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## 9.3 The Theory of the Second Best

### Learning Objectives

1. Understand the key features of the theory of the second best.
2. Distinguish between first-best and second-best equilibria.
3. Distinguish between first-best and second-best policies.

The theory of the second best was formalized by Richard Lipsey and Kelvin Lancaster in 1956. The primary focus of the theory is 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 also many other government policies.

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 is 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 from the maximizing behavior of producers and consumers. Thus the solution is also called an optimum.

For example, a standard perfectly competitive model includes the following equilibrium conditions: (1) the output price is equal to the 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—that is, supply does not equal demand in that one market? Would it still be appropriate for the firms to set the price equal to the 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 deviated from these conditions? Lipsey and Lancaster show that, generally, when one optimal equilibrium condition is not satisfied, for whatever reason, all the other equilibrium conditions will change. Thus if one market does not clear, it would no longer be optimal for firms to set the price equal to the marginal cost or for consumers to set the price ratio equal to the marginal rate of substitution.

## First-Best versus Second-Best Equilibria

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

The optimal government policy in this case is laissez-faire. With respect to trade policies, 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 equilibriumA market equilibrium that arises in the absence of any market imperfections or distortions; in other words, under the standard assumptions of perfect competition..

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, and so on. 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 sever 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 the marginal cost rather than equal to the 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 equilibriumA market equilibrium that arises in the presence of one or more market imperfections or distortions.. Second-best equilibria arise whenever all 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. They can apply these to production, to consumption, or to factor usage. Sometimes they even apply two or more of these policies simultaneously in the same market. Trade policies, like tariffs or export taxes, are designed to directly affect the flow of goods and services between countries. Domestic 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.

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 improve welfare. If any such policy raises welfare to a lesser degree than a first-best policy, then it would be called a second-best policyA policy whose best effect is inferior to another policy.. If there are many policy options that 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 (and so on) policies are not commonly denoted.

## Trade Policies in a Second-Best World

In a 1971 paper, Jagdish Bhagwati provided a framework for understanding the welfare implications of trade policies in the presence of market distortions.See J. N. Bhagwati, “The Generalized Theory of Distortions and Welfare,” in Trade, Balance of Payments and Growth, ed. J. N. Bhagwati, R. W. Jones, R. A. Mundell, and J. Vanek (Amsterdam: North-Holland Publishing Co., 1971). 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 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, voluntary export restraints (VERs), and export taxes, a 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 a 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 that corrects the distortion or imperfection sufficiently to outweigh the detrimental effects of the policy itself. In other words, whenever market imperfections or distortions are 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 a trade policy the first-best policy choice to correct a market imperfection or distortion. Instead, a trade policy is second best. The first-best policy, generally, would be a purely domestic policy targeted directly at the market imperfection or distortion.

In the remaining sections of this chapter, 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.

### Key Takeaways

• A first-best equilibrium occurs in a perfectly competitive market when no imperfections or distortions are present.
• A second-best equilibrium arises whenever a market includes one or more imperfections or distortions.
• A first-best policy is that policy that can improve national welfare to the greatest extent when beginning in a second-best equilibrium.
• A second-best policy is one whose best national welfare effect is inferior to a first-best policy when beginning in a second-best equilibrium.
• As a general rule of thumb, beginning in a second-best equilibrium, the first-best policy will be a policy that attacks the market imperfection or distortion as directly as possible.
• As a general rule of thumb, domestic policies are usually first-best policies, whereas trade policies are usually second-best policies.
• One exception to the previous rule of thumb is that a trade policy is the first-best policy choice to correct the imperfection of a large country in international markets.

### Exercise

1. Jeopardy Questions. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”

1. The term used to describe an equilibrium that arises in the presence of market imperfections and distortions.
2. The term used to describe a policy action that can raise economic efficiency to the greatest extent possible.
3. The names of the economists who first formalized the theory of the second best.
4. The term used to describe an equilibrium that arises in the absence of market imperfections and distortions.
5. The term used to describe a policy action whose best effect is inferior to another policy option.