Studying Optimal Paternalism, illustrated by a Model of Sin Taxes

Ted O’Donogue and Matthew Rabin

Presented by Julia Sonina & Liliana Perez

December 2011 – Université Paris 1

Objective:

to prove that economic policy prescriptions might change once it is recognized that human choices are not rational

Classical Approach

•People always respond optimally to the costs and benefits of their available choices.

•There are many arguments against paternalism, traditionally to prove that paternalistic policies do more harm than good.

•Traditionally economists take for granted that choices are optimal for the people who make them. Becoming a heroin addict is the optimal choice for a person?

Questions:

Can optimal paternalism help people make better choices?

What are the possible advantages of paternalistic policies that help people make better choices?

O’DONOGHUE & RABIN Proposal

to treat the analysis of optimal paternalism as a mechanism-design problem when some agents might be limitedly rational

Economists analyze optimal commodity taxations based on an assumption that people’s choices reflect their own best interests. The proposed approached is based solely on the harm consumers

may do to themselves.

Advantages:

•It addresses how an economist can contribute to policy debates.

•It studies the impact of self control problems: Ex: addictions

•It forces to look the best feasible policy.

•It highlights how heavy-handed interventions are least used.

•It proves that minimal paternalism sometimes is misplaced.

Results: they prove that imposing seemingly large sin taxes on unhealthy items while lowering taxes on other items may not hurt rational consumers by much and can create significant benefits for those who overconsume the unhealthy items due to self-control problems.

Ut: instantaneous utility in period T. δ: standard time-consistent impatience;β: time-inconsistent preference for immediate gratification (self control problem) β<1 extra bias for now over the future. (an error for the analysis ) β=1: no self control problems

Illustration: Analysis of a simple model of sin taxes for unhealthy goods.

A person’s intertemporal preferences at time t are given by

Simple consumption model (F. Ramsey, 1927)

Assumptions:Economy with 3 goods:

Potato chips Carrots Numeraire (leisure)

MC(potato chips) = MC (carrots) = 1All markets are competitiveP (numeraire) = 1 P (carrots) = P (potato chips) = 1 + t

Single representative consumer His period t consumption of potato chips –

carrots - numeraire –

Instantaneous utility: Carrots and numeraire – standard goodsConsumption of potato chips creates negative effects in the future

Budget constraint:

tx

ty

tz

)ln()ln()ln( 1 ttttt xzyxu 0,,

Bzypxp yx

Single representative consumer

Self-control problems:

Optimal behavior: 1,1 1,1

zyxzyxu ttttt )ln()ln()(),,(*

)(*

*

*

pz

py

px

t

yt

xt

B

tttttt zyxzyxu )ln()ln()(),,*(*

)(**

**

**

pz

py

px

t

yt

xt

B

*** xx

Self-control problems leads to overconsumption

Government

Optimal taxes:

Optimal behaviour ( ) Self-control problems ( )

Rytxtts

zyx

yx

**___.

max**)ln(*)ln()(

RR

Rt

RR

Rt

y

x

)1(

))/()(1(

*

*

1 yx tt

1 yx tt

Heterogeneous consumersTrade off: help for β <1 and hurt for β = 1It’s better to impose higher taxes on unhealthy

good than taxes all goods equally:1. Enormous benefit fir those who have self-

control problems (correct its behaviuor)2. The harm from distortion from optimal taxation

for normal consumers is very smallIncreasing taxes on unhealthy goods may be

worth doing even if we suspect only few of consumers have extra bias for present over future

Speculation about other efficient mechanisms:

•Electronic cards that determine their tax schedules.

•Non refundable coupons in advance that give the right to purchase the items.

•Sin licenses: one time payment for the right to purchase an item. •$5000 for un ID = 2500 packs tax free.•Illegal to buy cigars without the id.

Critics to the approach:•Who can determine what is best for people?•It is not possible to determine all the plausible mistakes people can make.

•Consumption distortions derived from Taxes are second-order relative to the benefits from reducing over-consumption by people with self-control problems.

•This second-order cost to 100% rational consumers can have a first-order benefit to those with mild self control problems.

•Under quite reasonable conditions, it is possible to tax potato chips in a way that on average helps both people with self-control problems and those without:

•People with self control problems gets controlled with tax•People with self control problems pays more, thus, income is redistributed naturaly to those without the problem.

Conclusions:

FIN