roduction to Economics
Introduction to Economics
Efficiency of a competitive general equilibrium
Begg et al: Ch. 13
, 14 (especially 13.1
14.3) or Sloman and Wride ch. 11
Competitive general equilibrium
When we consider a single market, for example the labour market, we make a Partial
Equilibrium Analysis. This means that we focus on that market only without looking
at the possible link
s with other markets. However, in an economy all markets are
normally linked. If something happens in one market, it will affect also other markets.
For example, recently the house market in US went down. That affects the credit
market. The fact that the c
redit market went down affects the goods market and also
the labour market (more unemployment), etc. etc.
We will focus on an economy with few markets: there will be two goods produced, so
we have two goods market, and two factor markets, one for labour an
d one for capital.
All markets will be competitive.
We want to see w
hat the main properties of that economy in terms of efficiency
First we need to introduce a way to
measure efficiency. The concept of efficiency we
use is the Pareto Efficiency crite
2) Pareto Efficiency
The Pareto criterion is a key value judgement.
it says that situation A is preferred to situation B if in A at least one
person is better off and no one is worse off than in B
This is a very stringent criterion. Ho
wever, it is simple and it gives a clear idea about
what efficiency is.
Example: sharing a cake between two people.
At point A individual A has the whole cake and gets utility UA; at point B individual
B gets the whole cake and gets utility UB.
say whether allocation C is Pareto superior to either A or B because as
compared with C one person is worse off.
Allocation E is Pareto superior to C, because both individuals are better off. But D is
not superior to C.
At any point inside the frontier th
ere is a range of Pareto superior allocations. Note
that here some of the cake is lost or wasted; at least one person could be made better
off if this inefficiency was eliminated.
Points like D and E (and A and B) are Pareto efficient. One person cannot be
made better off without making another person worse off
Pareto efficient points are points of maximum efficiency.
note that Pareto efficiency is of no help in resolving distributional issues.
A, B, D and E are all Pareto efficient. We have no
way of choosing between them
unless we are willing to make additional value judgements
This means that a point like A where one agent gets everything while the other gets
nothing can be efficient. It mat not be fair according to our moral judgement but it
may be efficient.
3) General competitive equilibrium and Pareto efficiency
Suppose that there are two consumers, A and B (we may think that are many
consumers but half of them are equal to consumer A and the other half is equal to
two goods in the economy, X and Y.
Suppose that here are two firms, each
producing one of the two goods (again, we can think at the case where there are many
firms in each, but they are all equal, etc. etc.).
Consumers A and B consume both goods.
ets fro good X and Y are
Rational consumers will choose the quantity of X and Y to consume in order to
maximise their utilities.
Since the market are competitive, each consumer takes the prices of the two goods as
given. Denote with
the price of good X and with P
the price of good Y.
3.1) Efficiency in consumption
From consumer theory we know that each consumer will consume a bundle
containing X and Y such that his marginal rate of substitution is equal to the price
is the marginal rate of substitution between X and Y for consumer A.
The conditions above imply that
in competitive markets
Efficiency in consumption:
Suppose that th
e two goods are books and CDs.
• A is willing to exchange 2 books for one CD.
• B is willing to exchange 4 books for one CD.
That must mean that MRS
; in particular
in absolute values we have
=2 and MRS
=4. This also implies that the ratio of ma
rginal utilities cannot be
the same for the two individuals.
In this example, B values books less than A, while it values a CD more than A.
The following exchange will make both persons better off:
• B gives 3 books to A
• A gives one CD to B
As long as MR
there is scope for exchanges that make one person better
off without making the other worse off. (So there is a Pareto superior allocation).
Consumption efficiency requires that MRS
is absolute values.
If that is true, we are in a Pareto ef
ficient situation an
it is impossible to improve the
situation of one consumer without worsening the situation of the other. Therefore the
fact that markets are competitive together with the fact that consumers are rational
a Pareto efficient outc
ome in the consumption activity.
3.2) Efficiency in production
Firms in each
X and Y, will try to produce each good minimising the costs of
If the markets for the two inputs, K and L, are competitive, the conditions for cost
is the marginal rate of technical substitution for the firm producing
good X, while
is the unit cost of labour and
is the rental cost of capital.
The conditions above imply:
iency in production
Factors of production (K and L) are allocated across industries with maximum
efficiency when the marginal rate of technical substitution between factors is the same
across all industries.
Again the condition for
efficiency in production implies a Pareto efficient allocation
of resources (in this case K and L) across sectors.
3.3) Efficiency in output choice
Since the firms are producing at the cost minimising level, they are using efficiently
their resources (K
and L). Therefore, they must produce on the Production Possibility
Frontier of our economy.
