Lecture 2

1. Lecture 2 Market Allocations and Efficiency Suggested Readings: Conolly & Munro, The Economics of the Public sector, chapter 2

2. Market Allocations and Efficiency • Scope for collective or government action in the economy exists when individuals fail to reach a good outcome on their own (when there is a market failure) • To properly understand and apply this proposition we require a definition of a good outcome • knowledge of how markets work in different circumstances • In doing so, we will derive Adam Smith’s so-called Invisible Hand somewhat formally • Definition: An allocation is Pareto efficient if it is not possible to make any individual better off without making another individual worse off. • weak but natural criteria (although some might object) • based on individualistic values/consumer sovereignty

3. Perfectly Competitive Market Benchmark • Assume • well-behaved preferences (complete, reflexive, transitive, local non-satiation) • no increasing returns to scale in production • price taking behavior • complete markets

4. Exchange Efficiency • No production, just an endowment of N goods For simplicity, consider an exchange economy with two people A(nne) and B(ill) endowed with two goods, X and Y. • Anne and Bill have complete, reflexive, local non-satiated preferences for the two goods that can be represented by indifference curves

5. Edgeworth Box • 1. The length of the side of the box measures the total amount of the good available. • 2. Anne’s consumption choices are measured from the lower left hand corner, Bill’s consumption choices are measured from the upper right hand corner. • 3. We can represent an initial endowment, (EAx,EAy), (EBx,EBy) as a point in the box. This is the allocation that consumers have before any exchange occurs.

6. EBx Good x Bill Good y Edgeworth Box Diagram EBy EAy Good y EAx Good x Anne

7. Good x EBx Bill Good y EBy EAy ICA Good y EAx Good x Anne

8. EBx Good x Bill Good y E • EBy EAy ICA ICB Good y EAx Good x

9. Pareto-Efficiency in an Exchange economy • Consider the initial endowment • Question: is the initial endowment point pareto-efficient? • As we can see, whenever the indifference curves are not tangent, there is always scope for a pareto-improving exchange

10. Pareto-Efficiency in an Exchange economy • More formally • Efficiency condition: Equal Marginal Rates of Substitution for all consumers and all goods, that is • for all individuals A and B and any two goods X and Y • Mathematical derivation • Set of Pareto-optimal consumption bundles is described by the so-called contract curve which generates the utility possibility frontier (UPF) • All points on the UPF are Pareto-efficients, but the distribution of utilities varies substantially!

11. xB EBx Good x Bill Good y The Contract Curve • yB yA • E EBy EAy Good y xA EAx Good x Anne

12. Utility possibility frontier (UPF) UB • A • C • B UA

13. Utility possibility frontier (UPF) • All points on the Utility Possibility frontier correspond to allocations that are Pareto-Efficient • Points inside the UPF do not represent Pareto-Efficient allocations • Consider Point C: can you show the points on the UPF that would constitute a Pareto-improvement over C?

14. Competitive equilibrium in an exchange economy • Suppose that starting from an initial endowment Anne and Bill can increase their utility by exchanging the two goods. How is the competitive equilibrium achieved? • Remember that in a competitive equilibrium • prices are such that all markets clear • individuals maximize their utility

15. Price-Offer Curve • Let’s first see how much of each good each individual is willing to sell (buy) for any given price (price-offer curve) • Then we will show that the competitive equilibrium will just be a point where the price-offer curves for the two agents will cross • total endowment of good j = X,Y • budget constraint for person i=A,B:

16. Price Offer Curve y Price-offer curve x

17. Competitive equilibrium in an exchange economy • Note that the points on the price-offer curve give us the quantity of the two goods that for any given price maximize the utility of the agents • When the two price-offer curves cross, the market for each good clears (each agent buys exactly what the other agent wants to sell) and both agents maximize their utility. • Hence, in the competitive equilibrium the following holds:

18. xB EBx Good x Bill Good y • yB yA • E EBy EAy Budget constraint Good y xA EAx Good x Anne

19. First Fundamental Welfare Theorem • A general competitive equilibrium is Pareto efficient • a market equilibrium results in an allocation on the Utility Possibility Frontier • one interpretation: with perfectly functioning markets, governments not are needed to achieve efficiency • this is our formal expression of Adam Smith’s invisible hand • Result that markets are good is not surprising - markets are institutions based on exploiting gains from trade

20. Second Fundamental Welfare Theorem • Any Pareto efficient allocation can be supported as competitive equilibrium with lump sum transfers. • any point on the Utility Possibility Frontier can be attained as a market outcome after redistribution. • one interpretation: governments need only to redistribute (if possible) and ensure that markets achieves a given outcome (for example a more equitable one) • Problem: does the government have all the information, before individuals have taken any consumption or production decision, to reallocate resources and achieve then through the market a given point on the UPF?

21. Market failure • Conditions necessary for competitive equilibria • price taking, i.e. no market power or monopoly • no interference with markets - no distortions or impediments to trade • perfect/symmetric information • complete markets • tastes are given • If these conditions are not satisfied, then markets may not work well and collective choice/public policy may improve matters

22. Market failure • Caveat: Just because there is scope for improvement does not imply government interference will improve matters. • government may also fail for some reason • before looking at the failure of public choice decision need first to look at scope for such action, that is when markets fail • Market failures occur when prices do not fully reflect either the marginal social benefits or costs • such failures provide scope for government intervention • how does this happen?

23. Market failure • Potential sources of market failure • Monopoly • Barriers to trade (Taxes, subsidies) • Externalities • Public Goods • Imperfect information • Rationality and consistency of agents

24. Questions (prepare and answer all questions before next week seminar) • Questions • Anne and Bill are endowed with two goods and share the same preferences, represented by the following utility function: • Show in a diagram the set of Pareto-optimal consumption bundles for Anne and Bill. Explain carefully your reasoning. • Draw in a diagram the utility associated with all the Pareto-optimal consumption bundles you described in the previous question and indicate the egalitarian utility outcome • Suppose that, given the two initial endowments and the initial prices, the competitive equilibrium would be such that Anne would receive a much higher utility than Bill. Can the government intervene to restore the egalitarian outcome where Anne and Bill would achieve the same utility? Explain your answer. • State the first and second theorem of welfare economics