Single output. Production is often based on units (e.g. flour mills) which produce a single output from more than one input. A separable production set has a single output if exactly one field contains a positive entry. Labour consumption. Labour is usually an input to all elements of a production set which have any positive output. Irreversibility. If and y≠0 then Always holds in practice. Convexity. If two vectors lie within the production set, then so do all intermediate points. This often holds as an approximation but cannot apply exactly if inputs or outputs comprise discrete units. Additivity (or free entry). This property is relevant to the production set of an industry or of an economy but not for instance to a single flour mill. It means that if production vector y is possible, and so is y', then so too is y+y'. So if a mill can be built with a view to running in one way, and another mill can be built with a view to running in another way, then both can be built to produce the sum of intended outputs from the sum of intended inputs. Free entry is a postulate of perfect competition. Returns to scale and economies of scale. See below. The production function If a production set is separable and has a single output, then a function F(y) can be constructed whose value is the maximum quantity of output obtainable for given inputs, and whose domain is the set of input subvectors represented in the production set. This is known as the production function. If a production set is separable then we may define a "production value function" fp(x) in terms of a price vector p. If x is a monetary quantity, then fp(x) is the maximum monetary value of output obtainable in Y from inputs whose cost is x. Returns to scale Constant returns to scale mean that if y is in the production set, then so too is λy for any positive λ. Returns might be constant over a region; for instance, so long as λ is not too far from 1 for a given y. There is no entirely satisfactory way to define increasing or decreasing returns to scale for general production sets. If the production set Y can be represented by a production function F whose argument is the input subvector of a production vector, then increasing returns to