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 (with a > 0 and 0 < b < 1) has a diminishing average product, one must show that its marginal product is always less than its average product. Arrange the following steps into the correct logical sequence to complete this proof.

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?