generic manufacturing.

Why it works (intuition):

• Workers get faster as they repeat a task.
• Tooling, fixtures, and processes are refined.
• Defect rates fall, so less rework.
• Designs are simplified — features get removed once they prove unnecessary.

In engineering economics, learning curves matter for repetitive production: estimating total labour for a fleet of identical units, comparing a one-off design with a mass-produced alternative, forecasting cost reductions as production volume grows. Solar PV is the modern example. Costs have fallen on roughly a 20%-learning curve (each doubling of cumulative deployment cuts cost by 20%) for decades.

Caveats: the curve is empirical, not a guarantee. It captures historical patterns but extrapolation past current cumulative volume can fail. Step-changes in technology can break the curve (cheaper underlying physics, a new manufacturing process). And the curve runs on cumulative production, not per year of production, so a stagnant industry won’t move along it.

The learning curve is one input to Parametric cost estimation.