Lecture Notes: Public Economics - University of Pennsylvania

[Pages:148]Lecture Notes: Public Economics

Fall 2018

Contents

I Public Goods

6

0.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

0.1.1 What are Public Goods? . . . . . . . . . . . . . . . . . . . . . . . . . 7

0.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

0.3 Optimal Provision of Pure Public Good . . . . . . . . . . . . . . . . . . . . 8

0.4 Can the Optimal Allocation be Decentralized? . . . . . . . . . . . . . . . . 12

0.5 Lindahl Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

0.5.1 Is Lindahl Equilibrium a Reasonable Market Mechanism? . . . . . . 16

0.5.2 Nash Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 20

0.6 Positive Models of Private Provision of Public Goods . . . . . . . . . . . . . 23

0.6.1 A Static Model of Private Contributions . . . . . . . . . . . . . . . . 24

0.6.2 Comparative Statics Regarding Changes in the Wealth Distribution 30

0.6.3 Multiple Public Goods and Spheres of Inuence . . . . . . . . . . . . 32

0.7 Does Public Provision Crowd Out Private Provision? . . . . . . . . . . . . . 33

0.7.1 Guide to the Recent Literature . . . . . . . . . . . . . . . . . . . . . 34

0.8 Dynamic Voluntary Provision of Public Goods . . . . . . . . . . . . . . . . 40

0.8.1 Admati and Perry (ReStud, 1991) . . . . . . . . . . . . . . . . . . . 40

0.8.2 Marx and Matthews (ReStud 2000) . . . . . . . . . . . . . . . . . . 44

0.9 Provision of Public Goods with Private Information . . . . . . . . . . . . . 46

0.9.1 An Illustrative Example: two agent case . . . . . . . . . . . . . . . . 46

0.9.2 Impossibility Result for Large Economies (Mailath and Postlewaite,

REStud (1990) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

0.10 Local Public Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

0.10.1 A Class of Tiebout Models (Bewley Econometrica 1981) . . . . . . . 52

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0.10.2 Are Tiebout Equilibria Pareto E? cient? . . . . . . . . . . . . . . . . 54 0.10.3 A Tiebout Model with E? cient Equilibrium . . . . . . . . . . . . . . 57 0.10.4 Empirical Studies Related to Tiebout Hypothesis . . . . . . . . . . . 60 0.11 Public Goods Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

II Social Arrangements

63

0.12 A model incorporating social arrangements: . . . . . . . . . . . . . . . . . . 64

0.12.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

0.12.2 Related empirical work . . . . . . . . . . . . . . . . . . . . . . . . . 70

0.13 Applications of concern for rank . . . . . . . . . . . . . . . . . . . . . . . . 71

0.13.1 E?ort choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

0.13.2 Conspicuous consumption . . . . . . . . . . . . . . . . . . . . . . . . 72

0.13.3 Investment: "Investment and concern for relative position,"(with H.

Cole and G. Mailath) Review of Economic Design 6, 241?261 (2001). 75 0.14 Social Assets Mailath and Postlewaite IER (2006) . . . . . . . . . . . . . . 77

0.14.1 Model: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 0.14.2 Social Arrangements Bibliography . . . . . . . . . . . . . . . . . . . 82

III Public Choice (Silverman)

90

0.15 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

0.16 Models of Political Competition . . . . . . . . . . . . . . . . . . . . . . . . . 91

0.16.1 The Downsian Model of Political Competition . . . . . . . . . . . . 91

0.16.2 Criticisms and Weaknesses with the Downsian Model . . . . . . . . 94

0.16.3 Probabilistic Voting Models (minor footnote) . . . . . . . . . . . . . 94

0.16.4 Supermajorities (interesting footnote) . . . . . . . . . . . . . . . . . 96

0.16.5 Citizen Candidates (important class of models) . . . . . . . . . . . . 97

0.16.6 Equilibrium in Citizen Candidate Model . . . . . . . . . . . . . . . . 98

0.17 Comparing Political Institutions . . . . . . . . . . . . . . . . . . . . . . . . 101

0.17.1 Lizzeri and Persico (AER 2001) . . . . . . . . . . . . . . . . . . . . . 102

0.17.2 Diermeier, Eraslan & Merlo (Econometrica 2003) . . . . . . . . . . . 104

0.17.3 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

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IV Discrimination and A? rmative Action

