To produce a given level of output, a firm maximizes profits when the marginal rate of technical substitution is equal to the ratio of factor prices. This principle is known as

Diminishing marginal productivity
Increasing marginal productivity
Equi-marginal productivity
Law of diminishing returns

The correct answer is C. Equi-marginal productivity.

The marginal rate of technical substitution (MRTS) is the rate at which one input can be substituted for another while maintaining a constant level of output. The ratio of factor prices is the price of one input divided by the price of another input.

A firm maximizes profits when it produces at the point where the MRTS is equal to the ratio of factor prices. This is because at this point, the firm is using the inputs in the most efficient way possible.

A. Diminishing marginal productivity is the principle that as more of an input is added to a production process, the marginal product of that input will eventually decline.

B. Increasing marginal productivity is the principle that as more of an input is added to a production process, the marginal product of that input will increase.

D. The law of diminishing returns is the principle that as more of an input is added to a production process, the marginal product of that input will eventually decline.

The law of diminishing returns is a special case of diminishing marginal productivity. It applies when the amount of one input is increased while the amounts of all other inputs are held constant. In this case, the marginal product of the first input will eventually decline.