Economics Stack Exchange is a question and answer site for those who study, teach, research and apply economics and econometrics. It only takes a minute to sign up.
Sign up to join this community
I have been teaching intermediate microeconomics and have come across a formula a number of times relating the tax rate at which revenue is maximized if elasticities are constant. This formula is defined as follows:
$$T_{max}=\frac{\varepsilon}{\varepsilon-1}\left(\frac{1}{\eta}+\frac{1}{\varepsilon}\right)$$
where $\varepsilon$ is our price elasticity of demand and $\eta$ is our price elasticity of supply.
This seems to be just a spin on Ramsey's rule. By Ramsey's rule (derived through Lagrangian method assuming zero cross-elasticities) the optimal tax for a market where supply is not explicitly modeled is given by:
$$\frac{t}{1+t}=\frac{1}{\epsilon}$$
Well technically it is $\frac{t}{1+t}=\frac{1-b}{\epsilon}$ but $b$ which is parameter that depends on marginal cost of public funds is often omitted/assumed to be zero in introductory problems for students.
The Ramsey rule above can be solved for $t$ as:
$$t = \frac{\epsilon}{\epsilon-1} \left( \frac{1}{\epsilon}\right)$$
The version you showcase is just derived with also explicitly taking into account supply as opposed to just from consumer problem where supply is not explicitly modeled showed above.
Given that I think it would still be called 'optimal Ramsey taxation'. To my best knowledge this kind of tweaking of the model would not have it's own special name, but I also tried to do literature search on Ramsey models with supply elasticity which did not yielded any results, but absence of evidence is not necessarily evidence of absence.
