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From Wikipedia

Experience curve effects

Experience curve' re-directs here. For its use in video games seeExperience point.


Learning curve and learning curve effect

The experience of "learning curves" was first observed by the 19th Century German psychologist Hermann Ebbinghaus according to the difficulty of memorizing varying numbers of verbal stimuli. Subsequent learning about the complex processes of learning are discussed in the Learning curve article.

The experienced learning rates for exploratory discovery and development processes, for individuals and organizations, is more the focus of the main Learning curve article.

The rule used for representing the learning curve effect states that the more times a task has been performed, the less time will be required on each subsequent iteration. This relationship was probably first quantified in 1936 at Wright-Patterson Air Force Base in the United States, where it was determined that every time total aircraft production doubled, the required labour time decreased by 10 to 15 percent. Subsequent empirical studies from other industries have yielded different values ranging from only a couple of percent up to 30 percent, but in most cases it is a constant percentage: It did not vary at different scales of operation. Learning curve theory states that as the quantity of items produced doubles, costs decrease at a predictable rate. This predictable rate is described by Equations 1 and 2. The equations have the same equation form. The two equations differ only in the definition of the Y term, but this difference can make a significant difference in the outcome of an estimate.


\ Y_x = K x^{\log_2 b}


  • \ K is the number of direct labour hours to produce the first unit
  • \ Y_x is the number of direct labour hours to produce the xth unit
  • \ x is the unit number
  • \ b is the learning percentage


\overline{Y_x} = K\frac{\frac{1}{1+\log_2b}x^{1+\log_2{b}}}{x}


  • \ Y_x is the average number of direct labour hours to produce First xth units
  • \ x is the unit number
  • \ b is the learning percentage

The experience curve

The experience curve effect is broader in scope than the learning curve effect encompassing far more than just labor time. It states that the more often a task is performed, the lower will be the cost of doing it. The task can be the production of any good or service. Each time cumulative volume doubles, value added costs (including administration, marketing, distribution, and manufacturing) fall by a constant and predictable percentage.

In the late 1960s Bruce Henderson of the Boston Consulting Group (BCG) began to emphasize the implications of the experience curve for strategy.

Research by BCG in the 1970s observed experience curve effects for various industries that ranged from 10 to 25 percent.

These effects are often expressed graphically. The curve is plotted with cumulative units produced on the horizontal axis and unit cost on the vertical axis. A curve that depicts a 15% cost reduction for every doubling of output is called an â€œ85% experience curveâ€�, indicating that unit costs drop to 85% of their original level.


  • \ C_n = C_1 n^{-a}


  • \ C_1 is the cost of the first unit of production
  • \ C_n is the cost of the nth unit of production
  • \ n is the cumulative volume of production
  • \ a is the elasticity of cost with regard to output

Reasons for the effect


NASA quotes the following experience curves:



Learning curve



Learning curve in psychology and economics



Broader interpretations of the learning curve


Common terms







Yield curve

Not to be confused with Yield-curve spread - seeZ-spread


The yield of a debt instrument is the overall rate of return available on the investment. For instance, a bank account that pays an interest rate of 4% per year has a 4% yield. In general the percentage per year that can be earned is dependent on the length of time that the money is invested. For example, a bank may offer a "savings rate" higher than the normal checking account rate if the customer is prepared to leave money untouched for five years. Investing for a period of time t gives a yield Y(t).


The yield curve function Y is actually only known with certainty for a few specific maturity dates, while the other maturities are calculated by interpolation (seeConstruction of the full yield curve from market data below).

The typical shape of the yield curve



The opposite position (short-term interest rates higher than long-term) can also occur. For instance, in November 2004, the yield curve for UK Government bonds was partially inverted. The yield for the 10 year bond stood at 4.68%, but was only 4.45% for the 30 year bond. The market's anticipation of falling interest rates causes such incidents. Negative liquidity premiums can exist if long-term investors dominate the market, but the prevailing view is that a positive liquidity premium dominates, so only the anticipation of falling interest rates will cause an inverted yield curve. Strongly inverted yield curves have historically preceded economic depressions.




Types of yield curve



Horizontal plane







Practical use in daily life




From Yahoo Answers

Question:Here is my question that I have NO IDEA how to answer :P It would be great if you could help me out, thank you! A ball is thrown out of a window at a horizontal speed of 20 m/s. The window is 45 metres from the ground. The ball has a mass of 6.2 kg. Assume that gravitational acceleration of 9.8 metres per second squared. How much horizontal distance, in centimetres, will the ball travel from the house before hitting the ground?

Answers:Treat x and y separately (break it down to components) First solve for t Yf=Yo + vt + 1/2*a*t^2 0=45m + 0*t + 1/2(-9.8)t^2 -45/-4.9 = t^2 t = 3.03 s to hit the ground Then solve for x Xf=Xo + vt + 1/2*a*t^2 Xf=0 + 20(3.03) + 0 Xf = 60.6 m ---> convert to cm **mass has nothing to do with it

Question:How do i find the intersection of two lines (one following y=ax^2+bx+c and the other y=ax+b) with a calculator or other technology. I know how to do this by calculating, but is there any way i can just insert these into a calculator or something and get the answers...?

Answers:You can use matlab or excel. You specify the constants,the equations, set an interval for x to run and just set the two equations equal to each other. You may need a "for" loop and a logic function in the end (outside the loop) that is "yes" when they intersect and "no" when they don't. e.g. y1=ax^2+bx+c y2=ax+b a=.. b=.. c=.. for 0
Question:I am studying for upcoming exams. And in previous exams you need to calculate the horizontal speed of a ball, and later it asks "Identify the assumption needed to calculate vertical acceleration" Answers will be much appreciated

Answers:My guess is effect of air resistance can be ignored so vertical acceleration depends only on gravity.

Question:I do not know the function of the normal distribution curve used to calculate z- scores and their corresponding area under the curve as percentiles.. Is it something like f(x) = ln(x) or something --> i know thats not it just providing a template for the answer i have been searching for. From there i need to find the definite integral from - infinite; to -2, for x, i know this should be .05 i just need the function to perform the equation/proof for an upcoming test, and i know how to find the definite integral i just had a question about the function

Answers:Refer to this link to think about the normal distribution curve: http://www.netmba.com/statistics/distribution/normal/ You will need this to answer your problem! Make sure to know how you will approach this problem.

From Youtube

Horizontal and Vertical Tangent Lines to Polar Curves :This video explains how to determine the points on a polar curve where there are horizontal and vertical tangent lines. mathispower4u.yolasite.com

25. Adding Demand and Supply Curves Horizontally :This video demonstrates the concept of summing horizontally to obtain market demand and supply curves using a concrete example. In particular, I show how to aggregate the demands of two types of consumers to a market demand, and how to aggregate the supply curves of identical firms to a market supply. At the end, I find the equilibrium price and quantity. The video is a nice application of various tools in the microeconomist's toolkit. For a complete listing of my videos, check out my video website: sites.google.com