Definition
The cost function c(w, q) is the optimized value of CMP, or the minimization of cost to produce q output, given the price vector of input 
q: expected quantity of production. f(z) > q
w: price of inputs. 
is the cost
z: input
Properties of cost function c(w, q)
(1) c is homogeneous of degree 1 in w and increasing in q
(2) c is a concave function of w
(3) Shephard's Lemma: if z is single valued, then c is differentiable with respect to w and 
, which gives conditional demand correspondence z(q, w).
(4) If z is a differentiable function then 
is symmetric, negative semi-definite and 
See also:
- Production function f(z)
- Profit function π(p)