[benp84]

Counterexample: Suppose I'm selling a product with zero cost and I've determined the profit-maximizing price to be $1.00. This means profit as a function of price is maximal and therefore the slope is zero, i.e. raising the price by 1% makes sales go down by 1% and vice versa.

Now suppose my cost to produce goes from zero to $0.99 per unit, which drops my profit to $0.01. Now that 1% increase in price that only drops sales by 1% is well worth it because my profit per unit doubles. The profit-maximizing price is now likely well over $1.

[ddingus]

Then one must still consider demand and how buyers value the product.

Max profit becomes far more complex!

A second order view might be:

Say at $1.99 one gets X sales, Y sales at $2 (and yes, that is a real thing), Z at $3, $5 etc...

Clearly, selling for the $5 maximizes profit per unit sale, but if volume is more than double at $3.99, overall profit will be maximized by far higher unit sales.

The buyers will weigh product benefits vs their time, liquid dollars and competing products.

Fewer of them see a favorable value proposition at $5 than do at $3.99. Maybe more see it at $2.50, but not enough more to make more profit over the life of the product.

And a third order strategy could be:

One layer above that is time. Early on, if the product is well differentiated, has a strong value proposition, max money may in fact linked to a price ramp downward.

Start at $5, then drive new sales at $4.50, etc, until late in the cycle to sell against competition, one is selling down at $1.99. While this is being done, cost reductions and other product enhancements can keep margin high.

[OJFord]

Or perhaps even clearer: go to the other limit, cost of $1; drop in sales while going from break even to profitable.