Understanding the Scope of Public Economics

1. 8 October 2007 EC426 MSc Public Economics 2007/8http://darp.lse.ac.uk/EC426.htm The Scope of Public Economics

2. Public economics • Purpose of this lecture • What is the purpose of public economics? • What does it attempt to do? • Introduce the rest of the course. • Is PE some special case? • A minor subset of microeconomic analysis? • Particular variants of standard models? • Is PE some kind of intruder? • An aberration from “conventional” economics? • An unnecessary complication? • Begin with something simple…

3. The Scope of Public Economics Overview... The private economy “Market Failure” The standard story of the microeconomic system. A place for public economics? Redistribution Looking forward

4. Positive economics • How does the economy work? • Standard story based on a well-known set of models • Challenge on functionality? • Do the models work? • Do they provide useful predictive power? • Challenge on completeness? • Do the models appropriately cover the world as we know it? • Do they address the appropriate questions? • Let’s look at the standard story…

5. A standard approach: outline • We use a model of the private economy • Two main features: • private internal economic mechanism – the market • private external frame of reference – rules of the game • Competitive markets • Perfect [?] information • No restraint on trade • Minimal market power • Effective coverage • Rules of the game • Incomes determined by property • Guaranteed private property rights

6. A standard approach: result • Use the private-economy model • Additional assumptions: • Small agents • Large numbers • Convexity? • Equilibrium • The existence of competitive equilibria • If well-behaved – stability etc • Interpretation: • An “Adam Smith” result • Decentralisation • Each agent max/min with just price guidance

7. Implementation through the market Uh(xh) = Uh(x*h) f h q2 x2 Ff(qf) = 0   p1 — p2 p1 — p2 q*f x*h f` h` q1` x1`

8. A standard approach: implication • Is the private-economy model a good one? • What do you mean by “good?” • Predictive power? • Empirical relevance? • Welfare significance? • Can consider the model in terms of efficiency: • Will the equilibrium be efficient? • Can we use the market to implement any efficient outcome? • Focus on two important theorems • One on implication • One on implementation

9. Welfare theorem 1 • Assume a competitive equilibrium. • What is its efficiency property? • THEOREM: if all consumers are greedy and there are no externalities then a competitive equilibrium is efficient. • Explanation: • If they are not greedy, there may be no incentive to trade. • If there are externalities the market takes no account of spillovers.

10. Welfare theorem 2 • Pick any Pareto-efficient allocation • Can we find a property distribution d so that this allocation is a CE for d? • THEOREM: if, in addition to conditions for theorem 1, there are no nonconvexities then an arbitrary PE allocation be supported by a competitive equilibrium. • Explanation: • If “lump sum” transfers are possible then we can arbitrarily change the initial property distribution. • If there are nonconvexities the equilibrium price signals could take us away from the efficient allocation...

11. b a a b x1 x1 x2 x2 ^ • [x] Supporting a PE allocation Ob • The contract curve • An efficient allocation [R] • Supporting price ratio = MRS • The property distribution • A lump-sum transfer • Support the allocation by a CE. • This needs an adjustment of the initial endowment. • Beware: lump-sum transfers may be tricky to implement p1  p2 Allocations where MRS12a = MRS12b Oa

12. ^ qf Supporting a PE allocation (production) q2f • Firm f’s technology set • f’s net output in the efficient allocation • Supporting price ratio = MRT • f’s net output in the allocation is profit-maximising for f. p1  p2 what if preferences and production possibilities were different? q1f 0

13. Private model: limitations • The Adam Smith result is fairly demanding • Not hard to think of practical instances where these don’t hold. • Should we speak of “market failure”? • A convenient shorthand • But is it appropriate? • Or limits of private economics? • Labelling is not so important.. • Provides one important route into Public Economics

14. Where the private model doesn’t “work” • Useful to look at the separate reasons why… • A typology of difficulties • Market deficiency • Nonconvexities • Externalities • Public consumption • Perhaps only the first two are really “failure” • But all provide a normative role for public economics • Look at these briefly • First an important methodological point

15. Competitive Failure and Efficiency • The market “failures” raise two classes of problem that lead to two distinct types of analysis: • The characterisation problem • Description of modified efficiency conditions… • …when conditions for the welfare theorems are not met. • The implementation problem • Design of a mechanism to achieve the allocation. • These two types of problem pervade nearly all of modern micro economics • It’s important to keep them distinct in one’s mind

16. The Scope of Public Economics Overview... The private economy “Market Failure” • Market deficiencies • Nonconvexities • Externalities • Public consumption Where markets do not quite do the business… Redistribution Looking forward

17. Market deficiencies – 1 • A further typology: • Distorted markets • Monopoly • Restrictive practices • Missing markets • Futures? Risk? • Highly specialised commodities • Thin markets • Not enough traders • Highly specialised commodities • Problems of information • Imperfect / incomplete • Asymmetric • The role for intervention…?

