Which of the following statements best describes the relationship between output-per-worker and capital-per-worker?

• A. There is no relationship between capital-per-worker and output-per-worker.
• B. As capital-per-worker increases, output-per-worker generally increases due to higher productivity.
• C. As capital-per-worker increases, output-per-worker generally decreases due to diminishing returns.
• D. As capital-per-worker increases, output-per-worker always remains unchanged.

Answer: (B)

Verified step by step guidance

1. Understand the key economic concepts: 'output-per-worker' refers to the average productivity of each worker, while 'capital-per-worker' refers to the amount of capital (like machinery, tools, equipment) available to each worker.
2. Recall the production function in microeconomics, which typically shows output as a function of inputs such as labor and capital. Output-per-worker can be expressed as a function of capital-per-worker, often written as \(y = f(k)\), where \(y\) is output per worker and \(k\) is capital per worker.
3. Recognize the principle of diminishing marginal returns: as capital-per-worker increases, output-per-worker tends to increase but at a decreasing rate. This means each additional unit of capital adds less to output than the previous one, but output still rises overall.
4. Evaluate the given statements in light of this principle: the statement that output-per-worker generally increases with capital-per-worker aligns with economic theory, while the others either deny any relationship, suggest a decrease, or no change, which are inconsistent with standard microeconomic understanding.
5. Conclude that the best description is that as capital-per-worker increases, output-per-worker generally increases due to higher productivity, reflecting the positive but diminishing impact of capital on worker output.