General Equilibrium and the Welfare Theorems

A pure exchange economy

• Aim to describe an economy through simple concepts

• We need three objects, a set of traders, preferences, and resources (each agent is given some endowment)

• Generally we’ll use the simple framework of two agents and two goods

The Edgeworth Box

• Consists of fitting the different indifference curves of the different agents into the same graph, from opposite origins, where the sizes of the edges represent the total resources in the economy

• There are equilibrium trades where the indifference curves intersect

The contract curve

• Is on the same Edgeworth box as the other utility curves, and is the set of all possible Pareto efficient allocations 

• The set of Pareto efficient allocations which improve upon the original endowment is called the core 

Allocation in competitive markets 

• The main mechanism for allocation is price, meaning individuals simply maximise where their income is the value of their endowment (endowment is valued in monetary terms)

• A competitive equilibrium occurs when there is an allocation that maximises each person’s utility at a set of prices (they are price-takers) and the market clears 

• On the Edgeworth box, the difference between the original equilibrium and the competitive equilibrium can be conceived of in terms of an agents excess supply and excess demand 

What is the first fundamental theorem of welfare?

• Competitive equilibrium allocations are Pareto Efficient

• Requires some monotonicity of preferences as an assumption

• This tells us that a competitive economy will end up at some point on the contract curve; a lump sum transfer is a way of transferring money to change the initial endowment and end up on a better place on the contract curve

What is the second fundamental welfare theorem?

• For each allocation on the contract curve, there is a price that supports it as a competitive equilibrium 

• The results requires convexity of preferences and tells us what we can achieve with redistribution 

• Every point on the contract curve can be reached through decentralised trade

What are political implications of the welfare theorems?

• Markets can produce good results

• Perfectly competitive markets provide the benchmark

• Government redistribution can help ease ethical concern within the market

The second theorem and lump sum transfers

• The second theorem assumes we can do lump sum (costless and immediate) transfers (presumably done by the government through taxation)

Situations in which markets are inefficient

• Market power: there are agents big enough to be price-makers rather than price-takers

• Externalities, where one individuals welfare depends on the consumption of others 

• If information is incomplete, trading might be obstacled leading to inefficiency 

• The pricing of public goods by private sectors doesn’t result in efficient allocation