Economics 2450A: Public Economics Section 2: Introduction to Optimal Income Taxation

Our goal for most of this class is to derive the properties of optimal taxes in di↵erent context. We will define the tax in a flexible way using the mathematical object T (z), where z is the income reported by the agent. The tax T (z) generates the retention function R (z) = z T (z). R (z) measures how much the agent can retain out of total income z. We denote transfers to income z with T (z) so that the transfer T (0) to non-working individuals is the intercept of the retention function. If T (z) is di↵erentiable, T 0 (z) represents the marginal tax rate. It measures how much the agent gets taxed out of one additional dollar of income. In order to study the extensive margin decision between working and remaining unemployed, we need to know the participation tax rate ⌧p = T (z) T (0) z . It is the fraction of income that an agent pays in taxes when she moves from 0 income to z.