Public Economics Lectures Part 1: Introduction

Ramsey Model: Government’s Problem
For maximization problem, Lagrangian for government is:
L G = V (q, Z ) + λ[∑ τ i x i (q, Z ) − E ]
i
⇒ ∂L G
∂q i
=
∂V
∂q i
}{{}
Priv. Welfare
Loss to Indiv.
+ λ[ x i
}{{}
Mechanical
Effect
+ ∑ τ j ∂x j /∂q i ] = 0
j
} {{ }
Behavioral
Response
Using Roy’s identity ( ∂V
∂q i
= −αx i ):
(λ − α)x i + λ ∑ τ j ∂x j /∂q i = 0
j
Note connection to marginal excess burden formula, where λ = 1 and
α = 1
Public Economics Lectures () Part 4: Optimal Taxation 12 / 121