Answer :
The per-worker production function has a decreasing slope due to the principle of diminishing marginal returns, where each additional unit of capital produces less output than the preceding one. Therefore the correct option is (A .
If an increase in capital per worker leads to increased output per worker, but by decreasing amounts as capital increases, the per-worker production function has a decreasing slope. This is due to the principle of diminishing marginal returns, which states that while adding more of a productive input, like capital, initially increases output, it does so at a declining rate if all other factors remain constant. The production function graphically illustrates this principle by showing a curve that gets flatter as the amount of capital per worker grows, indicating that each additional unit of capital contributes less to output than the previous unit.
The concept of a diminishing marginal product is crucial in understanding why the slope of the production function decreases. For example, when capital per worker increases from 1 to 2 units, the output might increase significantly. However, increasing the capital from 2 to 3 units produces a smaller increase in output, and so on. This behavior reflects a production function that continues to rise but at a diminishing rate, hence the decreasing slope.
