Public Economics Lectures Part 1: Introduction

Effi ciency Cost: Marshallian Surplus
2. In terms of total change in equilibrium qty caused by tax
Define η Q
= − dQ
d τ
p 0
Q
η Q
: effect of a 1% increase in price via a tax change on equilibrium
quantity, taking into account the endogenous price change
This is the coeffi cient β in a regression of the form
log Q = α + β τ p 0
+ ε
Identify β using exogenous variation in τ. Then:
EB = −(1/2) dQ
dτ dτdτ
= −(1/2) dQ
dτ ( p Q )(Q p )dτdτ
= (1/2)η Q
pQ( dτ
p )2
Public Economics Lectures () Part 3: Effi ciency 13 / 105