Interpreting/Deriving Wrights Law

[mikansang]

Hi there,

There is an equation which I am struggling to interpret what it means or how I would derive it. Wright's law is like Moores law and basically states that there is a learning curve associated with production. I.e. every time cumulative production doubles, the average cumulative time taken per unit is reduced by a 'learning rate' which is expressed as a %.

In Wright's Model, the learning curve function is defined as follows:

Y = aX^b

where:
Y = the cumulative average time (or cost) per unit.
X = the cumulative number of units produced.
a = time (or cost) required to produce the first unit.
b = slope of the function when plotted on log-log paper.
= log of the learning rate/log of 2.

The most I get is that b represents the rate at which the average time decreases, this cumulative rate is then multiplied by a to get an average rate at X. I don't understand how this is derived or the intuition behind the equation, even though it is a simple law to understand when explained, any help would be appreciated. Thanks!

 

[JeffM]

This is not my field, but Wright's Law is an empirical observation so you cannot derive or prove it mathematically. As for the intuition behind it, it simply states that as production increases people figure out how to produce more efficiently. I suspect that the law really conflates two things: (1) over time, individuals learn new things, and (2) in a literate and technological society with a mobile labor force, new knowledge is usually preserved and rapidly disseminated. I greatly doubt that Wright's Law applied to 9th century European agriculture.

I found some summaries of articles on line, but I suspect you will need to read actual journal articles for a deeper understanding.

Wright's Law

Wright's Law, formulated in 1936 by Theodore P. Wright, states that progress increases with experience — specifically, that each percent increase in cumulative production in a given industry results in a fixed percentage improvement in production efficiency.

itlaw.wikia.org

Wright's Law Edges Out Moore's Law in Predicting Technology Development

Economies of scale trump time as a factor in driving down costs, shows study of 62 different technologies

spectrum.ieee.org

The most sophisticated summary that I have seen (URL below) is one that recognizes that Wright's law itself is focused on inflation-adjusted unit costs, not time, and recognizes that to extend Wright's law into the future requires additional information about future rates of production and thus future demand.

Moore’s Law Isn’t Dead: It’s Wrong - Long Live Wright’s Law

If Moore’s Law is flawed, what is the best way to forecast a technology cost decline? Enter Wright's Law, which forecasts cost as a function of production.

ark-invest.com

 

[mikansang]

thank you!