This question is stemming from an economic context, but I am only interested in the mathematical formulation of the indifference curve itself. They are simple to draw free-hand, but I have no idea how to formally define one. Here is an example:
Question
How can we write mathematically the formula for an indifference curve, or even something that looks very close to it?
Notes:
- The ends don't quite reach either the x or y axis (the curves are just kind of floating)
- I would appreciate brief notes about which each part of the equation means (i.e. what makes it concave/convex, what governs the slope, ect)
- I prefer a solution that doesn't rely on domain notation