The correct answer is: A. AP rises when MP is above it, and falls when MP is below it.
The average product (AP) of a factor of production is the total product (TP) of that factor divided by the number of units of the factor employed. The marginal product (MP) of a factor of production is the change in total product that results from a one-unit change in the quantity of the factor employed.
In general, AP and MP are positively related. This means that when MP is above AP, AP will rise. When MP is below AP, AP will fall. This is because when MP is above AP, each additional unit of the factor employed is producing more output than the previous unit. This causes AP to rise. When MP is below AP, each additional unit of the factor employed is producing less output than the previous unit. This causes AP to fall.
However, there is a point at which MP reaches its maximum value and then begins to decline. This is the point at which the law of diminishing returns sets in. After this point, each additional unit of the factor employed produces less output than the previous unit. This causes AP to fall.
The point at which MP intersects AP is the point at which AP is at its maximum value. This is the point at which the firm is using the optimal amount of the factor of production.
Option B is incorrect because MP intersects AP at its maximum point, not its minimum point.
Option C is incorrect because AP is not always rising when MP is falling and vice versa. As explained above, AP and MP are positively related in general, but there is a point at which MP reaches its maximum value and then begins to decline. After this point, each additional unit of the factor employed produces less output than the previous unit. This causes AP to fall.
Option D is the correct answer because it is the only option that is not contradicted by the above explanation.