Tính lồi-lõm của hàm sản xuất một mức với độ co giãn thay thế không đổi

Abstract

On the base of the theorem [4]: Necessary and sufficient conditions for the constancy of elasticity of substitution (s_ij=s) of one – level production functions y=f(x₁, x₂,…, x_n) is d_jj +1/(s_ijx_j) = d_ji, where d_ji the following theorem is followed:

In the region W ={x_j ³ 0, j=1..n} the one-level production functions with constant elasticity of substitution s is:

a. Convex in W₁ ÌW if and only if

b. Concave in W₁ if and only if in this region to say   the least  of it     and

1. , where

{1,2,..,k} if {1,2,..,n} and k=1..n.