Learning Curve

A learning curve is a model that describes how the time, labor or cost required to produce each unit falls as cumulative output grows. The idea is that workers and organizations get faster and make fewer mistakes as they repeat a task, so the hundredth unit takes less effort than the first. The effect is usually expressed as a percentage: an 80 percent learning curve means that each time cumulative output doubles, the average time per unit falls to 80 percent of its previous level.

The concept was first described in 1936 by the aeronautical engineer Theodore Paul Wright, who observed that the labor hours needed to build aircraft fell predictably as production increased. It is now used in cost accounting, budgeting, pricing and capacity planning, particularly in industries with complex, labor-intensive products such as aircraft, ships, electronics and construction.

In the cumulative average model developed by Wright, the formula is:

• $Y$ is the cumulative average time (or cost) per unit.
• $a$ is the time (or cost) needed to produce the first unit.
• $X$ is the cumulative number of units produced.
• $b$ is the learning index, calculated as $\log(\text{learning rate}) \div \log 2$.

For an 80 percent curve, $b$ is the logarithm of 0.8 divided by the logarithm of 2, which is about negative 0.322. A lower learning rate means faster learning: a 70 percent curve shows more improvement than a 90 percent curve.

A shipyard builds a specialized vessel. The first unit takes 1,000 labor hours, and experience suggests an 80 percent learning curve. The results are:

The eight vessels together need 4,096 hours, not the 8,000 hours a simple estimate based on the first unit would suggest. At a labor rate of $60 per hour, the difference is about $234,000 of direct cost. Units five to eight need 4,096 minus 2,560, or 1,536 hours, an average of 384 hours each.

• Budgeting: a flexible budget that ignores learning will overstate labor costs for later units and understate them for early ones.
• Standard costs: labor standards set from early production will produce large favorable variances later, so standards are often revised as learning takes place.
• Pricing and bidding: contractors bidding on a multi-unit order can quote a lower average price because they expect later units to be cheaper, though they must still fund the early losses.
• Make or buy and capacity decisions: expected learning affects whether an in-house process will become competitive with an outside supplier over time.

Learning curve effects interact with cost behavior analysis and cost-volume-profit planning, because labor costs that are treated as purely variable costs actually fall per unit as volume rises. Variances against a static labor standard should therefore be interpreted with the expected learning in mind, as part of normal budget variance review.

Learning eventually slows and stops, often once a process becomes highly automated, so the curve tends to flatten after many thousands of units. It also applies mainly to labor-intensive work; machine-paced operations show little learning. Staff turnover, long production breaks and design changes can push a business back up the curve. The learning curve is related to, but different from, economies of scale: scale effects come from producing more at one time, while learning effects come from accumulated experience over time. The broader experience curve, popularized by the Boston Consulting Group in the 1960s, applies the same idea to total costs rather than labor alone, and also influences estimates of marginal cost in strategic pricing.