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### Lecture 2

Market Allocations and Efficiency

Suggested Readings: Conolly & Munro, The Economics of the Public sector, chapter 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

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

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

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.

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

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!

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?

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

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:

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:

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

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?

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

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?

Market failure

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

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

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