Answer :
The per-worker production function exhibits diminishing marginal returns, characterized by a positive but (A) decreasing slope as capital per worker increases.
When an increase in capital per worker leads to increased output per worker, but with decreasing additional gains as more capital is added, the production function is said to exhibit diminishing marginal returns. In this scenario, the production function graph would display a constantly positive slope that diminishes as the amount of capital per worker rises.
Therefore, the correct answer to the question is that the per-worker production function has a decreasing slope. This is because each additional unit of capital generates less and less extra output, even though the output per worker continues to rise.
To illustrate with an example, if going from 1 to 2 units of capital raises output by 26 units, and then going from 2 to 3 units of capital only increases output by 18 units, the production function's slope is positive but decreasing.
This pattern of output increasing at a diminishing rate due to the diminishing marginal product of capital is a fundamental concept in economics, particularly in the study of production and growth.
