The Production Possibility Set with Public Intermediate Goods
证明在常规模报酬、无联合产品且无技术外部性条件下，可行净生产点集是凸集，但其上界（转换面）可能包含线性段，其平坦程度与初级要素投入矩阵的秩相关。
Publisher Summary This chapter explains that the set of feasible net production points is convex if the underlying production functions are of the constant returns, no-joints-products type, and if there are no technological externalities. However, the upper boundary of the set, that is, the transformation surface, is not necessarily strictly concave; it may contain linear segments or, more generally, flats of dimension possibly greater than one. Recently, it has been shown that the degree of flatness is related to the rank of the matrix of primary factor inputs. It has been shown that if at any point P in the transformation surface, there are s industries active, then the surface contains an (s-r)-dimensional flat embracing P if and only if at P there are exactly r linearly independent vectors of primary-factor inputs. As corollary, if the number of primary factors is less than s, then P necessarily lies in a flat of dimension at least one.