Public Economics Lectures Part 1: Introduction

Expenditure Function
Fix utility at U and prices at q
Find bundle that minimizes cost to reach U for q:
e(q, U) = min q · c s.t. u(c) ≥ U
c
Let µ denote multiplier on utility constraint
First order conditions given by:
q i = µu ci
These generate Hicksian (or compensated) demand fns:
c i = h i (q, u)
Define individual’s loss from tax increase as
e(q 1 , u) − e(q 0 , u)
Single-valued function → coherent measure of welfare cost, no path
dependence
Public Economics Lectures () Part 3: Effi ciency 28 / 105