106

0.18 Theoretical Models of Discrimination . . . . . . . . . . . . . . . . . . . . . . 107

0.18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

0.19 Taste-Based Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

0.20 Statistical Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

0.20.1 Phelps (AER, 1972) . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

0.20.2 Arrow (1973) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

0.20.3 Coate and Loury (AER, 1993) . . . . . . . . . . . . . . . . . . . . . 113

0.21 Discrimination Due to Inter-Group Interactions . . . . . . . . . . . . . . . . 118

0.21.1 Moro and Norman J. Public Econ (2003) . . . . . . . . . . . . . . . 118

0.21.2 Mailath, Samuelson and Shaked (AER, 2000) . . . . . . . . . . . . . 119

0.21.3 Eeckhout (REStud, 2006) . . . . . . . . . . . . . . . . . . . . . . . . 121

1 A? rmative Action

123

1.1 Origins of A? rmative Action . . . . . . . . . . . . . . . . . . . . . . . . . . 123

1.2 Theoretical Studies of the E?ect of A? rmative Action . . . . . . . . . . . . 125

1.2.1 Coate and Loury's Patronizing Equilibrium . . . . . . . . . . . . . . 125

1.2.2 Moro and Norman (2001) . . . . . . . . . . . . . . . . . . . . . . . . 129

1.2.3 Fang and Norman (2001) . . . . . . . . . . . . . . . . . . . . . . . . 130

1.2.4 Fryer (2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

1.3 Evaluation of the E?ects of A? rmative Action . . . . . . . . . . . . . . . . 132

1.3.1 Donohue and Heckman (1991) . . . . . . . . . . . . . . . . . . . . . 132

1.3.2 Moro (2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

V Welfare Reform and Social Security

135

2 Welfare Reform

136

2.1 Some Institutional Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

2.2 Welfare Reform Bill of 1996 . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

2.3 Incentive E?ects of the Welfare System (Mo? tt 1992) . . . . . . . . . . . . 140

2.4 Workfare versus Welfare: Besley and Coate (1992) . . . . . . . . . . . . . . 140

2.5 A Proposal for Welfare Reform (Keane 1995) . . . . . . . . . . . . . . . . . 146

2.6 Is Time-limited Welfare Compassionate? (Fang and Silverman 2001) . . . . 147

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Acknowledgement These notes began from notes written by Hanming Fang and Dan Silverman. I have

edited them substantially in several places and added entirely new sections. They should not be held responsible for errors or omissions.

Part I

Public Goods

6

0.1. INTRODUCTION

7

0.1 Introduction

0.1.1 What are Public Goods?

A good is called a pure public good if "each individual's consumption of such a good leads to no subtraction from any other individual's consumption" (Samuelson 1954, p387) This is commonly referred to as non-rivalry in use. There are two important areas of economics in which public goods play an important role. The ...rst is the case of spending on things such as national defense: the cost of providing a missile defense system is independent of the number of people inhabiting the protected area, and it is impossible to defend some but not all the inhabitants. This is the prototypical example used to motivate the role of government in providing such public goods.

Historically, this was the set of problems that motivated the interest in public goods. While interesting, more recently a second class of problems in which public goods play an important role is family economics. A married couple jointly consumes many goods and shares the cost of those goods. How a couple decides on the amount of time spent on child rearing and how much each contributes to that amount is central to understanding child development, labor force participation, the degree of matching assortivity and probabilities of divorce. Chapters 2 and 3 in Browning, Chiappori and Weiss (2014) are a good reference to this area.

We will primarily consider the simplest case with a single private good and a single public good.

0.2 The Model

n consumers, indexed by i = 1; :::; n xi : agent i's consumption of private good and denote x = (x1; :::; xn) as the vector of private consumption G: the (common) consumption of public good Agent i's preference described by the utility function

ui (xi; G)

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which is di?erentiable and increasing in both arguments, quasi-concave and satis...es Inada Condition

wi : agent i's endowment of private good and Xn

W = wi

i=1

is the total endowment of private good; and public good endowment is taken to be zero

Public good may be produced from the private good according to a production function f : R+ ! R+ where f 0 > 0 and f 00 < 0: That is, if z is the total units of private goods that are used as inputs to produce the public good, the level of public good produced will be

G = f (z) :

0.3 Optimal Provision of Pure Public Good

We ...rst ask the normative question of what is the optimal level of pure public good. We assume that the government of a fully controlled economy chooses the level of G; and the allocation of private goods x = (x1; :::; xn) to agents according to the Pareto criterion.

De...nition 1 An allocation (x;G) 2 R+n+1 is feasible if there exists some z

Pn

i=1

xi

+

z

W;

0 s.t.

G f (z) :

Alternatively we could de...ne that an allocation (x;G) 2 R+n+1 is feasible if

Xn xi + f 1 (G) W:

i=1

De...nition 2 A feasible allocation (x; G) is Pareto optimal if there exists no other feasible allocation (x0; G0) s.t.

ui x0i; G0 ui (xi; G) 8i = 1; :::; n

and for some i 2 f1; :::; ng ;

ui x0i; G0 > ui (xi; G) :

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