Final answer:
When a production function shows diminishing marginal product, the corresponding total-cost curve will have a slope that starts out moderate or flat and then curves upwards sharply as the cost of producing each additional unit increases with the addition of more labor.
Step-by-step explanation:
If a production function exhibits diminishing marginal product, it indicates that as more units of labor are added, the additional output from each new unit of labor decreases. This general rule is crucial in understanding the behavior of production costs in response to changes in output. As production increases and marginal productivity declines, the costs associated with producing each additional unit—marginal costs—begin to rise.
Since the total cost curve is a graphical representation of the relationship between the production level and total costs, the relationship between the marginal product and the total cost curve can be established. When the marginal product is diminishing, it implies that the marginal cost is rising, leading to an upward slope in the total cost curve; however, the exact shape of the total cost curve can be more complex, typically starting out flat or with a gentle slope and then bending upwards sharply as diminishing marginal productivity sets in and marginal costs increase.