Editing Learning curve (section)

==In economics==

=== History ===
[[File:Learning curve cycle.png|thumb|]]
In 1936, [[Theodore Paul Wright]] described the effect of learning on [[production costs]] in the [[aircraft industry]] and proposed a mathematical model of the learning curve.<ref name="Wright, T.P. 1936"/>

In 1952, the US Air Force published data on the learning curve in the [[airframe]] industry from 1940 to mid-1945.<ref>Air Materiel Command Wright-Patterson AFB OH. "[https://purl.stanford.edu/dg041ny3484 Source Book of World War II Basic Data-Airframe Industry. Volume 1. Direct Man-Hours-Progress Curves]." (1952): 0201.</ref> Specifically, they tabulated and plotted the direct man-hour cost of various products as a function of cumulative production. This formed the basis of many studies on learning curves in the 1950s.<ref>Asher, H. (1956). ''Cost-quantity relationships in the airframe industry'' (Doctoral dissertation, The Ohio State University).</ref>

In 1968 [[Bruce Henderson]] of the [[Boston Consulting Group]] (BCG) generalized the Unit Cost model pioneered by Wright, and specifically used a [[Power Law]], which is sometimes called ''Henderson's Law''.<ref>{{Cite web |title=What is Henderson's Law? |url=http://www.davidrusseltrask.com/what-is-hendersons-law |website=Henderson's Law |language=en-US |access-date=2020-06-02}}</ref> He named this particular version the '''experience curve'''.<ref>
Henderson, Bruce (1968-01-01) [https://www.bcgperspectives.com/content/Classics/strategy_the_experience_curve/ The Experience Curve]. ''Boston Consulting Group''</ref><ref name="Grant2003">{{Citation |last=Grant |first=Robert M. |title=Contemporary strategy analysis |year=2004 |publisher=Blackwell publishing |location=US, UK, Australia, Germany |isbn=1-4051-1999-3 |url-access=registration |url=https://archive.org/details/contemporarystra00gran_4 }} <!-- note first published in 1991 --></ref>
Research by BCG in the 1970s observed [[experience curve effects]] for various industries that ranged from 10 to 25 percent.<ref name="HaxMajluf">{{Citation
  | last1 = Hax
  | first1 = Arnoldo C.
  | last2 = Majluf
  | first2 = Nicolas S.
  | title = Competitive cost dynamics: the experience curve
  | journal = Interfaces
  | volume = 12
  | issue = 5| pages = 50–61
  | date = October 1982
  | doi = 10.1287/inte.12.5.50 | s2cid = 61642172
 }}</ref>

=== Models ===
[[File:Learning curve models- Wright, Plateau, Stanford-B, DeJong, S-curve.svg|thumb|307x307px|The main learning curve models on a log-log plot. Wright, Plateau, Stanford-B, DeJong, S-curve.]]
The main statistical models for learning curves are as follows:<ref name=":0">{{Cite journal |last=Yelle |first=Louis E. |title=The Learning Curve: Historical Review and Comprehensive Survey |date=April 1979 |url=https://onlinelibrary.wiley.com/doi/10.1111/j.1540-5915.1979.tb00026.x |journal=Decision Sciences |language=en |volume=10 |issue=2 |pages=302–328 |doi=10.1111/j.1540-5915.1979.tb00026.x |issn=0011-7315|url-access=subscription }}</ref><ref>{{Cite journal |last1=Anzanello |first1=Michel Jose |last2=Fogliatto |first2=Flavio Sanson |date=2011-09-01 |title=Learning curve models and applications: Literature review and research directions |url=https://www.sciencedirect.com/science/article/pii/S016981411100062X |journal=International Journal of Industrial Ergonomics |language=en |volume=41 |issue=5 |pages=573–583 |doi=10.1016/j.ergon.2011.05.001 |issn=0169-8141|url-access=subscription }}</ref>

* Wright's model ("log-linear"): <math>y = Kx^n</math>, where 
** <math>y</math> is the cost of the <math>x</math>-th unit, 
** <math>x</math> is the total number of units made,
** <math>K</math> is the cost of the first unit made,
** <math>n</math> is the exponent measuring the strength of learning. 
* Plateau model: <math>y = \max(Kx^n, K_0)</math>, where <math>K_0</math> models the minimal cost achievable. In other words, the learning ceases after cost reaches a sufficiently low level.
* Stanford-B model: <math>y = K(x+B)^n</math>, where <math>B</math> models worker's prior experience.
* DeJong's model: <math>y = K(M + (1-M)x^n)</math>, where <math>M</math> models the fraction of production done by machines (assumed to be unable to learn, unlike a human worker).
* S-curve model: <math>y = K(M + (1-M)(x+B)^n)</math>, a combination of Stanford-B model and DeJong's model.

