With a cubic production function of the form $Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }$ ,in order for the average and marginal product functions to have their usual theoretical properties,it must be the case that A)a 0 B)a 0,b

Question

With a cubic production function of the form $Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }$ ,in order for the average and marginal product functions to have their usual theoretical properties,it must be the case that A)a < 0,b > 0 B)a > 0,b < 0 C)a < 0,b < 0 D)a > 0,b > 0

Quizplus · Accepted Answer

In order for the average product of both inputs to be positive and decreasing as inputs increase, a must be negative. In order for the marginal product of each input to have the usual property of being positive and decreasing as the input increases, b must be positive. Therefore, the correct choice is A, where a < 0 and b > 0.

With a Cubic Production Function of the Form Q=aK3L3+bK−2L2Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }Q=aK3L3+bK−2L2

With a Cubic Production Function of the Form $Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }$