浅析生产函数g(x)=a+bx+cx~2+ex~3(e<0)合理生产阶段的划分

生产函数g(x)可获取最佳利润的资源施用量应同时满足下述条件:①dy/dx=px/py;,②’py·g(x)-p_x·x>p~y·g(0);当a=0时,生产函数g(x)=a+bx+cx~2+ex~3(e<0)成为典型生产函数f(x)=bx+cx~2+ex~3(e<0)。这时,条件②’是式②p~yf(x)-p~x·x>0的一般形式;而式②是条件②’(当a=0时)的一个特例。生产函数g(x)=a+bx+ex~2+ex~3(e>0)当a≠0时,其合理生产阶段的起点不是边际产量最高点对应的资源施用量。对生产函数g(x)划分生产阶段时应先做变换:f(x)=g(x)-g(0),把g(x)变为典型生产函数f(x)的形式,然后对f(x)按传统方法划分阶段。生产函数g(x)与变换后的生产函数f(x)的合理生产阶段的起点完全相同。

ANALYSE THE PRQDUCTION FUNCTION g(x)=a+bx+cx~2+ex~3(e<0)SEPARATION OF REASONABLE PRODUCTION STAGE

In production function g(x), the quantity of used resource which is able to get the maximum profit must satisfies the following conditions; (1)dy/dx = px/py, (2)'py·g(x)-px·x≥py·g(0). When "a" eqals to "0", the production function g(x) = a+bx+cx~2+ +ex~3 (e<0) becomes the typical production function f(x) = bx+cx~2+ex~3(e< 0). In this context, condition (2) 'is the normal form of condition(2) py· f(x)-px·x≥0; and condition(2) is one of the special types of conduction(2)'. In the production function g(x) = a+bx+cx~2+ex~3(e<0), the starting point of rational production stage is not the quantity of used resource which is corresponding to the highest point of marginal production when "a" is not equal to "0". When the production stage is divided by the production function "g(x)", a change should be made first.That is, changing the production function from the form "g(x)"to its typical form "f(x)".Then, the f(x)can be divided acc- ording to tranditional method. The starting point of rational production stage in production g(x) is the same completely as in production function f(x).