In the singular interest of accounting for the unit of account in the interest rate

This is an update of this post where I've taken $\kappa = \kappa (NGDP, MB)$ such that

$$ \text{(1) } P = \frac{\log NGDP/c_0}{\log MB/c_0}\frac{NGDP}{MB} $$

The fit results in a marginal improvement (in the sense that deviations are more Gaussian) over the original (data is dashed green, light blue is the old fit and dark blue is the new fit):

Interestingly, the modified equation $\text(1)$ seems to do well (well, better than the original calculation) as a price ceiling where:

$$ \text{(2) } P \leq \frac{\log NGDP/c_0}{\log MB/c_0}\frac{NGDP}{MB} $$
which is relevant to the case of non-ideal information transfer (data in green, model in gray):