Perfectly competitive equilibrium is Pareto optimal. This is called fundamental theorem of welfare economics. This is also called the invisible hand theorem. The belief that competitive market economy provides an efficient means of allocating scarce resources goes back to Adam Smith in his famous book “wealth of nations” that individuals who pursue their self interest, they operating through market promote the welfare of others and welfare of the society as a whole. Thus individual consumers seek to maximise their own satisfaction and producers pursue to maximise their own profits. Even though promoting the interests of the society as a whole is not a part of their own profits intension but they are led by the invisible forces of market system to promote the interest of the society as a whole.
We have proved above that perfect competition in the market satisfies Pareto’s optimum condition of exchange, (1) that is any pair of individuals under it is the same, (2) Pareto optimum condition of production, that is any pairs of firms using the two factors for producing products under it is the same (3) Pareto’s condition for optimal direction of production (i.e. optimum product mix), namely MRT in production equals MRSXY of consumers (for details regarding proofs of these and other conditions).
However, the conditions under which a perfect competitive market system achieves Pareto-optimality or what is also called economic efficiency are quite restrictive. One important condition for the achievement of Pareto optimality is that the general competitive equilibrium exists. This requires that all markets concerned are in equilibrium simultaneously. If one market is not in equilibrium for some reason, the conditions for Pareto optimality would be violated which would leave unutilized the opportunities for Pareto improvement.
The second important requirement for the validity of the fundamental theorem of welfare economics homework help is that second order conditions for equilibrium must be fulfilled. This implies that consumer preferences (or indifference curves) are convex and also producer’s production sets (i.e. isoquent curves) are convex. This implies that consumer’s marginal rate of substitution and producer’s marginal rate of technical substitution (MRTS LK) must be diminishing at or near the equilibrium point. Further, the second order condition also requires that diminishing production transformation curves must be convex in the relevant region. The existence of perfect competition does not guarantee that these second order conditions will be fulfilled. In this context it may be noted that many areas of production there prevail increasing returns to scale. In case of increasing returns to scale equilibrium of competitive firms is not possible. This would ensure that general competitive equilibrium will not exist which will lead to the violation of the condition.
The third condition required for the fulfillment of fundamental theorem of welfare economics is that externalities in production and externalities in consumption do not exist. The assumption of the absence of production externalities implies that consumption production choices by any firm do not affect the production possibilities of other firms. Similarly, the assumption of the absence of consumption externalities implies that consumption decisions of a consumer do not affect the consumption possibilities of the other consumers. In case these externalities in production and consumption exist, the competitive equilibrium will not achieve Pareto optimality from the social point of view. How externalities prevent the achievement Pareto optimality and lead loss of welfare.
Lastly, it is important to note that the competitive equilibrium under the conditions mentioned above ensures Pareto optimality or efficiency in use and allocation of resources. It has nothing to do with desirable distribution of welfare. In other words, it ensures Pareto efficiency not justice. Pareto optimality analysis assumes the initial factor endowments causes inequalities which leads to non optimal distribution of goods and services and therefore loss of social welfare.
Further, it may be noted that perfectly competitive equilibrium achieves Pareto optimality when the second order conditions of equilibrium are satisfied. These second order conditions require that at or near the equilibrium are satisfied. However, perfect competition does not guarantee that second order conditions required for the achievement of Pareto optimality will also be fulfilled. Besides, when externalities, that is, external economies and diseconomies in production and consumption are present, perfect competition will not lead to Pareto optimality. When external economies and diseconomies either in production or consumption or consumption are present, social margin cost will diverge from private marginal cost. Thus, the existence of externalities obstructs the perfect competition prevails in the economy.