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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

Lecture 2

Market Allocations and Efficiency

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

market allocations and efficiency
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
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
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
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.
slide6
EBx

Good x

Bill

Good y

Edgeworth Box Diagram

EBy

EAy

Good y

EAx

Good x

Anne

slide7
Good x

EBx

Bill

Good y

EBy

EAy

ICA

Good y

EAx

Good x

Anne

slide8
EBx

Good x

Bill

Good y

E

EBy

EAy

ICA

ICB

Good y

EAx

Good x

pareto efficiency in an exchange economy
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 economy10
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
xB

EBx

Good x

Bill

Good y

The Contract Curve

yB

yA

E

EBy

EAy

Good y

xA

EAx

Good x

Anne

utility possibility frontier upf13
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
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
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:
price offer curve16
Price Offer Curve

y

Price-offer curve

x

competitive equilibrium in an exchange economy17
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:
slide18
xB

EBx

Good x

Bill

Good y

yB

yA

E

EBy

EAy

Budget constraint

Good y

xA

EAx

Good x

Anne

first fundamental welfare theorem
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
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
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 failure22
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 failure23
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 (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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