Keynesian Taxation: How Differentiated Savings Rates Alter Optimal Income Tax Rates

I intend to include a consideration apparently omitted by the optimal tax theory, at least as exposed in the seminal paper [#Saez2001]: demand side. Indeed, according to Keynesianism, as the marginal propensity to save of rich households is significantly above that of poor ones, a redistribution would increase aggregate demand and have an expansionary effect on the economy. I will show how new terms appear in the formula of optimal income tax rates, firstly with an illustrative approach, and then with a fully rigorous derivation.