Firms and production technology

We will represent production as organized in firms. A firm is characterized by its name, by the production technology to which it has access, and by who owns it, the shareholders. We postpone discussion of the ownership and distribution of profits to Chapter 6. The population of firms is the finite set F, indexed j = 1, …, #F. The typical firm is j ∈ F. Firm j's most distinctive characteristic is its production technology, represented by the set yj ⊂ RN.

The set yj represents the technical possibilities of firm j. A typical element y of the technology set, y ∈ yj, is a vector representing a technically possible combination of inputs and outputs. Negative coordinates of y are inputs; positive coordinates are outputs. For example, say y ∈ yj, y = (-2, -3, 0, 0, 1); this y ∈ yj means that an input of two units of good 1 and three units of good 2 will allow firm j to produce one unit of good 5. Each element y of yj is like a recipe in a cookbook or one of many blueprint plans for production, which can be implemented as a matter of choice by the firm. There is no guarantee that the economy can provide the inputs y ∈ yj specifies, either from endowment or from the output of other firms. Rather, y ∈ yj represents the technical output possibilities of production by firm j if the specified inputs are provided.