Download 1 Lecture 3: First and Second Theorems of Welfare Economics and

Lecture 3: First and Second Theorems of Welfare Economics and Market Efficiency
1) For the moment we are going to forget that this class is about the environment and
talk about basic welfare economics instead
a) Start with definitions
b) Move on to most powerful theorems of welfare economics
c) Talk about the conditions for these theorems to hold
2) Definitions
a) Welfare economics is the systematic method of evaluating the economic
implications of alternative resource allocations. Welfare analysis answers the
following questions:
i) Is a given resource allocation efficient?
ii) Who gains and who loses under various allocations, and by how much?
b) Competitive economy - an economy which consists of many small economic
units - each with no market power - conditions for competitive economy –
i) Q: What are the conditions for a competitive economy?
ii) mobile resources,
iii) many buyers and sellers,
iv) traded good is homogenous,
v) perfect information.
c) Pareto improvement: A reallocation of resources such that some individuals are
made better off while no individuals are made worse off.
d) Pareto efficiency - We say we have satisfied Pareto efficiency when there are no
opportunities for Pareto improvements
i) We say allocation/arrangement X is Pareto superior to Y if all individuals are
at least as happy with X as with Y, and at least one individual is happier.
ii) Consider the case of three boys who will earn (5,5,7) if they do chore X
together or (6,6,7) if they do chore Y together. the two tasks are equally
onerous and the employer is indifferent between the two chore-payment
arrangements. Then doing chore Y is Pareto superior.
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e) Kaldor-Hicks efficiency - We say X is Kaldor-Hicks superior to Y if there is a
state that is accessible from X that is Pareto superior to Y. This allows for the
theoretical possibility at least that everyone could be made better off by choosing
X.
i) What is a common application of the Kaldor-Hicks criterion? [Cost-benefit]
ii) We are mostly going to be talking about the Pareto criterion today.
3) Role of trade in an economy - Edgeworth box
a) We have talked in V517 about
i) Consumer and producer theory
ii) Inputs and input prices
iii) Have to ask, how do the right resources get to the right place?
b) Consumption Economy
i) Consider a very simple pure exchange economy: island economy - two
individuals, two goods, no production
(1) Call the individuals Gilligan and Skipper and the goods Coconuts and
Fish.
(2) There are C units of coconut and F units of fish that must be shared
(3) Each individual has a utility function that expresses their relative
satisfaction as a function of the amount of the two goods they consume.
The utility functions are monotonic and selfish,
(a) Monotonic - nonsatiation - more is better than less
(b) Selfish - independence of utility from consumption of others
(4) Must cover the entire range of consumption possibilities
(5) Can express the utility function
in graphical form, with
indifference curves
(a) The individual’s utility or
welfare level is the same
with any combination of
goods that are on the same
indifferent curve.
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(b) There is an decreasing marginal rate of substitution for either good
(6) Gilligan’s indifference curve: FLIP IT OVER and it still means the same
thing. In fact that is how we will represent Skipper’s indifference curve
(a) We can map out the entire
feasible distribution of
goods by laying one on top
of other
(b) Any point in this coconut
fish space represents a
distribution of all resources
among the two members of
the economy.
(c) Overlay the two sets of indifference curves to create a coconut-fish
distribution space and consider an initial distribution D. This is called
an Edgeworth Box. It is commonly used in microeconomics to
illustrate simple trading priniciples.
(d) Gilligan consumes a fish and b coconuts, so Skipper consumes (F-a)
fish and (C-b) coconuts.
(e) There are an infinite number of initial distribution points, D
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(7) Now, suppose that we allow Skipper and Gilligan to trade, essentially
reallocating resources from this initial distribution.
(a) How do we know where they will end up? What criteria must be
satisfied before they will stop trading?
(b) We apply two criteria
(i) Economic or allocative efficiency – Pareto Efficiency
(ii) Some traders better off, none worse off; that is the outcome needs
to be Pareto Superior to initial allocation
(c) Pareto Efficiency:
(i) Where are the Pareto efficient points in this coconut-fish space?
Marginal rate of substitution of fish for coconuts must be the same
for both Skipper and Gilligan
(ii) Defn: Number of units of coconuts that will give up for one unit of
fish, while remaining on same indifference curve. Equal to (1)(slope of indifference curve).
(iii)The marginal rates of
substitution are equal
only where the
indifference curves are
tangent.
(iv) How many tangents
are there. Remember
there are an infinite
number of indifference
curves in the coconut fish space, so there much be an infinite
number of tangent points. But each of Gilligan’s curves are tangent
to one and only one of Skipper’s curves.
(v) Contract curve
1. Def’n contract curve: set of points where MRSG=MRSS
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2. It actually looks like a small subset of all possible allocations,
but it is still an infinite
number of points. Shown in
green in this digram.
(d) Pareto Superiority:
(i) All points on the contract curve
are Pareto Efficient or Optimal.
