What is the name of the quadratic curve used to find optimal price? Does that optimal pricing curve have a special name?

Depends on the function. If the function is a quadratic, then it's called a polynomial of degree 2, or a second-order polyomial. In general this type of function is:


y = ax^2 + bx + c


Of course, pricing and demand models can be all sorts of different functions - 2nd order polynomials are often used becaiuse they make the homework assignments relatively easy, but depending how sophisticated you want to get you could come up with 3rd-order polynomials (or higher), or logarithmic functions, or hyperbolic functions. to name a few

Awesome - thanks!

2nd order polynomials are often used becaiuse they make the homework assignments relatively easy, ...

Roger that. To illustrate the basic ideas, price/demand curves are usually presented as linear; thus they can be expressed as Q = mP + b for some constant slope m (which will be negative, as Quantity is a decreasing function of Price).

Then since Total Revenue = PQ = mP^2 \ + \ bP , linear price/demand curves lead naturally to concave quadratic Tot Rev curves. Hence, finding the Price sweet spot that maximizes Revenue amounts to finding the vertex of the Tot Rev = f(Price) curve.