Interest rate semi-elasticity of money demand

I have a monetary model with a complicated (non-closed form) money demand function. I would like to compute interest rate semi-elasticity of money demand: \frac{\partial(m(i))}{\partial i}. But as I don’t have a closed expression for m(i), I’m not sure what could I do, then I’d be very grateful with some comments on that.

I’m aware there’s the possibility to implicitly find the derivative, which will be in terms of both m(i) and i, would that be correct?


My money demand function is something similar to:

m^{\omega-1}\left[\frac{x^2+y^2}{\alpha m^{2\omega}}-\beta\right]=\frac{i}{1+i}

0<\omega<0,\alpha,\beta>0. x and y are other positive variables.

It depends on the context, but usually, you can simply do a finite differences approximation to the function.

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