Final answer:
The least-cost combination of capital and labor for a given output level in a competitive market is when the ratio MPK/PK equals the ratio MPL/PL. This reflects the equimarginal principle, where each input's marginal return per dollar is balanced.
Step-by-step explanation:
The least-cost combination of capital and labor needed to produce a given level of output is achieved when the ratio of the marginal product of capital to its price is equal to the ratio of the marginal product of labor to its price. This condition is represented by the equation MPK/PK = MPL/PL, thus, the correct answer is A. MPK/PK = MPL/PL. In a competitive market, firms aim to maximize profits, and one way to do that is to use resources in the most cost-effective way. The equality of these ratios ensures that the last dollar spent on each input provides the same amount of additional output, which is called the equimarginal principle.
It is important to realize that the marginal product of an input decreases as the quantity of the input increases, due to the law of diminishing returns. However, as long as the firm is operating in a competitive market, the value of the marginal product of an input is its marginal product times the price of output, which in the case of labor, is the marginal revenue product (MRP) of labor. Therefore, firms typically continue hiring until the marginal revenue product of labor equals the market wage rate.