Production Frontier

BIBLIOGRAPHY

In economic theory a production frontier is a mathematical relationship describing the maximum quantity of output that an organization can obtain from a given collection of resources given the technology in use. An equivalent definition specifies the minimum resources an organization requires to produce a given quantity of output, again given the technology in place. A production frontier is thus the economist’s distillation of the detailed information contained in the engineer’s blueprints that describe what is possible. Organizations operating on the production frontier avoid waste and are technically efficient. Organizations operating beneath the production frontier waste resources and are technically inefficient. The degree of technical inefficiency increases with the distance to the production frontier.

A cost frontier is a dual mathematical relationship that describes the minimum expenditure an organization requires to produce some quantity of output given the prices it pays for the resources it employs in the production process and given the technology in place. Technical efficiency is necessary but not sufficient for operation on the cost frontier. A second requirement is that resources be allocated efficiently in light of the resource prices paid by producers. Organizations achieving both technical and allocative efficiency operate on the cost frontier and are cost efficient. However, if waste in the organization causes actual output to fall short of maximum possible output or if resources are misallocated in light of their respective prices, then actual cost exceeds minimum feasible cost. Organizations failing to fulfill both efficiency conditions operate above the cost frontier and are cost inefficient. The degree of cost-inefficiency increases with the distance to the cost frontier.

Over a short period of time the assumption of a given technology underlying a fixed frontier is reasonable. Over a longer period of time existing technology diffuses and new technologies are introduced. Technical progress shifts the production frontier up, increasing the maximum output that can be obtained from a given collection of resources, or reduces resource requirements for a given amount of output. Consequently, technical progress shifts the cost frontier down, reducing the minimum cost that must be incurred to produce a given quantity of output.

Just as it is not possible to know how fast a human can run one hundred meters, the production frontier and the cost frontier of economic theory are unknown. However, it is possible to identify faster runners and slower runners and to observe improvements in best practice through time. It is also possible to identify best-practice organizations and less efficient organizations and to track their performance through time. Thus, theoretical production and cost frontiers are approximated by best-practice production and cost frontiers.

Approximation requires an empirical technique. In 1957 Michael James Farrell used primitive linear programming techniques to construct a best-practice production frontier. However, his contribution remained largely overlooked for twenty years. In 1977 the team of Dennis J. Aigner, C. A. Knox Lovell, and Peter Schmidt and the team of Wim Meeusen and Julien van den Broeck used statistical techniques to develop a best-practice production frontier concept now known as stochastic frontier analysis. A year later the team of Abraham Charnes, William W. Cooper, and Edwardo Rhodes refined Farrell’s linear programming techniques to construct an alternative best-practice production frontier concept known as data envelopment analysis. Both approaches to the construction of best-practice production frontiers have been used to provide empirical measures of relative technical efficiency. Both approaches have been extended to the construction of best-practice cost frontiers and to the empirical measurement of relative cost efficiency.

Best-practice production and cost frontiers have been used to test a variety of hypotheses having a direct bearing on public policy. Perhaps the most significant hypothesis is that market structure matters. A highly competitive marketplace rewards organizations operating at or near best practice with growing market share and penalizes inefficient organizations with shrinking market share, often to extinction. A less competitive marketplace can shelter inefficient organizations. A popular example is provided by trade liberalization, which subjects domestic producers to increased foreign competition. A common empirical finding is that trade liberalization brings aggregate performance gains attributable among other factors to improvements in the efficiency of continuing domestic firms, to entry of relatively efficient foreign firms, and to exit of relatively inefficient domestic firms.

A second popular hypothesis is that ownership matters. Private organizations have different incentives and face different constraints than public organizations. When the two operate in the same marketplace, one group may operate closer to best practice than the other. Education and health care are two sectors in which numerous public/private performance comparisons have been conducted, with the empirical evidence being mixed.

A third hypothesis asserts that regulation matters. Ill-designed regulatory frameworks inhibit best practice by diverting resources away from production toward compliance. Thoughtfully designed regulatory frameworks can enhance best practice by providing incentives for organizations to operate efficiently and to improve their efficiency through time. One regulatory context in which theoretical predictions have been quantified by empirical investigation concerns the impact of alternative forms of environmental control on organizational performance. In this context, however, the private cost of reduced efficiency must be balanced against the social benefits of environmental protection.

The theoretical concept of production and cost frontiers is universally accepted. However, the empirical implementation of best-practice frontiers and their use in the policy arena has attracted some criticism. One criticism asserts that the mathematical framework is necessarily incomplete and fails to incorporate the objectives of and constraints faced by the organization and its stakeholders. In 1976 George J. Stigler claimed that “waste is not a useful economic concept. Waste is error within the framework of modern economic analysis” (p. 216). A second criticism asserts that the empirical implementation fails to control adequately for variation in the operating environment, thereby confusing variation in operating efficiency with variation in factors beyond the control of management. This concern has inhibited the use of best-practice frontiers in evaluating the relative performance of educational institutions, health care providers, and regulated utilities.

SEE ALSO Fixed Coefficients Production Function; Production; Production Function

BIBLIOGRAPHY

Aigner, Dennis J., C. A. Knox Lovell, and Peter Schmidt. 1977. Formulation and Estimation of Stochastic Frontier Production Function Models. Journal of Econometrics 6 (1): 21-37.

Charnes, Abraham, William W. Cooper, and Edwardo Rhodes. 1978. Measuring the Efficiency of Decision-Making Units. European Journal of Operational Research 2 (6): 429–444.

Farrell, Michael James. 1957. The Measurement of Productive Efficiency. Journal of the Royal Statistical Society, Series A, General 120 (3): 253–281.

Meeusen, Wim, and Julien van den Broeck. 1977. Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error. International Economic Review 18 (2): 435–444.

Stigler, George J. 1976. The Xistence of X-Efficiency. American Economic Review 66 (1): 213–216.

C. A. Knox Lovell