Public Economics Lectures Part 1: Introduction

Numerical Simulations
Use formula expressed in terms of F (w) to solve for optimal T (z):
T ′ (z(w))
(1
1 − T ′ (z(w)) = + 1 ) ( ) ∫ 1 ∞
[
ε wf (w) w
1 − G ′ (u(s))
p
]
f (s)ds,
where p = ∫ G ′ (u(s))f (s)ds is marginal value of public funds
Iterative fixed point method to solve for T (z):
Start with initial MTR schedule T ′ 0 and compute incomes z0 (w) using
individual FOCs
Get T 0 (0) using govt budget constraint, compute utilities u 0 (w)
Compute p 0 = ∫ G ′ (u 0 (s))f (s)ds
Use formula to calculate T 1 ′
Saez, Shephard 2009)
and iterate until convergence (Brewer,
Public Economics Lectures () Part 4: Optimal Taxation 76 / 121