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Consider a stylized economy in which all markets are perfectly competitive, there are no distortions, no externalities, and no public goods. All resources are privately owned and all agents maximize their respective welfare, consumers maximizing utility and firms maximizing their profit. All individuals possess perfect information and there are no impediments to trade so that all markets always clear (i.e., the quantity of goods supplied always equals the quantity of goods demanded). The resulting equilibrium in this idealized world is characterized by a set of optimality conditions, known as Pareto optimality conditions. This equilibrium is said to be a first-best optimum in which there is no welfare-improving role for government policy.

In a seminal paper published in 1956, Richard Lipsey and Kelvin Lancaster considered the consequences of introducing into this general equilibrium system a constraint (or distortion) that prevents one or more of the optimality conditions characterizing the first-best optimum from being attained. For example, suppose a firm has monopoly power, causing it to set a price above marginal cost, thus violating one of the conditions for the first-best equilibrium to prevail. Lipsey and Lancaster then showed that while the other optimality conditions characterizing the first-best outcome may still be attainable, in general it is no longer optimal to impose them. In other words, if one of the Pareto optimality conditions cannot be fulfilled, a second-best optimum is achieved only by deviating from all other optimality conditions.

This proposition has profound implications. First, the simple intuitive efficiency conditions characterizing the first-best optimum are replaced by complex nonintuitive optimality conditions characterizing the second-best equilibrium. Consequently in general nothing can be inferred about either the direction or the magnitude of the deviations of the second-best optimum from the first-best outcome. That depends upon the entire underlying economic structure and the extent to which the distortions relate to the rest of the economy. Second, the optimality conditions may introduce nonconvexities, which call into question whether the equilibrium is indeed an optimum. Third, the existence of such constraints restores a potential welfare-improving role for economic policy.

Although the concept of “second best” is identified primarily with Lipsey and Lancaster, it in fact appeared in the economics literature well before that time. References to it in the context of free trade versus protection can be found as early as the beginning of the twentieth century in the Italian economist Vilfredo Pareto’s original work on general equilibrium theory, while the concept is also discussed by Paul Samuelson in his 1947 book Foundations of Economic Analysis and in more detail by James Meade in his 1955 publication Trade and Welfare. The main contribution of Lipsey and Lancaster is to provide a more formal analysis of the concept and to highlight the consequences for policy makers.

Impediments To First-Best Optimum

Several types of distortions may prevent the first-best Pareto optimal outcome from being attained. Some, such as returns to scale (the relationship between proportionate changes in inputs and the resulting change in output), are technological in nature; while others, such as monopolistic market structures and barriers to entry, may be created by the private sector. These distortions may be neutralized, at least in part, by some form of government intervention. In some cases this may take the form of economic incentives, designed to discourage the behavior causing the distortion, while in other cases it may simply be an outright legal restriction. It is also possible for the government itself to be the source of the distortion. The need to provide public goods, financed by a distortionary tax, such as an income tax, is a familiar example.

While, as Lipsey and Lancaster highlighted, externalities and distortions generally lead to divergences from the Pareto optimal outcome, simple examples also exist where no divergence is created. For example, in their 2005 study Wen-Fang Liu and Stephen Turnovsky considered a neoclassical growth model with an inelastic labor supply in which utility depends upon the agent’s own consumption, together with economy-wide average consumption, a potential distortionary effect. They show that while the consumption externality influences the economy’s time path for capital accumulation, for a widely employed class of utility functions it causes no deviation from the Pareto optimal time path.

The presence of the constraints that, all other things being equal, would lead to the violation of the Pareto optimality conditions need not in fact preclude the attainment of the first-best optimum. In some instances the government may be able to neutralize fully the effects of the various distortions and externalities embodied in the constraints and thus mimic the first-best equilibrium. A well-known example of this was illustrated in a 1986 study by Paul Romer. In the study he introduced an endogenous growth model, in which private agents ignore the production externality due to aggregate capital and therefore overconsume and underaccumulate capital, relative to what is socially optimal. By appropriately subsidizing the return to capital, the government can induce the agents to adjust their consumption-savings behavior and thus attain the first-best optimal growth rate.

In most cases the policy maker is likely to have insufficient policy instruments to reach the first-best outcome, in which case the resulting equilibrium will be truly second-best. In such a situation a natural question to consider concerns the policy options available to improve social welfare relative to the second-best equilibrium. In the Romer model, for example, it is likely that to attain the first-best growth rate the required subsidy to capital income is too large to be politically feasible. The policy maker may therefore decide to target a more modest growth objective that can be achieved by different combinations of tax rates and subsidies. The policy maker is faced with several second-best choices and thus with ranking the set of alternatives.

As noted, the optimality conditions characterizing the second-best equilibrium are complex and therefore, as a practical matter, may be difficult, if not impossible, to implement. This issue was addressed by Yew-Kwang Ng in Welfare Economics: Introduction and Development of Basic Concepts (1979) when he proposed a “third-best” equilibrium. He suggested that in cases where policy makers have insufficient information to implement the second-best policies, they should seek to correct only the known distortions and leave the optimality conditions in the undistorted markets unchanged at their first-best levels. This is sometimes also referred to as “piecemeal” policy making.

Second-Best Versus First-Best

The issue of second-best versus first-best policy making is pervasive in economics. Early contributions were concentrated in the area of international economics and the debate between free trade versus protection. Subsequently it has played a central role in public economics, where governments face the issue of financing public goods, with the externalities they entail, using various fiscal instruments with their own distortionary effects. It has also been important in the area of applied microeconomics and industrial organization in dealing with issues related to market structure, barriers to entry, and deviations from competitive behavior. Finally, the existence of production externalities is a cornerstone of much of modern economic growth theory, where they have been important in giving the theory of the second best a dynamic dimension.

Bibliography:

Lipsey, Richard G., and Kelvin Lancaster. 1956. The General Theory of Second Best. Review of Economic Studies 24:11–32.
Liu, Wen-Fang, and Stephen J. Turnovsky. 2005. Consumption Externalities, Production Externalities, and Long-Run Macroeconomic Efficiency. Journal of Public Economics 89 (5–6): 1097–1129.
Meade, J. E. 1955. Trade and Welfare. London: Oxford University Press.
Ng, Yew-Kwang. 1979. Welfare Economics: Introduction and Development of Basic Concepts. London: Macmillan.
Romer, Paul. 1986. Increasing Returns and Long-Run Growth. Journal of Political Economy 94 (5): 1002–1037.
Samuelson, Paul Anthony. 1947. Foundations of Economic Analysis. Cambridge, MA: Harvard University Press.