On differentiability of cost functions (Q1088568)

The central point of the paper is the following theorem: Under usual conditions on the production function the following condition is necessay and sufficient for the differentiability of the cost function: for all efficient input vectors x,x', \(x\neq x'\), there exist efficient vectors \(\hat x\), \(\hat x'\) arbitrarily close to x resp. x', such that \(\lambda\hat x+(1-\lambda)\hat x'\) is not efficient for all \(\lambda\), \(0<\lambda <1\).