Finding the right price point to maximize profits

For many months now - perhaps over 2 years - I've been telling some of my friends a simple formula (over lunch table, or during other casual discussions) that companies perhaps-already-use / should-use to correctly price their products / services in the market.

"Correctly" refers to that optimal price point which maximizes the total profit.

The simple formula states that if

• X is the cost price per unit,
  
• Y is the selling price per unit,
  
• Z is the number of units that sell at Y price point, and
• P is the profit per unit (i.e., Y minus X)
  

Then a company should strive to find that value of Y, where the product PZ is maximum.

It is no rocket science that P and Z are generally inversely related to each other - as P increases, Z goes down, and vice versa. It is also trivial to understand that the relation between P and Z is not of the nature "PZ = constant" (that is, a particular increment in P will generally not cause so much decrement in Z so as to keep the product PZ unchanged). And finding the correct value of Y - and hence P - is not an easy task. It is a task that not only requires sound market research, it also requires sound knowledge of the consumers and the market, as well as sound judgment.

And here's a recent news story that has some interesting figures which demonstrate exactly this - the importance of the product PZ, and the effect of varying Y on PZ. An excerpt from the news story is:

...Valve's Gabe Newell revealed that a recent sale on the Steam version of Left 4 Dead led to an astounding sales increase of 3000 percent...


Update (14-Feb-10): It appears that the premise behind Laffer curve is analogous, in a way, to the thought I've outlined in this post

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