Public Economics Lectures Part 1: Introduction

Setup
Consider a static demand model; results hold in dynamic model
N individuals with quasilinear utility over two goods:
x
u i (x, y) = y + 1−1/ε
a i
1 − 1/ε
Agent i’s optimal demand for good x:
xi ∗ (p) = ( a i
p )ε
⇒ log xi ∗ (p) = α − ε log p + v i
where v i = α i − α denotes i’s deviation from mean demand
Under orthogonality condition Ev i |p = 0,
ε = E log x ∗ 1 − E log x ∗ 0
log p 1 − log p 0
→Observed response to price increase (p 0 to p 1 ) identifies ε.
Public Economics Lectures ()Part 5: Income Taxation and Labor Supply 185 / 217