In the last chapter the costs incurred by a firm were introduced as the sum of the costs of all the inputs employed, or in symbolic terms as
C = p1y1 + p2y2 + , …, pnyn, (10.1)
where C represents total costs, y1, y2, … yn the quantities of the various inputs employed and p1, p2, … pn their respective prices. Further, it was also pointed out that a profit-maximizing firm must seek to use the specific bundle of inputs that minimizes its costs, and to adjust its use of inputs, as it adjusts its output, along a particular expansion path, which is determined by the underlying production function and relative input prices. Points along that expansion path then determine the specific relationship between costs and output, constituting the firm’s cost function, which can, therefore, be expressed as
C = F(q), (10.2)
where, adapting the basic production function expression (9.1),
q = f(y1*, y2*, …, yn*),
in which y1*, y2*, … yn* define the cost-minimizing input quantities used in the production of output, q.