First define a Isovalue Function:
where V denotes the value of the production in the economy. The Isovalue function
tells you all the combi
nations of X and Y (the amounts of the two goods produced)
that give you the same value V. Since we are in competitive markets the prices of the
two goods are given.
From the isovalue function we can get the Isovalue Line:
nomy will produce an amount of good X and an amount of good Y where the
PPF is tangent with the highest Isovalue line.
The economy will produce an amount X
and an amount Y
of the two goods.
firm producing good X will maxi
mise its profits by producing at point E since at that
point is minimising its costs. The same for the firm in sector Y.
The slope of the PPF is the opportunity cost of X in terms of Y. We wrote a general
PPF therefore the opportunity cost is changing alo
ng the PPF.
Another way to call the slope of the PPF is the
Marginal Rate of Transformation
the rate at which the economy can transform one good into another (by
shifting the factors of production between industries)
The slope of the Isovalue line
At point E it must be true that:
The cost opportunity of X in terms of Y is exactly equal to the price ratio.
are in competitive markets, the market price of good X must be equal to the marginal
cost of producing X and the market price of Y must be equal to the marginal cost of
producing Y (remember that in a competitive market a competitive firm produces at
the point where P = MC).
We can write the condition above as:
Efficiency in output product
3.4) Putting production and consumption together: Allocation efficiency
Efficiency in output choice requires that
Efficiency in consumption requires that
Therefore, it must be
Therefore, we can write:
An important result in economics is that, under certain conditions, there exists a price
that can make the condition above to hold.
hat is true, we say a general economic equilibrium for our economy exists.
Suppose that all consumers in the economy are equal (the result will hold even if the
consumers are different), so that we can write an in
difference curve for a
representative consumer. The figure above says that there is a price ratio P
can make the MRT equal to the MRS of the consumers in the economy.
4) The First Fundamental Theorem of Welfare Economics
We can now summarise the
analysis done to see what are the efficiency properties of
market outcomes are.
In particular, is a perfectly competitive general equilibrium Pareto efficient?
A perfectly competitive general equ
librium is where there is perfect competition
in all markets
The specific conditions are:
Individuals maximise utility
and are price takers
Firms are price takers and maximise profits
All markets for goods and factors clear
(demand is equal to supply in each market)
First Welfare Theorem
if a general compe
titive equilibrium exists, then it must be
This result comes from the fact that in a competitive equilibrium we can obtain
efficiency in consumption, in production and in the final allocation of resources.
When we say that an equilibrium
is Pareto efficient we can say that we are at the
The First Welfare Theorem provides a general confirmation of Adam Smith’s
asserted “Invisible Hand” property of competitive markets.
Perfect competition achieves a Pareto efficient
allocation of resources.
There is no explicit coordination: the price mechanism provides the right sign
an efficient allocation of resources.
This is a very strong result since it says that in a
market in which there are so many buyers and seller
s that no individual believes he
can affect the market prices, individuals will coordinate toward a Pareto efficient
allocation of resources. Hence, the First Welfare Theorem gives a theoretical
justification on the fact that Governments should not interfe
re with the economic
activity in a competitive market.
The intuition is the following: if there is some
commodity or service individuals value but that is not currently being produced, then
they will be willing to pay something for it. If the cost of produ
cing such good or
service is lower than the value the individuals assign to it, then firms, in their search
for profits, will produce it. Similarly, if there is a cheaper way to produce a certain
good than the one currently used, firms will adopt that chea
p way, since by that they
can cut costs and raise profits.
4) The Second Fundamental Theorem of Welfare Economics
The first welfare theorems does not say anything about the distribution of resources.
For example, a situation where few consumers get most
of the goods produces and
many consumers get very few can be Pareto efficient.
The second welfare theorem deals with distributional issues in a general competitive
The Second Welfare Theorem
optimal allocation can be obtained via
general competitive equilibrium, provided the government is able to implement the
required system of lump
sum taxes and transfers.
The second welfare theorem says that the issue of efficiency and the issue of
distribution can be separated in principle.
Suppose an economy where there are two consumers, one is very rich, meaning that is
born with already a lot of resources. The other consumer is born with very few
resources. A government can take some of the resources from the rich and transfer
them to th
e poor guy and then let the market working as usual. The final result will be
Pareto efficient, but the final allocation of resources the two consumers can get (how
much they consume of different goods) can be more equal now.
Differently from the first we
lfare theorem, the second welfare theorem gives a
justification for Governments to intervene in the economy by changing the initial
resource allocation among the agents.
