Saddle Point versus Equilibrium Point with respect to marginal utility curve
There is an interesting theory in calculus. It is the saddle point and equilibrium point. There is a concept of local and global minima.
Lets us take an example of a function.
f(x) = x^3 – 2x^2 – 3x + 5
In this case, the curve has a non-linear function which can fall and rise in the Y-Value versus the X-base. There can be more than two places where the curve dips than any other place- this is termed as local minimum. If the curve dips at a greater level in the Y-Value, it is called the global minima. Generally, the equilibrium points are settled for a curve at such dips known as the minima, where the second derivative is negative.
The saddle point can also be an infinite minimum. For example, if a curve dips infinitely, a point of reference for the x-coordinate is taken for a local lift, which is the last point for rise before the infinite minimum. This is called as the orthogonal saddle point, also known as the monkey saddle- two legs and one tail.
When the marginal utility curve is respected, with respect to price, volume and break-even point as the three coordinates for an equilibrium bucket, the elasticity is determined by the shift of the Y-Value. Saddle points in such cases lead to undetermined answers in price and volume elasticity, known the n-th degree curve of elasticity.