Transcript Efficiency in product mix - will get through comparison

Chapter 7
General Equilibrium and
Market Efficiency
Outline.

A simple exchange economy

Efficiency in production

Efficiency in product mix

Sources of inefficiency
A simple exchange economy

Consider a simple economy in which there
are only two consumers A (Ann) and B
(Bill) and two goods: food and clothing.

Available quantities of goods are exogenous:


Food = 100
Clothing = 200

An allocation is an assignment of these
quantities between A and B.

The amounts of goods with which A and B
start each period are called their initial
endowments.
Personal bargaining

What do A and B do with their initial
endowments?

They may either consume what they
already have or to engage in exchange
one with the other.

Exchange is purely voluntary so it only takes
place if it is beneficial to both parties

Exchange makes someone better off if it places
him on a higher indifference curve
The Edgeworth Box
Improving utility through exchange
Further improving utility through
exchange
Reaching a Pareto-optimal allocation
The Contract Curve
From initial endowments to the contract
curve
Market economies

In our very simple example, exchange
took place through personal bargaining.
In market economies, most exchanges
have a more impersonal character.

People have given endowments and they face
given prices. They then decide how many
goods and services they want to buy and sell.

We can introduce market-type exchanges by
assuming that there exists a third (fictive)
person playing the role of an auctioneer.
Exchanges in a market economy
General equilibrium in a market
economy
The first theorem of welfare economics

It is also called the theorem of the
Invisible Hand.


It can be stated as follows: an equilibrium
produced by competitive markets will exhaust
all possible gains from exchange.
Another way to put it is that equilibrium in
competitive markets is Pareto optimal:
competitive equilibrium is efficient
The second theorem of welfare
economics

It states that any allocation on the contract curve
can be sustained as a competitive equilibrium.


Why not redistribute initial endowments in order to
achieve the desired outcome directly?


The basic condition that assures this result is that
consumer indifference curves be convex when viewed
from the origin.
Lack of information on consumers' indifference curves
Consequence of the theorem: the issue of equity in
distribution is logically separable from the issue of
efficiency in allocation
Decentralisation of the optimum
Outline.

Efficiency in production

Efficiency in product mix

Sources of inefficiency
Efficiency in production

The product mix in an economy is the
result of the allocation of productive inputs

Suppose we add a productive sector to our
exchange economy.


It consists of 2 firms, each of them using capital K
and labour L.
Firm C produces clothing and firm F produces food.

Suppose the total quantities of the 2 inputs are
fixed with K = 50 and L = 100.

The production processes used by the 2 firms
give rise to conventional convex-shaped
isoquants.
The Edgeworth production box
U'h w
  w0
U'M p
The efficiency of general equilibrium


If firms maximise their profits, the resulting
general equilibrium will satisfy the requirements
of efficiency in production

Suppose that food and clothing prices are P*F and P*C.

Suppose that firms hire labour and capital on perfectly
competitive markets at hourly rates w and r.
If both firms minimise costs we have:
MPL C w

MPK C r

and
MPL F w

MPK F r
Given that the price of inputs is the same for
both firms, this yields
MRTSC = MRTSF
Outline.

Efficiency in product mix

Sources of inefficiency
Efficiency in production mix

An economy may be efficient in production and,
at the same time do a very poor job in satisfying
the wants of its members

So, there is one more efficiency criterion of concern
which is whether the economy has an efficient mix of
the two products
 To define the efficient product mix, it is useful to
translate the contract curve from the Edgeworth
production box into a production possibilities
frontier

Definition: this is the set of all possible output
combinations that can be produced with given quantities
of capital and labour.
The marginal rate of transformation

The slope of the production possibilities
frontier at any point is called the marginal
rate of transformation (MRT)


It measures the opportunity cost of clothing in
terms of food.
For the economy we consider, the MRT
increases when we move to the right. This is
always the case as long as there are constant
or decreasing returns to scale.
Efficiency in product mix

In order for an economy to be efficient in terms
of production mix, the MRS for each consumer
has to be equal to the MRT
General equilibrium and efficiency in
product mix

Let P*F and P*C denote the equilibrium
prices for food and clothing.


As we have seen for the simple exchange
economy, in equilibrium, the MRS of every
consumer will be equal to the ratio of these
prices P*C / P*F.
In order to show that the general equilibrium
is efficient, we need to show that the MRT is
*
*
also equal to P C / P F
Demonstration

Let’s show that at any point on the production
possibilities frontier he MRT is equal to the ratio
of the marginal cost of clothing (MCC) to the
marginal cost of food (MCF).

The MRT is given by:
F
MRT 
C

It is the amount of food you have to give up in order to
get one more unit of clothing.

In order to produce one more unit of clothing, we need
to use a bundle of inputs the value of which is MCC.
Demonstration (ctd1)


In order to get that bundle of input, we need to
produce less food.

For each unit of food we give up, we get an input bundle
which is worth MCF.

So, in order to get an input bundle worth 1, we need to
give up 1/ MCF units of food

In order to get an input bundle worth MCC, we need to
give up MCC / MCF units of food.
So,
F MC C
MRT 

C MC F
Demonstration (ctd2)

The equilibrium condition for food and clothing
producers is that product prices be equal to the
corresponding marginal costs.
P*F = MCF

and
P
*
C
= MCC
So,
PC*
MRT  *  MRS
PF

So, an economy in competitive general equilibrium
is simultaneously efficient (i.e. Pareto optimal) in
consumption, production and in the choice of
product mix.
Outline.

Sources of inefficiency
Taxes in general equilibrium
Taxes and inefficiency in the product
mix

Even with the tax on food, consumers have a
common value of MRS in equilibrium and that
producers have a common value of MRTS. So, the
economy is efficient in consumption and
production.

The tax causes producers to see a different price ratio
from the one seen by consumers: consumption decisions
are based on gross prices whereas production decisions
are guided by net prices.

So, the MRS and MRT can never be equal in equilibrium.

So, the tax leads to an inefficient production mix.
Minimising Distorsions

Subsidies, like taxes upset the conditions
required for efficiency

The tax system has to be designed in
order to minimise distorsions

Taxing food and clothing at the same rate t.


Lump-sum taxes


But in general, comodity taxes will have distortionary
effects
But generate equity problems
The best tax: tax levied on activities of which
there would otherwise be too much
Externalities


Another source of inefficiency occurs when
production or consumption activities involve
benefits or costs for people not directly involved
in them. Such benefits and costs are called
externalities

Example of negative externality: pollution

Example of positive externality: flowers
Externalities create a problem very similar to
taxes: they cause producers and consumers to
react to a different set of relative prices .
Externalities (ctd)


Solution

Tax negative externalities

Subsidise positive externalities
The existence of externalities is a good
example of market failure

It is a case in which the outcome generated by
the working of the market is no optimal.

This sets the ground for public intervention in
the economy.
Public goods

Pure public goods have 2 characteristics
 They are non-rival: the fact that one person
uses the good does not reduce the amount of
good that can be used by another person.


They are non-excludable: it is impossible to exclude
somebody who does not pay from using the good.


Example: radio or TV programs, national defence.
Example: TV programs before cable TV, radio programs,
national defence
There is no reason to presume that private
markets will supply optimal quantities of pure
public goods
Public goods (ctd)


The problem is less acute with goods that
are non-rival but excludable.

Example: cable TV. It is possible to exclude
people from watching programs they do not
pay for.

But even here there are likely to be
inefficiencies: Once a TV program has been
produced, it costs society nothing to let an
extra person see it.
Here again, these market failures set the
ground for public intervention in the
economy.