: To change the distribution of income in an economy, one needs to
only the distribution of initial endowments. The initial endowment of a given
normally consists of his labour power. That is the amount of labour (how
many hours, or days, etc. etc.) that he could consider selling, not the amount of labour
actually ends up selling it.
However, we normally do not know the POTENTIAL VALUE OF LABOUR of each
person (their endowment). We can see their labour income, and therefore we can tax
that. However, by taxing labour income we will create distortion and dead
losses. Therefore we will lose efficiency by doing that.
sum taxes and transfers are NON DISTORTIONARY, but normally it difficult
to implement them, and in many cases they are not fair. An example of a possible
lump sum tax is the “citizenship
tax”. Each citizen in a given economy are taxed by
the same amount, say £10, just because they are citizens. This is not very fair because
a very reach citizen ends up paying the same amount as a very poor citizen. However,
this kind of tax does not creat
e deadweight losses, since everybody pays the same
amount, and so in relative terms nothing as changed.
The competitive market mechanism has several important
• It coordinates decentralised decisions by a very large number of econ
without the need for conscious control.
• It provides strong incentives and disciplines producers against the wasteful use of
• Price signals convey information about changing market conditions which guides
• It d
oes not usually lead to an excessive concentration of economic power.
• It does not ensure a ‘fair’ distribution of income.
• It requires very stringent conditions that are associated with perfect competition.
6) Market Failures
general the conditions required under the first and second fundamental theorems
are rarely satisfied in practice. There are a number of sources of inefficiency in the
Those inefficiencies create a justification for Governments to intervene
The main inefficiencies in an economy are: imperfect competition, public goods,
externalities, missing markets and incomplete information.
All those inefficiencies are called
. They are called market failures
because in thos
e cases the market outcome is inefficient (compare to the competitive
6.1) Imperfect competition
Suppose an economy with two goods, X and Y.
Suppose that there is perfect competition in the industry producing good Y so that P
opoly in the industry producing X, so P
The condition for allocation is violated since:
In practice, we have that too few of god X is produced compared to what it is socially
optimal (what it should be produced if all the ma
rkets were competitive). Indeed we
know that a monopoly creates a “deadweight loss” in social welfare. Therefore,
having some sectors that are imperfectly competitive will create inefficiencies and the
general equilibrium will not be Pareto efficient.
So far all the goods we talked about were
. A good is private if a
consumer that buys that good
other consumers to consume that good and
if there is
in consumption. For example, if you buy a car, other consum
cannot drive your car.
However, consider a public park in the middle of a town. Everybody can in principle
walk in the park and enjoy it even if they didn’t pay anything for building the park.
Pure Public Good
) is a good that sati
sfies the following
. This means that my enjoyment or consumption of the good does not
prevent or reduce your enjoyment or consumption of it.
. A person cannot be excluded from consuming it even if
e does not pay for that consumption.
National defence is an obvious example, but there are other more locally provided
public goods such as public parks, roads etc (assuming
Suppose that a private firm provides a public good, like a park in
a town. Since there
is not a market for parks, the private firm should ask the people in the town how much
they will be willing to pay to have a park in their town.
I would be willing to pay towards the building of a park. But if it does get built, you
ill enjoy it too at no cost. You have an incentive to say that you do not value it so
that you don’t pay for the park.
This creates the
Free Rider problem
an individual has an incentive to say that is
unwilling to pay for a public good since he knows tha
t once the public good is
available it cannot be excluded from consuming it
If everybody behaves in the same way as a free rider, the public may not be provided
at all by the private firm.
In general, as a result of the free rider problem there will be
public goods by the private market.
This is why public goods are usually supplied by the government and financed
arise when one agent (an individual or a firm) imposes costs or benefits
another agent in a way other than by changing prices
A noisy airport can impose a negative externality on nearby residents.
A beautiful garden may impose a positive externality on neighbours.
externalities have economic value (positi
ve or negative) but there
is no market for them
When there are externalities (side effects of production and consumption) there will
be a difference between the
Marginal Private Costs
Marginal Social Costs
and between the
Marginal Private Benefit
Marginal Social Benefits
There are 4 possible externalities.
6.3.1) Negative externality of production
Suppose a chemical firm that produces some products. However, in order to produce
it pollutes the air.
The community is ne
gatively affected by the pollution.
The marginal private cost
C) of the chemical firm is just its marginal cost of
production. The firm does not take into account the fact that its pollution has negative
effects on the community.
The marginal social co
st (MSC) is given by the marginal private cost plus the external
costs for the community created by the pollution. Therefore, MSC > MC.
