PARETO-OPTIMALITY DEFINED

A pareto-optimal allocation of goods or services occurs when no one in the society can be made better off without making at least one person worse off.  As a result, there are no more gains in trade to be made.  In a two-person, two-good society, a pareto-optimal allocation can be demonstrated graphically as the point where two indifference curves are tangent.  At this point, the following mathematical conditions are true:

(1) Marginal Rate of Substitution (MRS) = dQ_y/dQ_x = MU_x/MU_y=P_x/P_y
(2) MRS¹ = MRS²

In words, goods x and y have been distributed among individuals in society so that the added utility for each dollar spent on a good is the same for all goods and for all individuals.

The MRS is simply the slope of a line drawn tangent to the indifference curves.

PERFECT COMPETITION DEFINED

A perfectly competitive market is one which has the following characteristics:

(1) Perfect Information:  All individuals have immediate access to accurate information about prices and quality of goods and services.  Moreover, they know the implications of current actions on future welfare.

(2) Price Taking:  The behavior of buyers and sellers in a market does not influence the price of goods or services in that market  Each buyer or seller represents a very small share of the market.

(3) Free Entry and Exit:  Business can easily move into or out of a market.  This is generally characterized by large numbers of producers or "potential" producers.

(4) No Externalities:  Individual choices do not affect the welfare of others.  Decisions and their consequences are private.  Therefore, the marginal social cost of a good and the marginal social benefit of a good are reflected in the price of the good (i.e. MSB_x=P_x=MSC_x).

(5) No Public Goods:  Goods may not be both non-rival and non-excludable.  It must be possible to withhold the good from those who haven't paid for it  (i.e. the good is exclusive in consumption); or it must be true that the consumption of the good by one person reduces the availability of the good for other persons  (i.e. the good is rival in consumption).  When a good is non-rival, it has a zero marginal cost of production. An additional person may enjoy the good with no added costs to production.

THE SOCIAL WELFARE CRITERION DEFINED

There are two welfare theorems.

(1) The first theorem states that all general equilibria in perfectly competitive markets are pareto optimal.

(2) The second theorem state that all Pareto-optima can be achieved in a perfectly competitive market through the appropriate initial division of productive resources, and through optimizing behavior on the part of citizens.
 

PIGOU'S CONJECTURE DEFINED

(1) Markets are inefficient, as a means of allocating resources, to the extent that the social cost of a resource diverges from its price, or the private cost to the user.

Corollaries
    (a) Inefficiency derives from the overuse of a resource if its social cost is greater than its price, or underuse if its social cost is less than its price.

    (b) Taxes and subsidy programs can be used to make the price of a resource better reflect its social cost.

COASE'S COUNTER-CONJECTURE

(1)  If property rights are clearly and exclusively defined, and the costs of writing and enforcing contracts (i.e. transaction costs) are not too high, market forces will make the social cost and the price of a resource converge.

Corollaries
    (a)  Government can assist in helping to define property rights and creating a legal system in which individuals can recover damages through the courts.

    (b)  Procedures or institutions that minimize transaction costs will improve the functioning of the market.

PUTTING IT TOGETHER
Together, these ideas make up the "Market Failures" framework for rational policy analysis.

The social welfare theorems indicate that under conditions of perfect competition, market exchanges will result in a distribution of goods and services that maximize the overall welfare or utility of individuals in society.  Thus, individual self-interest results in a distribution of goods and services that is in the publics interest as well.

They also provide a rationale for government intervention. Government may intervene to (1) make a market behave more competitively. (2) re-direct the final allocation of goods and services by making small changes to the initial endowments of resources in the economy through taxation and subsidy programs (Pigou's Conjecture), (3) clearly define property rights when these rights are not well-defined (Coase's Theorem), or (4) provide a court system through which conflicts over property rights may be re-dressed.