In economics the production set is a construct representing the possible inputs and outputs to a production process. A production vector represents a process as a vector containing an entry for every commodity in the economy. Outputs are represented by positive entries giving the quantities produced and inputs by negative entries giving the quantities consumed. If the commodities in the economy are (labour, corn, flour, bread) and a mill uses one unit of labour to produce 8 units of flour from 10 units of corn, then its production vector is (–1,–10,8,0). If it needs the same amount of labour to run at half capacity then the production vector (–1,–5,4,0) would also be operationally possible. The set of all operationally possible production vectors is the mill's production set. If y is a production vector and p is the economy's price vector, then p·y is the value of net output. The mill's owner will normally choose y from the production set to maximise this quantity. p·y is defined as the 'profit' of the vector y, and the mill-owner's behaviour is described as 'profit-maximising'. Properties of production sets The following properties may be predicated of production sets. Non-emptiness. The producer has at least one possible course of action. Always holds. Closure. The production set includes its own boundary. This is a technical property which always holds in practice. Separability. A production set is separable into inputs and outputs if every field is either non-negative in all elements or non-positive in all elements. This normally holds for individual enterprises but not, for instance, for a national economy. No free lunch. It is impossible to produce something from nothing. Mathematically there is no vector in the production set with at least one positive entry and no negative entries. Always holds. Possibility of inaction. The zero vector belongs to the production set; in other words, it is possible to produce nothing by consuming nothing. This property almost never holds exactly: resources will be needed either to wind up a concern or to maintain it while dormant. The property may be a useful approximation. Free disposal. If y is an element of production set Y, then so is any vector which consumes more of a given input or produces less of a given output. Mathematically, if e is a vector none of whose entries is negative, and if , then This too may be a useful approximation.