Suppose that the firm sells its product in a competitive market. The fir
m will produce
an amount Q
that is where P = MC. Since it does consider the external effects of its
production (pollution) it produces more than it socially optimal. The socially optimal
quantity is where P = MSC and it is Q
Therefore, when there is a
negative externality of production, the quantity produced of
the good producing the externality is higher than the optimal social level.
For the firm
is the optimal choice, but for the society is not.
In the figure the external cost faced
by the society
is measured as the vertical distance between the MSC and the MC.
6.3.2) Positive externality of production
In some cases, the side effects of production can be positive. For example a forestry
company that plants new woodlands create positive effects f
or the society since it
helps in reducing the CO2 emission in the atmosphere.
In this case the Marginal Social Costs are lower than the Marginal Private Cost of the
The quantity produced when there is a positive externa
lity in production is lower than
the social optimum.
6.3.3) Negative externality in consumption
When you drive a car you affect other people in the road since you are adding
congestion, noise etc. etc. (think about the congestion tax in London). In this c
there is a difference between the Marginal Private Benefits (
nd the Marginal Social Benefits
. In particular the
Benefits from using the car is going to be lower than the marginal private benefits.
is depicted in the following figure. P in that figure can be thought as the price of
When there is a negative externality in consumption of a given good (for example
driving a car), agents tend to consume more of it
than it socially optimal.
6.3.4) Positive externality in consumption
Suppose using the train instead of the car. Other people will benefit from that since
there will be less congestion on the road, less noise, less accidents etc. etc.
In this case the Marginal Social Benefits are higher than the marginal private benefits.
When there is a positive externality in consumption of a given good, agents tend to
consume less of it than it is socially optimal.
Possible solutions t
o the externality problem
Consider the case of a firm that produces steel and pollute
a river that is used by a
The steel producer has the following cost function:
, where Q
quantity of steel produced and P is th
e level of pollution. We assume that:
as the quantity produced increases, costs increases.
as pollution increases costs decreases.
Think for example at the case
where the firm must invest in a cleaner technol
ogy to pollute less, and that cleaner
technology is costly.
The profit function of the steel firm is:
where S is the price of steel. Assume that steel is sold in a competitive market.
The steel firm chooses Q
such that the price
of steel is equal to the marginal cost:
The level of pollution that maximises profits of the steel firm is
given by the
since the marginal revenue of pollution is zero.
, in order to have
P must be quite high.
The fish firm has a cost function given by:
, with the properties that:
costs of the fish firm increases as production increases.
the cost of the fish firm increases as pollution increases.
The profit function of the fish firm is:
Here the fish firm is negatively affected by the pollution of the steel firm
, since its
. However, the s
teel firm does not recognise this effect when it decides
how much to pollute.
7.1) Internalisation of the externality
A possible solution of that externality problem is for the steel firm to buy the fish firm
(or vice versa).
In this case the profit func
tion of the new firm is the sum of the profits previously
The level of pollution that maximises profit is
given by the following condition
Before we had
, while now the marginal cost of pollution for the
steel firm is equal to the marginal cost of pollution of the fish firm. Since
, the level of pollution chosen by this joint firm is lower than before.
The externality is intern
alised, and in deciding how much to pollute the negative
effect on the fish firm is taken into account.
Now the marginal private cost will be
equal to the marginal social cost. This gives us an efficient solution.
7.2) Pigouvian Tax
Suppose that we can ta
x the level of pollution made by the steel firm. Denote with
the tax rate.
The profit function of the steel firm becomes:
Now the level of pollution that maximises profits is given by
we obtain the same result as in the case of internalisation.
: we need to know how pollution affects the cost of the fish firm. In many
cases it is not easy to have such information.
erty Rights and the Coase Theorem
The problem of externality arises because the property right are not perfectly
assigned. Suppose we give to the steel firm the right to pollute. The steel firm can sell
this right on a market. The fish firm can then buy th
at right from the steel firm and
reduce the amount of pollution made by the steel firm.
Denote with q the price obtained by the steel firm that sells its right to pollute.
The profit function of the steel firm becomes:
The profit fu
nction of the fish firm is now:
The quantity of pollution that maximises the profits of the steel firm is found by the
The quantity of pollution that maximises the profits of the fish firm is found
Using this into the condition of the steel firm we have=
That is the same condition found in the internalisation case.
The same results can be found if we give th
e right not to be polluted to the fish firm.
The fish firm can sell that right to the steel firm. The result will be that the externality
will be internalised. This is the essence of the
. If we can assign
property rights (independently on who
has the legal right to pollute or not to be
polluted) the parties can bargain about the level of the externality and the externality
will be internalised. The socially efficient level of output will be reached.