Final answer:
To minimize costs, a firm must compare the marginal products of labor and capital. In a competitive market, the firm will hire workers up to the point where the market wage equals the marginal revenue product of labor. For example, if the wage is $20, and the marginal revenue product for the fourth worker is $20, the firm should employ 4 workers.
Step-by-step explanation:
To hire the least-cost combination of labor and capital, the firm must compare the marginal product of labor and the marginal product of capital. The aim is to utilize each factor where its marginal product per dollar spent is the highest, which is where the ratio of the marginal product to its price is equal for all inputs.
To determine the value of the marginal product at each level of labor, a firm assesses the additional output generated by employing one more unit of labor while holding other factors constant. The additional revenue generated from this additional output is the marginal revenue product (MRP). A firm in a perfectly competitive labor market, where the going market wage is $12, will maximize profits by hiring workers up to the point where this market wage equals the marginal revenue product of labor.
If the marginal revenue product of labor is greater than the market wage, it is profitable for the firm to hire additional workers. Conversely, if the marginal revenue product of labor falls below the market wage, it would be unprofitable to do so. For example, if the going market wage is $20 and the firm's marginal revenue product for the fourth worker is $20, then the profit-maximizing level of employment is 4 workers.