At a lower price, say $10, more buyers will purchase your product. At a higher price, say $20, fewer buyers will purchase the product. But the math says at $15 is the price at which profit is greatest.

Let's say 15 people may buy the product at $10, 10 buy at $15 and 5 buy at $15. Remember the cost of each item to you is $5.

- At $10, your profit is: number of buyers x (price - cost) = 15 x ($10 - 5) = $75.
- At $15, your profit is: number of buyers x (price - cost) = 10 x ($15 - 5) = $100.
- At $20, your profit is: number of buyers x (price - cost) = 5 x ($20 - 5) = $75.

Yet, this is a model that assumes the market is efficient - that the buyer and seller have all the information they need to make their decisions. That they are not affected by marketing or other intangibles that distort how they view the value of the product. In the real world, all these factors come into play.

In reality, the real profit maximizing price is that which allows every buyer to pay whatever they are most willing to pay for the product, without bad feeling that others are paying less. In this world, our example would play out as follows

- The five people willing to pay $20 for the product would do so, giving us profit from them of: 5 x ($20 - $5) = 75.
- Then there were five who would pay at the $15 price for the product, giving us profit from them of 5 x ($15 - 5) = $50.
- And lastly, there is the $5 willing to pay just $10, giving us profit from them of 5 x ($10 - 5) = $25.
- So, in total, across these 15 individuals, the profit would be $75 + $50 + $25 = $150.

** This post was written in a rush. Some of my numbers could be wrong. **