Public economics docx

Public economics c Mattias K. Polborn prepared as lecture notes for Economics 511 MSPE program University of Illinois Department of Economics Version: August 8, 2009 Contents I Competitive markets and welfare theorems 6 1 Welfare economics 7 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Edgeworth boxes and Pareto efficiency . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 First theorem of welfare economics . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5 Efficiency with production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6 Application: Emissions reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.7 Second theorem of welfare economics . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.8 Application: Subsidizing bread to help the poor? . . . . . . . . . . . . . . . . . . 25 1.9 Limitations of efficiency results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.9.1 Redistribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.9.2 Market failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.10 Utility theory and the measurement of benefits . . . . . . . . . . . . . . . . . . . 29 1.10.1 Utility maximization and preferences . . . . . . . . . . . . . . . . . . . . . 30 1.10.2 Cost-benefit analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.11 Partial equilibrium measures of welfare . . . . . . . . . . . . . . . . . . . . . . . . 39 1.12 Applications of partial welfare measures . . . . . . . . . . . . . . . . . . . . . . . 42 1.12.1 Welfare effects of an excise tax . . . . . . . . . . . . . . . . . . . . . . . . 42 1.12.2 Welfare effect of a subsidy . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.12.3 Price ceiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.12.4 Agricultural subsidies and excess production . . . . . . . . . . . . . . . . 45 1.13 Non-price-based allocation systems . . . . . . . . . . . . . . . . . . . . . . . . . . 46 II Market failure 50 2 Imperfect competition 51 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.2 Monopoly in an Edgeworth box diagram . . . . . . . . . . . . . . . . . . . . . . . 52 1 2.3 The basic monopoly problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4 Two-part pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.4.1 A mathematical example of a price-discriminating monopolist . . . . . . . 56 2.5 Policies towards monopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.6 Natural monopolies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.7 Cross subsidization and Ramsey pricing . . . . . . . . . . . . . . . . . . . . . . . 61 2.8 Patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.9 Application: Corruption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.10 Introduction to game theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.11 Cournot oligopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3 Public Goods 71 3.1 Introduction and classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.2 Efficient provision of a public good . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.3 Private provision of public goods . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.4 Clarke–Groves mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.5.1 Private provision of public goods: Open source software . . . . . . . . . . 80 3.5.2 Importance of public goods for human history: “Guns, germs and steel” . 80 4 Externalities 82 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2 “Pecuniary” vs. “non-pecuniary” externalities . . . . . . . . . . . . . . . . . . . . 82 4.3 Application: Environmental Pollution . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3.1 An example of a negative externality . . . . . . . . . . . . . . . . . . . . . 83 4.3.2 Merger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.3.3 Assigning property rights . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3.4 Pigou taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.4 Positive externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.5 Resources with non-excludable access: The commons . . . . . . . . . . . . . . . . 90 5 Asymmetric Information 92 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2 Example: The used car market . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2.1 Akerlof’s model of a used car market . . . . . . . . . . . . . . . . . . . . . 93 5.2.2 Adverse selection and policy . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3 Signaling through education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.4 Moral Hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.4.1 A principal-agent model of moral hazard . . . . . . . . . . . . . . . . . . . 96 2 5.4.2 Moral hazard and policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 III Social choice and political economy 102 6 Social choice 103 6.1 Social preference aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.1.1 Review of preference relations . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.1.2 Preference aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.1.3 Examples of social aggregation procedures . . . . . . . . . . . . . . . . . . 109 6.2 Arrow’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.2.1 Statement and proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.2.2 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.3 Social choice functions (incomplete) . . . . . . . . . . . . . . . . . . . . . . . . . 115 7 Direct democracy and the median voter theorem 118 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.2 The median voter theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.2.1 Example: Voting on public good provision . . . . . . . . . . . . . . . . . . 121 7.3 Multidimensionality and the median voter theorem . . . . . . . . . . . . . . . . . 122 8 Candidate competition 126 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 8.2 The Downsian model of office-motivated candidates . . . . . . . . . . . . . . . . . 128 8.3 Policy-motivated candidates with commitment . . . . . . . . . . . . . . . . . . . 128 8.4 Policy-motivated candidates without commitment: The citizen-candidate model . 