Final answer:
If a production function exhibits diminishing marginal product, the slope of the production function becomes flatter as the quantity of the input increases. This is because each additional unit of input contributes less to the total output due to the diminishing marginal product of labor. Therefore, the final answer to the student's question is option (2) the slope becomes flatter as the quantity of the input increases.
Step-by-step explanation:
When discussing a production function that exhibits diminishing marginal product, we are referring to the principle that as additional units of labor are employed, the increase in the output produced by each additional unit of labor tends to become smaller. This is a common observation in the short run when at least one input is fixed (such as capital). The diminishing marginal product indicates that there is only so much productivity that can be gained from increasing labor, especially when other factors of production cannot be increased at the same rate to complement the additional labor.
In terms of the slope of the production function, which represents the change in output resulting from a change in input, a diminishing marginal product implies that as the quantity of the input increases, the slope becomes flatter. This means that for every additional unit of input (like labor), the increase in output gets progressively smaller. In the context of the options provided, the correct response would be (2) that the slope becomes flatter as the quantity of the input increases.
As a visual representation, if you imagine a graph where the amount of labor is plotted on the x-axis and the output on the y-axis, initially, as labor increases, output increases at a faster rate, but after a certain point, the curve starts to flatten out. This slowdown in the growth rate of output reflects the diminishing marginal product of labor. Therefore, the final answer to the student's question is option (2) the slope becomes flatter as the quantity of the input increases.