In this chapter we introduce the basic concept of the production set of an economy and discuss some of its properties (Section 3.2). We shall describe how the production set can be viewed as the aggregate of a population of firm-specific technologies (Section 3.3). Associated with each production set we will define a number of derived, but nevertheless important, concepts such as the distance function, the normal manifold, and the profit function (Section 3.4). Finally, smoothness concepts and hypotheses (Sections 3.5 and 3.6), examples (Section 3.7), and a notion of proximity for production sets (Section 3.8) are discussed.

Production sets and efficient productions

The technological possibilities open to an economy are represented by a set Y ⊂ Rℓ, called the production set, of feasible input-output, or production, vectors. If y ᄐY, then it is understood that it is technologically possible to produce the output vector defined by max {yi, 0} by using the input vector defined by max{–yi, 0).