18. Market deficiencies – 2 • Role for public sector in each of these cases. • Distorted markets • Monopoly / Anti trust legislation • Missing markets • Pension / social security provisions • Internal markets in health • Thin markets • Franchising • Private finance initiatives • Problems of information • Regulation

19. The Scope of Public Economics Overview... The private economy “Market Failure” • Market deficiencies • Nonconvexities • Externalities • Public consumption Large firms, large projects and infrastructure Redistribution Looking forward

20. Nonconvexities • Nonconvexities: ugly name for a crucial issue • Covers many well-known things • Increasing returns • Fixed costs • Weird tastes • But includes other stuff too • Interactions amongst agents… • …positive externalities • The market may not actually fail completely • Could still get decentralisation • But under what circumstances? • Let’s see why the second W-theorem does not work

21. ~ xh ^ xh Household h makes “wrong” choice x2h • Household h ’s utility function violates second theorem • Suppose we want to allocate this consumption bundle to h. • Introduce prices • h's choice given this budget • Nonconvexity leads to “market failure” p1  p2 x1h 0

22. ^ qf ~ qf Firm f makes “wrong” choice q2f • Firm f ’s production function violates second theorem • Suppose we want to allocate this net output to f. • Introduce prices. • f's choice at those prices • Another example of “market failure” p1  p2 q1f 0

23. Nonconvexities: a case for public intervention? • The conditions for the second W-theorem are violated • But this does not automatically mean to say that the market won’t “work” • Do nonconvexities require intervention in the market? • there’s a large-numbers argument • “induced” convexity • argument for effective competition laws… • …for example in the EU • But what if large-numbers argument doesn’t apply?

24. Nonconvexities that won’t go away • Sometimes the large-numbers argument is implausible. • Big firms • Boeing • Microsoft • Strategic suppliers • Network rail • Electricity / gas distribution • There may be other cases for a “natural monopoly” • Can see what happens in the case of a large fixed-cost firms

25. The “infrastructure problem” • Represent the analysis in terms of a two-good model. • Take something like electricity, highways – good 1 • To be paid for by sacrifice of all other goods – good 2 • Basic questions: • Should good 1 be produced at all? • If so, how much should be produced? • The answer depends on people's preferences • A simple diagram

26. x2 x1 Efficiency and non-convexities in production: case 1 • Endowment of good 2 • Fixed set-up cost to produce good 1 • Possibilities once fixed-cost has been incurred • x° • Reservation indifference curve • Indifference map • Point where MRS=MRT • Efficient point • Attainable set is shaded area + “spike” • x′ • In this case MRS=MRT is not sufficient • Utility is higher if x1 = 0 0

27. x2 x1 Efficiency and non-convexities in production: case 2 • Attainable set as before • Indifference map • Consumption if none of good 1 is produced • x° • The efficient point • x′ 0

28. x2 • x° • x′ x1 0 Nonconvexity: effect of the competitive market • Efficient to produce where MRS=MRT • Iso-profit-line • Profit-maximisation over the attainable set p1 — p2

29. x2 • x° • x′ x1 0 Nonconvexity: efficient fee schedule • Efficient to produce at x' • MRS=MRT • Fixed charge • Variable charge p1 — p2

30. Nonconvexities: the role for public economics • Focus on issues raised by the infrastructure problem • Generalise to more complex cases • Foundation of large sub-branch of public economics • Determination of willingness to pay • Often assumed away in private model – consumer sovereignty • But emerges in many applied public problems • Used as the basis of CB analysis… • …see below • The science of regulation • Fairly clear for a world of certainty • But tricky if there is uncertainty about costs • Typically the case where there are few producers

31. The Scope of Public Economics Overview... The private economy “Market Failure” • Market deficiencies • Nonconvexities • Externalities • Public consumption Beneficial and harmful spillovers. A special type of transaction? Redistribution Looking forward

32. The nature of externality • An externality is a kind of “involuntary” transaction • A case where market allocation methods don’t work • Agents cannot be excluded from the transaction using conventional price mechanism • An example of “market failure”? • Externalities can be detrimental or beneficial • Normally concerned with two broad types: • Production externalities • Consumption externalities

33. Production externality • One firm influences another’s production conditions • Affects other firms’ cost curves. • Not effect of wage or input price changes… • …externality is outside the market mechanism. • Model this as a parameter shift • If firm f’s output produces an externality… • …production function of firm k has f’s output as a parameter… • … or MC curve of firm k has f’s output as a parameter. • Example: networking • One firm’s activity creates pool of skilled workers from which neighbouring firms may benefit. • Example: pollution • One firm’s activity (glue production) causes emissions to the detriment of its neighbours (restaurants)

