The theory of a second-best solution

The theory of a second-best solution

The theory of a second-best solution concerns the events that happen when a condition for an optimal outcome isn't met. In that case a second-best solution should be sought. But the second-best solution isn't always the one where every other condition is met except the one missing to make the solution optimal. Thus, in order to get the second-best solution where one or more necessary conditions haven't been met, it isn't necessary, it is in fact a bad idea to try to keep the other, already met conditions. In other words, one should allow the market deficiencies to cancel themselves out. E.g. in a perfect competitive state the optimum is found if the price and border cost is equal in all market sectors. Should the price in a sector grow above the border costs, the second-best solution will, for example, require taxes to make the prices grow elsewhere, because that way the consumers' border decisions about the allocation of their budget to various products stay almost unchanged. After being brought up in the 1965 work by a Canadian, Richard Lipsey (born in 1928) and an Australian, Kelvin Lancaster (1924-1999), the theory was also used, except in economy, in the legislative sciences. The Theory of the Second-BestThe theory of the second-best was formalized by Richard Lipsey and Kelvin Lancaster in 1956.

The primary focus of the theory is on what happens when the optimum conditions are not satisfied in an economic model. Lipsey and Lancaster's results have important implications for the understanding of, not only, trade policies but many other government policies as well.

In this section we will provide an overview of the main results and indicate some of the implications for trade policy analysis. We will then consider various applications of the theory to international trade policy issues.

First of all, one must note that economic models consist of exercises in which a set of assumptions are used to deduce a series of logical conclusions. The solution of a model is referred to as an equilibrium. An equilibrium is typically described by explaining the conditions or relationships that must be satisfied in order for the equilibrium to be realized. These are called the equilibrium conditions. In economic models these conditions arise out of the maximizing behavior of producers and consumers. Thus the solution is also called an optimum.

For example, in a standard perfectly competitive model, the equilibrium conditions include, 1) output price equal to marginal cost for each firm in an industry, 2) the ratio of prices between any two goods is equal to each consumer's marginal rate of substitution between the two goods, 3) the long-run profit of each firm is equal to zero, and 4) supply of all goods is equal to demand for all goods. In a general equilibrium model, with many consumers, firms, industries and markets there will be numerous equilibrium conditions that must be satisfied simultaneously.

Lipsey and Lancaster's analysis asks the following simple question: What happens to the other optimal equilibrium conditions when one of the conditions cannot be satisfied for some reason? For example, what happens if one of the markets does not clear, i.e. supply does not equal demand in that one market? Would it still be appropriate for the firms to set price equal to marginal cost? Should consumers continue to set each price ratio equal to their marginal rate of substitution? Or, would it be better if firms and consumers deviate from these conditions? Lipsey and Lancaster show that, generally, when one optimal equilibrium condition is not satisfied, for whatever reason, all of the other equilibrium conditions will change. Thus if one market does not clear, it would no longer be optimal for firms to set price equal to marginal cost or for consumers to set the price ratio equal to the marginal rate of substitution.

First-Best vs. Second-Best Equilibria

Consider a small perfectly competitive open economy that has no market imperfections or distortions, no externalities in production or consumption, no public goods. An economy in which all resources are privately owned, where the participants maximize their own well-being, firms maximize profit and consumers maximize utility always in the presence of perfect information. An economy in which markets always clear, in which there are no adjustment costs or unemployment of resources.

The optimal government policy in this case is laissez-faire. With respect to trade policy the optimal policy is free trade. Any type of tax or subsidy implemented by the government under these circumstances can only reduce economic efficiency and national welfare. Thus with a laissez-faire policy the resulting equilibrium would be called first-best.. It is useful to think of this market condition as economic nirvana since there is no conceivable way of increasing economic efficiency at a first-best equilibrium.

Of course, the real world is unlikely to be so perfectly characterized. Instead markets will likely have numerous distortions and imperfections. Some production and consumption activities have externality effects. Some goods have public good characteristics. Some markets have a small number of firms, each of which has some control over the price that prevails and makes positive economic profit. Governments invariably set taxes on consumption, profit, property and assets, etc. Finally, information is rarely perfectly and costlessly available.

Now imagine again a small open perfectly competitive economy with no market imperfections or distortions. Suppose we introduce one distortion or imperfection into such an economy. The resulting equilibrium will now be less efficient from a national perspective than when the distortion was not present. In other words the introduction of one distortion would reduce the optimal level of national welfare.

In terms of Lipsey and Lancaster's analysis, the introduction of the distortion into the system would severe one or more of the equilibrium conditions that must be satisfied to obtain economic nirvana. For example, suppose the imperfection that is introduced is the presence of a monopolistic firm in an industry. In this case the firm's profit maximizing equilibrium condition would be to set its price greater than marginal cost rather than equal to marginal cost as would be done by a profit maximizing perfectly competitive firm. Since the economic optimum obtained in these circumstances would be less efficient than in economic nirvana, we would call this equilibrium a second-best equilibrium. Second-best equilibria arise whenever all of the equilibrium conditions satisfying economic nirvana cannot occur simultaneously. In general, second-best equilibria arise whenever there are market imperfections or distortions present.

