Recall from the preceding subsection that p and x denote the vector of input prices and the
vector of the quantity demanded of all factors, respectively, while p j is the price of production
factor j and x i is the quantity demanded of production factor i, where i; j ¼ 1; 2; . . . ; n. We denote
by y the output vector. Let us introduce the following definition (Shephard, 1970).