The key variable is the exponent <math>n</math> measuring the strength of learning. It is usually expressed as <math>n = \log(\phi)/\log(2)</math>, where <math>\phi</math> is the "learning rate". In words, it means that the unit cost decreases by <math>1-\phi</math>, for every doubling of total units made. Wright found that <math>\phi \approx 80\%</math> in aircraft manufacturing, meaning that the unit cost decreases by 20% for every doubling of total units made.

=== Applications ===
The economic learning of productivity and efficiency generally follows the same kinds of experience curves and have interesting secondary effects. Efficiency and productivity improvement can be considered as whole organization or industry or economy learning processes, as well as for individuals. The general pattern is of first speeding up and then slowing down, as the practically achievable level of methodology improvement is reached. The effect of reducing local effort and resource use by learning improved methods often has the opposite latent effect on the next larger scale system, by facilitating its expansion, or [[economic growth]], as discussed in the [[Jevons paradox]] in the 1880s and updated in the [[Khazzoom-Brookes Postulate]] in the 1980s.

A comprehensive understanding of the application of learning curve on managerial economics would provide plenty of benefits on strategic level. People could predict the appropriate timing of the introductions for new products and offering competitive pricing decisions, deciding investment levels by stimulate innovations on products and the selection of organizational design structures.<ref>{{Citation |last1=Abernathy |first1=W. J. |title=Limits of the learning curve |date=1974 |journal=Harvard Business Review |volume=52 |issue=5 |pages=109–119 |last2=Wayne |first2=K.}}</ref>
Balachander and Srinivasan used to study a durable product and its pricing strategy on the principles of the learning curve. Based on the concepts that the growing experience in producing and selling a product would cause the decline of unit production cost, they found the potential best introductory price for this product.<ref>{{Citation |last1=Balacahnder |first1=S. |title=Modifying customer expectations of price decreases for a durable product |date=1998 |journal=Managerial Science |volume=44 |issue=6 |pages=776–786 |doi=10.1287/mnsc.44.6.776 |last2=Srinivasan |first2=K.}}</ref> As for the problems of [[Manufacturing process management|production management]] under the limitation of scarce resources, Liao <ref>{{Citation |last1=Liao |first1=W. M. |title=Effects of learning on resource allocation decisions |date=1979 |journal=Decision Sciences |volume=10 |issue=1 |pages=116–125 |doi=10.1111/j.1540-5915.1979.tb00011.x}}</ref> observed that without including the effects of the learning curve on labor hours and machines hours, people might make incorrect managerial decisions. Demeester and Qi <ref>{{Citation |last1=Demeester |first1=L. L. |title=Managing learning resources for consecutive product generations |date=2005 |url=https://ink.library.smu.edu.sg/lkcsb_research/1060 |journal=International Journal of Production Economics |volume=95 |issue=2 |pages=265–283 |doi=10.1016/j.ijpe.2004.01.005 |s2cid=154822091 |last2=Qi |first2=M.}}</ref> used the learning curve to study the transition between the old products' eliminating and new products' introduction. Their results indicated that the optimal switching time is determined by the characteristics of product and process, market factors, and the features of learning curve on this production. Konstantaras, Skouri, and Jaber <ref>{{Citation |last1=Konstantaras |first1=I. |title=Inventory models for imperfect quality items with shortages and learning in inspection |date=2012 |journal=Applied Mathematical Modelling |volume=36 |issue=11 |pages=5334–5343 |doi=10.1016/j.apm.2011.12.005 |last2=Skouri |first2=K. |last3=Jaber |first3=M. Y. |doi-access=free}}</ref> applied the learning curve on demand forecasting and the economic order quantity. They found that the buyers obey to a learning curve, and this result is useful for decision-making on [[Field inventory management|inventory management]].

Learning curves have been used to model [[Moore's law]] in the semiconductor industry.<ref>{{Cite journal |last=Mack |first=Chris A. |date=May 2011 |title=Fifty Years of Moore's Law |url=https://ieeexplore.ieee.org/document/5696765 |journal=IEEE Transactions on Semiconductor Manufacturing |volume=24 |issue=2 |pages=202–207 |doi=10.1109/TSM.2010.2096437 |issn=1558-2345|url-access=subscription }}</ref>

When wages are proportional to number of products made, workers may resist changing to a different post or having a new member on the team, since it would temporarily decrease productivity. Learning curves has been used to adjust for temporary dips so that workers are paid more for the same product while they are learning.<ref name=":0" />