128 8.5 Probabilistic voting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 8.6 Differentiated candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 9 Voting as information aggregation mechanism 133 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 3 Preface This file contains lecture notes that I have written for a course in Public Economics in the Master of Science in Policy Economics at the University of Illinois at Urbana-Champaign. I have taught this course four times before, and this version for the 2009 course is probably reasonably complete: Students in my class may want to print this version, and while I will update this material during the fall semester, I expect most of the updates to be minor, not requiring you to reprint material extensively. If there are any major revisions, I will announce this in class. This class covers the core topics of public economics, in particular welfare economics; reasons for and policies dealing with market failures such as imperfect competition, externalities and public goods, and asymmetric information. In the last part, I provide an introduction to theories of political economy. In my class, this book and the lectures will be supplemented by additional readings (often for case studies). These readings will be posted on the course website. Relative to previous years, I have added, rewritten or rearranged some sections in Parts 1 and 2, but most significantly, in Part 3. This is also the part where most remains to be done for future revisions. The reason for why I have chosen to write this book as a supplement to my lectures is that I could not find a completely satisfying textbook for this class. Many MSPE students are accomplished government or central bank officials from a number of countries, who return to university studies after working some time in their respective agencies. They bring with them a unique experiences in the practice of public economics, so that most undergraduate texts would not be sufficiently challenging (and would under-use the students’ experiences and abilities). On the other hand, most graduate texts are designed for graduate students aiming for a Ph.D in economics. These books are often too technical to be accessible. My objective in selecting course materials, and in writing these lecture notes, is to teach the fundamental concepts of allocative efficiency, market failure and state intervention in markets in a non-technical way, emphasizing the economic intuition over mathematical details. However, non-technical here certainly does not mean “easy”, and familiarity with microeconomics and optimization techniques, as taught in the core microeconomics class of the MSPE program, is assumed. The key objective is to achieve an understanding of concepts. Ideally, students should 4 understand them so thoroughly that they are able to apply these concepts to analyze problems that differ from those covered in class, and later, to problems in their work environment. Several cohorts of students have read this text and have given me their feedback (many thanks!), and I always appreciate additional feedback on anything from typos to what you like or dislike in the organization of the material. Finally, if you are a professor at another university who would like to use this book or parts of it in one of your courses, you are welcome to do so for free, but I would be happy if you let me know through email to polborn@uiuc.edu. Mattias K. Polborn 5 Part I Competitive markets and welfare theorems 6 Chapter 1 Welfare economics 1.1 Introduction The central question of public economics and the main emphasis of our course is the question of whether and how the government should intervene in the market. To answer this question, we need some benchmark measure against which we can compare the outcome with and without government interference. In this chapter, we develop a model of a very simple market whose equilibrium is “optimal” (in a way that we will define precisely). The following chapters will then modify some assump- tions of this simple model, generating instances of market failure, in which the outcome in a private market is not optimal. In these cases, an intervention by the government can increase the efficiency of the market allocation. When correcting market failures, the state often takes actions that benefit some and harm other people, so we need a measure of how to compare these desirable and undesirable effects. Hence, we need an objective function for the state. We start this chapter by using an Edgeworth box exchange model to define Pareto opti- mality as efficiency criterion, and prove the First Theorem of Welfare Economics: A market equilibrium in a simple competitive exchange economy is Pareto efficient. This result is robust to incorporating production in the model, and, under certain conditions, the converse of the First Theorem is also true: Each Pareto optimum can be supported as a market equilibrium if we distribute the initial endowments appropriately. However, we also points out the limitations of the efficiency results. The First and Second Theorems of Welfare Economics are derived in a general equilibrium framework. While theoretically nice, general equilibrium models are often not very tractable when, in reality, there are thousands of different markets. Often, we are particularly interested with the consequences of actions in one particular market, and in this case, partial equilibrium models are helpful, and we analyze several applications. Pareto optimality, our measure of efficiency, is in many respects a useful concept. However, 7 when the government intervenes in a market (or, indeed, implements any policy), it is very rare that all individuals in society are made better off, or that all could be made better off with some other feasible policy. Most of the time, a policy benefits some people and harms others. In these cases, it is useful to have a way to compare the size of the gains of winners with the size of the costs of losers. In the 18th century, “utilitarian” philosophers have suggested that the objective of the state should be to achieve the highest possible utility for the largest number of people. Unfortunately, utility as defined by modern microeconomic theory is an ordinal rather than cardinal concept, and so the sum of different people’s utilities is not a useful concept. We explain why this is the case and, more constructively, how we can make utility gains and losses comparable by the use of compensating and equivalent variation measures. Finally, we also discuss other methods of allocating goods, apart from selling them. For example, in many communist economies, some goods were priced considerably below the price that people were willing to pay, but there was only a limited supply available at the low price, with allocation often determined through queuing. 1.2 Edgeworth boxes and Pareto efficiency Economists distinguish positive and normative economic models. Positive models explain how the economy (or some part of the economy) works; for example, a model that analyzes which effect rent control has on the supply of new housing or on how often people move is a positive model. In contrast, normative models analyze how a given objective should be reached in an optimal way; for example, optimal tax models that analyze how the state should raise a given amount of revenue while minimizing the total costs of citizens are examples of normative models. One important ingredient in every normative model is the concept of optimality: What should be the state’s objective when choosing its policy? One very important criterion in economics is called Pareto optimality or Pareto efficiency. We will develop this concept with the help of some graphs. Figure 1.1 is called an Edgeworth Box. It has the following interpretation. Our economy is populated by two people, A and B, and there are two types of goods, clothing and food. The total amount of clothing available in the economy is measured on the horizontal axis of the Edgeworth box, and similarly, the total amount of food is measured as the height of the box. A point in the Edgeworth box can be