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. The basic condition that assures this result is that

consumer indifference curves be convex when viewed from the origin.

Why not redistribute initial endowments in order to achieve the desired outcome directly? 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

0M

h wp

w

'U

'U

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:

Given that the price of inputs is the same for both firms, this yields

r

w

MPK

MPL

C

C and r

w

MPK

MPL

F

F

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:

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.

C

FMRT

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

C

MC

MC

C

FMRT

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,

So, an economy in competitive general equilibrium is simultaneously efficient (i.e. Pareto optimal) in consumption, production and in the choice of product mix.

MRSP

PMRT

*F

*C

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. But in general, comodity taxes will have distortionary

effects

Lump-sum taxes 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.

Example: radio or TV programs, national defence.

They are non-excludable: it is impossible to exclude somebody who does not pay from using the good.

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.