Public Economics Lectures Part 1: Introduction

Chetty 2008: Value Functions
Value function for agent who finds a job in period t:
V t (A t ) = max
A t+1 ≥L u(A t − A t+1 + w − τ) + V t+1 (A t+1 )
Value function for agent who does not find a job in period t:
U t (A t ) = max
A t+1 ≥L u(A t − A t+1 + b t ) + J t+1 (A t+1 )
where J t+1 (A t+1 ) is value of entering next period unemployed.
Agent chooses s t to maximize expected utility
J t (A t ) = max
s t
s t V t (A t ) + (1 − s t )U t (A t ) − ψ(s t )
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