34. q2 k k q1` Externality: Production possibilities • Production possibilities, firm k • Production possibilities, if firm f’s emissions increase low emissions by firm f high emissions by firm f

35. Consumption externality • One agent’s consumption of a good directly affects another • A’s consumption of good 1 is an argument of agent B’s utility function • Related to the analysis of public goods (below) • Consumption externalities can be seen as qualitatively different • Formal analysis may look similar • But informational problems differ

36. Externalities and the welfare theorems • What is the role in the fundamental results? • Equilibrium may be inefficient. • If agents are guided just by prices • Then they get misleading signals • A clear case for public concern? • In the case of production, perhaps not • See the externality as special transaction – missing market • Perhaps you just need to extend the coverage of markets • Then let trading happen in the extended markets • But it’s difficult to do this for some types of externality – particularly consumption • An essential role for “public” solutions.

37. The Scope of Public Economics Overview... The private economy “Market Failure” • Market deficiencies • Nonconvexities • Externalities • Public consumption Characteristics of public goods Redistribution Looking forward

38. Public consumption and public goods • An important instance. • not so much of market failure… • …but of limitations of private model • A different characteristic of goods and services in the economy • Variety of types of institution to provide • What are the public goods? • Defined by their economic characteristics

39. Characteristics of public goods • Two key properties that we need to distinguish: • Excludability • You are producing a good. • A consumer wants some. • Can you prevent him from getting it if he does not pay? • Rivalness • Consider a population of 999 999 people all consuming 1 unit of commodity i. • Another person comes along, also consuming 1 unit of i. • Will more resources be needed for the 1 000 000? • These properties are mutually independent • They interact in an interesting way

40. Typology of goods: classic definitions Rival? [ Yes ] [ No ] [??] [ Yes ] pure private Excludable? pure public [??] [ No ]

41. How the characteristics interact Example: Bread (E) you can charge a price for bread (R) an extra loaf costs more labour and flour • Private goods are both rival and excludable • Public goods are nonrival and nonexcludable • Consumption externalities are non-excludable but rival • Non-rival but excludable goods often characterise large-scale projects. Example: bread Example: National defence (E) you can't charge for units of 'defence‘ (R) more population doesn't always require more missiles Example: defence Example: Scent from Fresh Flowers (E) you can't charge for the scent (R) more scent requires more flowers Example: flowers Example: Wide Bridge (E) you can charge a toll for the bridge (R) an extra journey has zero cost Example: bridge

42. Public goods and the welfare theorems • Why is implementation likely to be difficult in the case of pure public goods? • Private provision will be inefficient • We have an extreme form of the externality issue. • But there is a fundamental difference from private model • Rationality and self interest: • Unambiguous for the pure private world • Ambiguous here • Therefore we may need different solution method

43. Example • Good 1 - a pure public good • Good 2 - a pure private good • Two persons: A and B • Each person has an endowment of good 2 • Each contributes to production of good 1 • Production organised in a single firm

44. Public goods: strategic view (1) • If Alf reneges [–] then Bill’s best response is [–] • If Bill reneges [–] then Alf’s best response is [–] Alf [+] 2,2 0,3 • Nash equilibrium [–] 3,0 1,1 [+] [–] Bill

45. Public goods: strategic view (2) • If Alf plays [–] then Bill’s best response is [+]. • If Bill plays [+] then Alf’s best response is [–]. Alf [+] 2,2 1,3 • A Nash equilibrium • By symmetry, another Nash equilibrium [–] 3,1 0,0 [+] [–] Bill

46. Which paradigm? • Clearly the two simplified +/– models lead to rather different outcomes. • Which is appropriate? Will we inevitably end up at an inefficient outcome? • The answer depends on the technology of production. • Also on the number of individuals involved in the community.

47. The Scope of Public Economics Overview... The private economy “Market Failure” Public economics and the rules of the game Redistribution Looking forward

48. Redistribution • Move away from private-only model • Slightly odd preoccupation • Define public economics as a “complement” • Move away also from simple efficiency • Pareto criterion • Potential Pareto • An area where private economy approach is (almost) silent • Two broad areas for consideration • Motivation • Implementation

49. The Scope of Public Economics Overview... The private economy “Market Failure” A framework for analysis? • Motivation • Implementation Redistribution Looking forward

50. Normative economics • How should the economy be organised? • On what basis make the recommendation? • Could argue that we’ve already strayed into this territory • Efficiency is a normative criterion? • Distinguish three approaches: • Constitution • Principles • SWF • Have use for all three in Public Economics