interpreted as an allocation of the two goods to the two individuals. For example, the bullet in the box means that A gets C A units of clothing and F A units of food, while the remaining units of clothing (C B ) and food (F B ) initially go to individual B. We can also add the two individuals’ preferences, in the form of indifference curves, to the graphic. The two regularly-shaped (convex) curves are indifference curves for A, and the two 8 A B C F • C A F A F B C B Figure 1.1: Allocations in an Edgeworth box other ones are indifference curves of individual B. Note that individual B’s indifference curves “stand on the head” in the sense that B likes allocations that are to the southwest better, and so, seen from B’s point of view, his indifference curves are just as “regularly-shaped” (convex) as A’s ones. Note that the indifference curves for both individuals are not restricted to the allocations inside the box; the individuals’ preferences are defined for all possible positive levels of consumption, not restricted to what is available in this particular economy. The allocation that is marked with the dot in the previous figure is called an initial endowment. It is interpreted as the original property rights to goods that the two individuals have before they possibly trade with each other and exchange goods. Consider now the two indifference curves, one for A and the other one for B, that pass through the initial endowment marked X in Figure 1.2. The area that is above A’s indifference curve consists of all those allocations that make A better off than the initial endowment. Similarly, the area “below” B’s indifference curve (which is actually above B’s indifference curve, when seen from B’s point of view) contains all allocations that are better for B than the initial allocation. Hence, the lens-shaped, shaded area that is included by the two indifference curves that pass through the initial endowment is the area of allocations that are better for both A and B than the initial endowment. If A and B exchange goods, and specifically if A gives some clothing to B in exchange for some food such that they move to a point like Y in the shaded area, then both individuals will be better off than before. Such an exchange that makes all parties involved better off (or, at least one party better off, without harming the other party) is called a Pareto improvement. We also say that allocation Y is Pareto better than allocation X. 9 [...]... countries) National defense is therefore what is called a public good If public goods were provided individually by private agents, there would likely be a level of provision that is smaller than the efficient level, because each private individual that contributes to the public good would primarily consider his own cost and benefits from the public good, but neglect the benefits that accrue from his provision... thus x1 = 125 and x2 = 75, just as in the social optimum 1.7 Second theorem of welfare economics The second theorem of welfare economics states that (under certain conditions) every Pareto optimum can be supported as a market equilibrium with positive prices for all goods Hence, together with the first theorem of welfare economics, the second theorem shows that there is a one-to-one relation between market... 1.10.1 Utility maximization and preferences I assume that you have already taken a course in microeconomics, so the content of this section should just be a quick refresher If you feel that you need a more thorough review, I recommend that you go back to your microeconomics textbook The household in microeconomics is assumed to have a utility function that it maximizes by choosing which bundle of goods... suggested by the second theorem of welfare economics is that the government redistribution of endowments does not have to go to a Pareto optimum directly, but can bring us to a point like R, and starting from this point, individuals can start the market exchange of goods, which will eventually bring us to P 24 B F P •R ! E• A C Figure 1.10: Second theorem of welfare economics 1.8 Application: Subsidizing... this is a scientific consequence of economics in general and the first welfare theorem in particular In this section, we will briefly talk about the real-world and theoretical limitations of the efficiency results 27 1.9.1 Redistribution The first class of limitation arguments applies even within the simple exchange model that we used to derive the first theorem of welfare economics and notes that, while efficiency... the same price ratio Hence, the two indifference curves are tangent to each other, and the market equilibrium allocation is therefore a Pareto optimum This result is know as the First theorem of welfare economics It holds more generally, and it is the primary reason why economists usually believe that market equilibria have very desirable properties and are reluctant to intervene in the workings of a... Application: Subsidizing bread to help the poor? Many developing countries choose to subsidize bread (or other basic foods) in an attempt to help the poor In the previous section on the second theorem of welfare economics, we have already indicated that this might not be the most efficient way to implement this social assistance The following Figure 1.11 helps us to analyze the situation In the initial situation... than to increase the bread consumption, because there is a limit of how much bread one can reasonably consume 1.9 Limitations of efficiency results Often, the efficiency result of the first theorem of welfare economics is interpreted by (conservative) politicians in the sense that the state should not interfere with the “natural” working of the market, but rather keep both taxes and regulations to a minimum... unless there is a clear evidence that one of the assumptions of the theorem is violated It is instructive to give a non-geometric proof of this fundamental theorem Proposition 1 (First Theorem of Welfare Economics) Assume that all individuals have strictly monotone preferences, and all individuals’ utilities depend only on their own consumption Moreover, every individual takes the market equilibrium prices... inefficient, either because isoquants intersect, or because not all inputs are used F T E C Figure 1.8: Production possibility curve We are now interested in whether the result of the first theorem of welfare economics carries over to an economy with production Will a market economy achieve a technically efficient allocation? A profit maximizing firm’s objective is to produce its output in a cost-minimizing way . Public economics c Mattias K. Polborn prepared as lecture notes for Economics 511 MSPE program University of Illinois Department of Economics Version: August 8,. the core topics of public economics, in particular welfare economics; reasons for and policies dealing with market failures such as imperfect competition, externalities and public goods, and asymmetric. 135 3 Preface This file contains lecture notes that I have written for a course in Public Economics in the Master of Science in Policy Economics at the University of Illinois at Urbana-Champaign. I have taught