My first developing concerning economic applications is this one.
Indifference curves have the shape 2/x 3/x 4/x 5/x and so on...
My last formulae doesn't work properly so I have developed a new ones. They are only valid in the form 1/x 2/x ... And 1/x^2 2/x^3 5/x^4...
For the first kind of functions, valid as indifference curves I realized the formulae is:
Where a is the numerator of the function.
For the second ones I have developed this formulae:
Where b is the numerator of the derivative and m the exponent of the derivative.
You can find the better point of the indifference curve(taking into account that goods are normal goods) touching the linear function of disposable income, production, etc.
I can't get much more regarding other kind of equations, but I'll keep working on it. Now I have to find the pattern between the production function or budget constrain and the indifference curve to find values more exact taking into account normal goods based in elasticity equalized to 1.