Welfare Improving Policies in a Second-Best World

An economic rationale for government intervention in the private market arises whenever there are uncorrected market imperfections or distortions. In these circumstances the economy is characterized by a second-best rather than a first-best equilibrium. In the best of cases the government policy can correct the distortions completely and the economy would revert back to the state under economic nirvana. If the distortion is not corrected completely then at least the new equilibrium conditions, altered by the presence of the distortion, can all be satisfied. In either case an appropriate government policy can act to correct, or reduce the detrimental effects of the market imperfection or distortion, raise economic efficiency and improve national welfare.

It is for this reason that many types of trade policies can be shown to improve national welfare. Trade policies, chosen appropriate to the market circumstances, act to correct the imperfections or distortions. This remains true even though the trade policies themselves would act to reduce economic efficiency if applied starting from a state of economic nirvana. What happens is that the policy corrects the distortion or imperfection and thus raises national welfare by more than the loss in welfare arising from the application of the policy.

Many different types of policies can be applied even for the same distortion or imperfection. Governments can apply taxes, subsidies or quantitative restrictions. It can apply these to production, to consumption, or to factor usage. Sometimes it even applies two or more of these policies simultaneously in the same market. Some policies, like tariffs or export taxes, are designed to directly affect the flow of goods and services between countries. These are called trade policies. Other policies, like production subsidies or consumption taxes, are directed at a particular activity that occurs within the country but is not targeted directly at trade flows. These can be referred to as domestic policies.

One prominent area of trade policy research focuses on identifying the optimal policy to be used in a particular second-best equilibrium situation. Invariably this research has considered multiple policy options in any one situation and has attempted to rank order the potential policies in terms of their efficiency enhancing capabilities. As with the ranking of equilibria described above, the ranking of policy options is also typically characterized using the first-best and second-best labels.

Thus, the ideal or optimal policy choice in the presence of a particular market distortion or imperfection is referred to as a first-best policy. The first-best policy will raise national welfare, or enhance aggregate economic efficiency, to the greatest extent possible in a particular situation.

Many other policies can often be applied, some of which would be welfare-improving. If any such policy raises welfare to a lesser degree than a first-best policy, then it would be called a second-best policy. If there are many policy options which are inferior to the first-best policy, then it is common to refer to them all as second-best policies. Only if one can definitively rank three or more policy options would one ever refer to a third-best or fourth-best policy. Since these rankings are often difficult, third-best, policies are not commonly denoted.

Trade Policies in a Second-Best World

In a 1971 paper titled "A General Theory of Domestic Distortions and Welfare", Jagdish Bhagwati provided a framework for understanding the welfare implications of trade policies in the presence of market distortions. This framework applied the theory of the second-best to much of the welfare analysis that had been done in international trade theory up until that point. Bhagwati demonstrated the result that trade policies can improve national welfare if they occur in the presence of a market distortion and if they act to correct the detrimental effects caused by the distortion. However, Bhagwati also showed that in almost all circumstances a trade policy will be a second-best rather than a first-best policy choice. The first-best policy would likely be a purely domestic policy that is targeted directly at the distortion in the market. One exception to this rule occurs when a country is "large" in international markets and thus can affect international prices with its domestic policies. In this case, as was shown with optimal tariffs, quotas, VERs and export taxes, trade policy is the first-best policy.

Since Bhagwati's paper, international trade policy analysis has advanced to include market imperfections such as monopolies, duopolies and oligopolies. In many of these cases it has been shown that appropriately chosen trade policies can improve national welfare. The reason trade policies can improve welfare, of course, is that the presence of the market imperfection means that the economy begins at a second-best equilibrium. The trade policy, if properly targeted, can reduce the negative aggregate effects caused by the imperfection and thus raise national welfare.

Summary of the Theory of the Second-Best

In summary the theory of the second-best provides the theoretical underpinning to explain many of the reasons that trade policy can be shown to be welfare enhancing for an economy. In most (if not all) of the cases in which trade policy is shown to improve national welfare, the economy begins at an equilibrium that can be characterized as second best. Second best equilibria arise whenever the market has distortions or imperfections present. In these cases it is relatively straightforward to conceive of a trade policy which corrects the distortion or imperfection sufficiently to outweigh the detrimental effects of the policy itself. In other words, whenever there are market imperfections or distortions present it is always theoretically or conceptually possible to design a trade policy that would improve national welfare. As such the theory of the second best provides a rationale for many different types of protection in an economy.

The main criticism suggested by the theory is that rarely is trade policy the first best policy choice to correct a market imperfection or distortion. Instead trade policy is second best. The first best policy, generally, would be a purely domestic policy targeted directly at the market imperfection or distortion.

On the following pages we use the theory of the second best to explain many of the justifications commonly given for protection or for government intervention with some form of trade policy. In each case we also discuss the likely first best policies.

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