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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.

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Lecture 2

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Lecture 2 l.jpg

Lecture 2

Market Allocations and Efficiency

Suggested Readings: Conolly & Munro, The Economics of the Public sector, chapter 2


Market allocations and efficiency l.jpg

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


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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


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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


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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.


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EBx

Good x

Bill

Good y

Edgeworth Box Diagram

EBy

EAy

Good y

EAx

Good x

Anne


Slide7 l.jpg

Good x

EBx

Bill

Good y

EBy

EAy

ICA

Good y

EAx

Good x

Anne


Slide8 l.jpg

EBx

Good x

Bill

Good y

E

EBy

EAy

ICA

ICB

Good y

EAx

Good x


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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


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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!


Slide11 l.jpg

xB

EBx

Good x

Bill

Good y

The Contract Curve

yB

yA

E

EBy

EAy

Good y

xA

EAx

Good x

Anne


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Utility possibility frontier (UPF)

UB

A

C

B

UA


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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?


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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


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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:


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Price Offer Curve

y

Price-offer curve

x


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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:


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xB

EBx

Good x

Bill

Good y

yB

yA

E

EBy

EAy

Budget constraint

Good y

xA

EAx

Good x

Anne


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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


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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?


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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


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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?


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Market failure

  • Potential sources of market failure

    • Monopoly

    • Barriers to trade (Taxes, subsidies)

    • Externalities

    • Public Goods

    • Imperfect information

    • Rationality and consistency of agents


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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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