Q. What is Production and Cost Function?

Production functions and cost functions are the keystones of managerial and business economics. A production function is a mathematical relationship which captures the essential aspects of the technology by which an organisation metamorphoses resources like land, capital and labour into services or goods like cement or steel. It's the economist's distillation of the salient information contained in engineer's blueprints. Mathematically, let Y denote the quantity of a single output produced by quantities of inputs denoted (x₁... x_n). Then production function f(x₁... xn) determines how a given output can be produced by an infinite combinations of inputs (x₁... x_n), given the technology in use. Various significant features of the structure of technology are captured by the shape of production function. Relationships among inputs include the degree of complementarily or substitutability among pairs of inputs, and the ability to aggregate groups of inputs into a shorter list of input aggregates. Relationships between inputs and the output include economies of scale and technical efficiency with which inputs are utilised to generate a given output.