Production Function Analysis

Consider a production function of the form g(h) = ah^b, where 'h' represents hours of input (h > 0), and 'a' is a positive parameter (a > 0). For the average product of this function to be always diminishing, what condition must the parameter 'b' satisfy?

To prove that a production function of the form g(h) = ah^b (where a > 0 and 0 < b < 1) has a diminishing average product, one must first derive the marginal product and the average product. For this production function, the marginal product is expressed as ________.

For a production function of the form g(h) = ah^b, where a > 0 and 0 < b < 1, the proof that the average product is diminishing involves relating several mathematical components. Match each component of this proof with its correct mathematical expression or definition.

Analyzing a Flawed Economic Proof

For a production function of the form g(h) = ah^b, where a > 0 and 0 < b < 1, the proof that the average product is diminishing ultimately relies on showing that the marginal product (abh^(b-1)) is less than the average product (ah^(b-1)). This inequality holds true because the parameter b is less than 1.

The Role of Output Elasticity in Production Analysis

The Critical Inequality in Production Theory

To prove that a power production function of the form g(h) = ah^b (with a > 0, h > 0, and 0 < b < 1) has a diminishing average product, one must show that its marginal product is less than its average product. Given that the marginal product is abh^(b-1) and the average product is ah^(b-1), the key step is to analyze the inequality abh^(b-1) < ah^(b-1). Which of the following statements provides the correct simplification and conclusion for this inequality?