U2L
U1L
OL X
Figure 1. Edgeworth box
The equality of the marginal rates of substitution does not lead to a single Pareto –optimal allocation. Any point on the contract curve is Pareto optimal. Thus the Pareto criterion still leaves a choice to be made among the infinitely many pareto-optimal allocations. However, the final choice requires interpersonal comparisons, because any movement along the contract curve always makes one person better off and the other worse off. Such interpersonal comparisons, however, presuppose a detailed specification of the social welfare function.
Furthermore, we cannot even conclude that every Pareto optimal allocation is better than every Pareto nonoptimal allocation.
What we can say is this. We do admit that not every optimal allocation is better than every nonoptimal allocation, but we can always identify some pareto-optimal allocations that are better than any given nonoptimal allocation.
Secondly, the economy must be on the production frontier (efficiency in production). Pareto optimality requires that factors of production are so allocated that society cannot increase the output of, say, good x without sacrificing any y. suppose that the opposite is true, that is, assume that society can so reallocate inputs as to increase the output of good x without sacrificing any good y. with more good x and no less good y, society can certainly keep all people at least as ell off as before, by merely allocating to them the exact amounts that they were consuming when less good x was available. That would, of course, leave the extra output of good x for further distribution. Any arbitrary distribution of the extra amount good x among consumers would improve the well being of some people without harming others. Hence more of any one commodity, the outputs of all other goods and services being constant, is socially desirable.
An Edgeworth box can represent the factor allocation problem graphically whose dimensions coincide with the fixed quantities of factors of production available to the economy. Each point in the box corresponds to a feasible factor allocation. But resources are allocated optimality only along the contract curve. at these points, the marginal rates of technical substitution of two factors, for example K and L, are equal between industries.
MRSLXY = MRS MXY
We therefore conclude that the equation above is the primary condition for Pareto optimality in the allocation of inputs between industries. When the equality of the marginal rates of technical substitution is satisfied, it is impossible to increase the output of one commodity without reducing the output of the other. If it is not satisfied, however, it is always possible to increase the output of one commodity without reducing the output of the other by a proper reallocation of inputs.
The optimal allocation of inputs, between industries can also be illustrated in terms of the production- possibilities frontier, because each point on the production frontier corresponds to appoint on the contract curve, and vice versa. Points on the production frontier itself represent the Pareto optimal combinations. Points lying inside the production frontier are inefficient or Pareto nonoptimal because society can move from one such point (N) to another lying on the production frontier (B) at which more of each output is available.
Y
A
B
C
0 X
Figure 2. Production possibilities frontier
The equality between marginal rates of technical substitution does not lead to a single Pareto-optimal allocation of inputs between industries; it generally leads to an infinite number of such Pareto optima. Furthermore, not every Pareto optimal factor allocation is better than every nonoptimal allocation. However, we can always identify some Pareto-optimal allocations that are better than any given nonoptimal allocation.
Given that the conditions necessary for the attainment of the production and exchange optima are met, one further condition is necessary for the attainment of overall Pareto optimality. This condition determines that the common slope of the indifference curves at appoint on the contract curve must be equal to the slope of the production frontier at the point representing the commodity bundle that is produced. An allocation will be Pareto optimal overall if it is not possible to reallocate production and distribution so as to make one person better off while making no one else worse off. This will be the case if the marginal rate of substitution between each pair of commodities equals the marginal rate of transformation. In a competitive economy in which all firms are price takers and face the same prices as consumers, this condition will be satisfied. Firms will all produce at the point where price equals marginal cost. Since the ratio of prices equals the marginal rate of substitution of households and the ratio of marginal costs equals the marginal rate of transformation, the overall efficiency condition is satisfied. This presumes that the exchange efficiency and production efficiency conditions are simultaneously satisfied.
We use the term market failure to cover all the circumstances in which equilibrium in free unregulated markets will fail to achieve an efficient allocation. Allocations, which are not Pareto optimal, are not use the resources of the economy efficiently, as it will always be possible to find another allocation of resources which make everybody better off. Market failure describes the circumstances in which distortions prevent the invisible hand from allocating resources efficiently. We now list the possible sources of distortions that lead to market failure.
