The area under the learning curve is the primary source of value for KM, in any organisation that involves repeat activity.
Generally, when we do repeat activity, we tend to get better at what we do. Every time your organisation does a task or a project or an activity again, you get a little bit better, you do it a bit faster or cheaper, because you are gaining experience and knowledge.
At the bottom of the learning curve, you are doing the job at minimum cost and maximum efficiency. The only thing that you have at the end of the learning curve that you did not have at the start, is knowledge. Knowledge gained through experience.
So the area under the learning curve but above minimum cost (the yellow section in the picture above) represents money spent in on-the-job learning and knowledge acquisition (or alternatively, money wasted through lack of knowledge).
This area represents the value which knowledge management can help liberate.
If you can reduce the yellow area, you can create value by learning more quickly and more efficiently. The higher the cost, and the more times you repeat this activity, the greater the value you can access. Building a number of hospitals, drilling a number of offshore wells, making a number of big bids to corporate clients, creating a number of major new products; in each case the area under the learning curve can be tens or hundreds of millions of dollars.
You can liberate this value, and reduce the area under the curve, in one of two ways. You can use knowledge management to learn faster, and so decrease cost more rapidly. This is known as "learning while doing", and can involve the use of After Action reviews, Retrospects, and a Lesson Learning system.
Or you can access knowledge from elsewhere before you start, so that you start operating from a full state of knowledge. You learn before doing, using Peer Assists and other similar methods.
By reducing or eliminating the yellow area below the learning curve, you create value through knowledge management. In a well-metricated company, with good historical cost statistics, you should be able to demonstrate and measure this value.