Fundamental Theorems of Welfare Economics :

We now discuss the two fundamental theorems of welfare economics. The first of these is named as  the First Fundamental Theorem of Welfare Economics. It provides a set of  conditions under which we can be assured that a market economy will achieve a Pareto optimal outcome. According to this theorem

(i)  If there are enough markets, i.e., if every  relevant good is  traded in a market at publicly known prices (that is, there is a complete set of markets)

(ii) If all consumers and producers behave competitively, and

(iii) If an equilibrium exists, the allocation of  resources in that equilibrium will be Pareto optimal. That is, when markets are complete,  any competitive equilibrium is necessarily Pareto optimal.

The result that competitiv-e markets will  automatically achieve a Pareto optimal outcome provides a formal and very general confirmation ofAdam Smith's asserted 'invisible hand' property of  the market. Intuitively,  first theorem of welfare economics indicates that equilibrium price signals are sufficient  to coordinate decentralized economic activities in a manner that is efficient according  to the Pareto criterion.

By her individual maximization  behavior, each economic  agent responds to prices by equating her marginal rates of substitution (for consumers)  and  transformation (for firms) to these prices. Since all agents fqce the same prices, all the marginal rates are equated to each other in equilibrium. Combined with market equilibria, these equalities characterize Pareto optima  in a convex environment.*

The Second Fundamental Theorem of welfare economics states  that (under suitable convexity hypothesis) every Pareto optimal allocation can be achieved  as a competitive allocation after an appropriate  lumpsum transfer of wealth. It tells us that through the use of appropriate lump-sum redistribution of wealth, a welfare authority can  implement any desired Pareto optimal allocation as a price taking equilibrium. This  theorem is fundamental  to understanding decentralized planning.

Note that Pareto optimality of the competitive equilibrium meets the criterion of efficiency, but does not address the issue of equity or justice.  It  is possible that allocations that meet Pareto optimality criterion  lead  to undesirable income distributions.  For example,  an allocation that allocates  entire set of  resources  to one individual in the economy  also meets  the Pareto criterion but may not ensure justice.

Second theorem of welfare addresses  this problem. According to the theorem,  take any Pareto optimum that meets the  justice criterion, it is possible to decentralize this allocation as a competitive equilibrium so long as the income of the agents  is chosen appropriately.

Despite these two strong theorems of welfare  economics, we witness abuse of natural resources and management of ecosystems.