The first cause of market inefficiency is imperfect competition. Under perfect competition no firm or consumer can affect prices, imperfect competition occurs when a buyer or seller can affect a goods price. When imperfect competition arises, society may move inside its production possibility frontier. This would occur, for example, if a single seller raised the price of a sky-high to earn extra profits. The output of that good would be reduced below the most efficient level, and the efficiency of the economy would thereby suffer. In such situation, the invisible hand property of markets may be violated. Imperfect competition leads to prices that rise above cost and to consumer purchases that are reduced below efficient levels. The pattern of too high price and too low output is the hallmark of the inefficiencies associated with imperfect competition.
The extreme case of imperfect competition is the monopolist - a single supplier who alone determines the price of a particular good or service. As is well known in the case of a monopoly seller, the price will not be set at marginal cost so the overall efficiency conditions will be violated. In this case, if the seller and buyers could negotiate, they could strike a bargain and make everyone better off. What prevents this from occurring is that there are a large number of buyers. The gains from trade take the form of consumers and producers surpluses, and these must be divided by a bargaining process. The bargain will entail each buyer contributing part of his consumer surplus. The contribution may differ from buyer to buyer. This is not possible when there are large numbers of buyers for, more generally, the same reasons that price discrimination is not possible. The possibility of resale means that the seller cannot enforce on consumers a price above the going market price. If it where not for the fact that a large number of buyers existed, the problem of inefficiency might not exist.
A third type of inefficiency arises when there are spillovers or externalities, which involve involuntary imposition of costs or benefits. Market transactions involve voluntary exchange in which people exchange goods or services for money. When you buy a haircut, the barber receives the full value for time, skills, and rent. But many interactions take place outside markets. While airports produce a lot of noise, they generally do not compensate the people living around the airport for disturbing their peace. On the other hand, some companies, which spend heavily on research and development, have positive spillover effects for the rest of society. In each case, an activity has helped or hurt people outside the market transaction; that is, there was an economic transaction without an economic payment. Externalities or spillover effects occur when firms or people impose costs or benefits on others outside the marketplace. Externalities generally reduce the efficiency of an economy because the optimal output is not produced. But this statement depends on the size of transaction costs, as the coase theorem shows. If transaction costs of bargaining and negotiating are low, then the parties affected by an externality can negotiate a side payment to arrange for production of the efficient output rate. High transactions costs, however, make such payments too costly to arrange.
The phenomenon of public goods is an extreme form of an externality. Public goods such as national defense, law and order, flood control, fireworks displays, radio and television signals, have in common an important property: once produced, they provide benefits to all citizens. No ones utility is reduced because others benefit from public goods. Furthermore, it is not possible to exclude any particular citizen from the benefits of public goods: your national defense is my national defense, your clean air is also mine. For this reason each person has an incentive not to produce a public good but to wait for others to do so. This is called the free rider problem. Obviously, the free rider incentive leads to suboptimal production and consumption of public goods. To remedy this situation, governments intervene; through compulsory taxation, they finance the production of public goods.
The fifth source of market failure arises from informational asymmetries. If some household has information that others do not have, the former may be able to exploit it much like a monopoly firm exploits its market power. One case of this is known as moral hazard and is found most obviously in insurance markets. Another instance of informational asymmetries is known as adverse selection. In this case a number of parsons are seeking to buy insurance but their risk characteristics differ.
Finally, taxes create output inefficiency in the same manner that a monopoly in the output market does. A unit tax of τ, for example, drives a wedge between the price consumers pay and the price received by producers. If consumers pay PgoodA, then producers receive (1-τ)PgoodA. Consumers achieve exchange efficiency because they all face the price ratio PgoodA/PgoodB. Producers, too, are efficient because they still face a common relative input price ratio. The difference now is that producers face a different relative (output) price ratio than consumers. Producers set ((1-τ)PgoodA equal to their marginal cost to determine their output rate. But this implies that the price consumers pay, PgoodA, exceeds the marginal cost in equilibrium. Thus, the marginal rate of transformation cannot equal the ratio of output prices in equilibrium. The economy is not output efficient. In effect, firms produce too little output relative to the perfectly competitive solution.
The existence of market failure provides a rational for having the planner interfere with the market mechanism. Of course, market failure is a necessary but not a sufficient condition for intervention since the planner may not be able to do any better than the market. Taken literally, no one could believe that a perfect and absolutely efficient competitive mechanism has ever existed.
