1. Chapter 7 General Equilibrium and Market Efficiency

2. Outline. A simple exchange economy Efficiency in production
Efficiency in product mix
Sources of inefficiency

3. 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.

4. 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

5. The Edgeworth Box

6. Improving utility through exchange

7. Further improving utility through exchange

8. Reaching a Pareto-optimal allocation

9. The Contract Curve

10. From initial endowments to the contract curve

11. 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.

12. Exchanges in a market economy

13. General equilibrium in a market economy

14. 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

15. 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

16. Decentralisation of the optimum

17. Outline. Efficiency in production Efficiency in product mix
Sources of inefficiency

18. 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.

19. The Edgeworth production box

20. 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

21. Outline.
Efficiency in product mix
Sources of inefficiency

22. 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.

24. 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.

25. 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

26. 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

27. 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.

28. 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,

29. 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.

30. Outline.
Sources of inefficiency

31. Taxes in general equilibrium

32. 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.

33. 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

34. 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 .

35. 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.

36. 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

37. 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.