First thing please accept my apologies for the way i'm explaining my question - I'm not a math or econ major.
I have a product that another company want to sell for me and pay me royalty in cents per unit sold.
now I need a formula that as number of sold units are going up, the royalty per unit decreases at the same time my income keep increase to make it interesting for both me and the sellers to keep working with each other. what that formula be so my income look like a square root graph.
Assuming indivisible units, if you want your total income to be exactly given by
$$f(x)=A\sqrt x, A>0$$
where $x$ is the number of units sold, your royalty per unit on the $x$th unit for $x\geq 1$ is simply
$$\Delta f(x)=A\sqrt{ x}-A\sqrt {x-1}.$$
For large $x$, this royalty per unit is approximately $\frac{A}{2\sqrt x}$ (in the sense that the ratio of this approximation to $\Delta f(x)$ tends to one).