Are all points on the contract
curve Pareto Suprerior to the
initial distribution point? No, they are not.
(ii) Find a point on the contract curve that is not Pareto Superior. How
do you know that it is not
Pareto Superior?
(iii)The set of points that are
Pareto superior to D are
called the Lens. These are
shown as the orange shaded
area in the diagram above.
They are the points
(distributions of goods) at
which both traders would be
at least as well off, and one trader better off. Therefore, they also
represent the points to which the traders would move voluntarily.
(iv) The Core is the set of
points that are both Pareto
superior and Pareto
efficient; it is the locus of
Pareto optimal points
within the lens shaped area
that is bounded by the
indifference curves passing
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through the initial allocation D.
1. At any place on the core the MRS of two traders is the same,
i.e. there are no more mutual gains from trade available.
Where on the core they end up will depend upon the relative
bargaining skills of the individual traders.
2. In a perfectly competitive economy, we get some outcome that
distributes goods among consumers based on an equilibrium
price system.
3. What is the relation between the theoretical market outcome
based on prices and the core?
4) First Fundamental Theorem of Welfare Economics
a) Definitions:
i) x is the allocation of goods to all traders in the economy - x is a matrix with
two dimensions: quantity of good and amount allocated to each trader
ii) p is a vector of prices for each good
b) First Fundamental Theorem of Welfare Economics. If all traders have
monotonic selfish utility functions, and if (x,p) is a competitive equilibrium, then
x is in the core, and is therefore Pareto optimal as well.
c) What this says is that the price system from a perfectly competitive economy,
induces selfish individuals independently maximizing their private well-being, to
bring the economy to a socially optimal state. Prices rise in response to excess
demand, fall in response to excess supply - adjust on their own.
d) Normatively, it says use the competitive mechanism - use the free market.
e) Read excerpt from Kahn p11, Adam Smith on invisible hand.
5) Second Fundamental Theorem of Welfare Economics
a) Besides prices, what determines which of the many Pareto efficient points on the
contract curve will result from the competitive equilibrium? [Initial allocation]
i) Does the FFTWE say anything about the initial distribution or about equity?
ii) Can the competitive equilibrium get you from a very uneven initial allocation
to a more equitable final allocation? Not really, the theorem takes initial
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distribution as given. Uneven initial allocation => uneven competitive
allocation.
iii) What are some examples of uneven initial allocations? E.g. talent, capital,
family etc.
iv) Why not just reallocate goods, move from one point to another? Take away
some of Skipper’s fish and give them to Gilligan
v) The problem is that in a real economy there are large numbers of goods and
consumers, not just two of each.
vi) E.g., of gasoline in 1979 - DOE reallocation of supplies by region. This made
a mess of the distribution system and was inefficient.
b) What would be an alternative mechanism? Simply reallocate one good - e.g.,
money. The price system can then facilitate exchange for Pareto efficient
outcomes in the core.
c) Definitions:
i) y is any Pareto optimal allocation that assigns positive quantities of every
good to every trader: yij > 0 for all I, j
ii) m is the number of goods in the economy
iii) n is the number of traders in the economy
d) Second Fundamental Theorem of Welfare Economics. There exists a vector of
bank balance transfers (T1, T2, ...,Tn) and a price vector p = (p1, p2, ...,pm) such
that y and p are a competitive equilibrium given the transfers.
i) What does this say?
(1) Choose an outcome that is economically efficient (i.e., it is on the contract
curve).
(2) You can get to that outcome by redistributing the initial allocation of
resources and then simply relying upon the competitive mechanism.
(3) C.f. western water supply – we know marginal cost pricing is superior to
subsidized system - but we have always worried about the distributional
effects it might have. If that is the case then simply redistribute the initial
property rights.
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(4) So the SFTWE says that the competitive mechanism, with modifications,
is even more robust than described by the FFTWE.
6) These two theorems taken together relieve the government of an enormous amount of
work - no need to decide every consumption decision/opportunity for every consumer
- just get the initial allocation close to an are you want, and you can let the market
take over.
a) Assumptions behind market efficiency
i) What are the assumptions behind perfectly competitive markets
(1) Costless entry and exit
(2) Homogenous goods
(3) Perfect info
(4) Many suppliers and buyers
ii) In the FFTWE and SFTWE what were the assumptions?
(1) Monotonic selfish utility functions - consumer sovereignty
(2) That if you don’t like the initial distribution you can redistribute wealth.
iii) Are there any other assumptions implicit in this
(1) Goods are all owned - i.e., there are property rights in each important good
– F&SFTWE apply to individual markets not whole economy
(2) They are consumption goods - if you use it, I don’t
(3) That I don’t steal your goods from you - No cheating
(4) In the marginal cost supply function - full costs of production are reflected
In the demand function full range of benefits is reflected
(5) In fact, demand and supply functions are based on individual assessments
of costs and benefits. Need to ask about the relation between social and
private benefits.
(6) No paternalism – we accept the consumer sovereignty
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