Public Economics Lectures Part 1: Introduction

Special Case 2: Uniform Taxation
Suppose ε ij = 0 if i ̸= j and ε xi ,w = ∂h i
w
w
h i
constant
Using following identity, ∑
j
∂h i
∂q j
q j + ∂h i
∂w
w = 0, we obtain
∂h i
∂q i
q i = − ∂h i
∂w w
Proof of identity (J good economy, no labor):
∑
j
∂h i
∂h j
q j = ∑ q j + ∂h i
q i
∂q j j̸=i ∂q i ∂q i
∂h j q j
= ∑
j̸=i ∂q i
+ ∂h i q i
∂q i
= ∂e
∂q i
− h i = 0
− h i
Public Economics Lectures () Part 4: Optimal Taxation 19 / 121