Final answer:
The relationship between marginal factor cost (MFC) and the value of marginal product (VMP) is such that, for a firm to maximize profits, MFC should equal VMP. This condition would be met in a perfectly competitive market where the firm can control quantity but not price.
Step-by-step explanation:
When discussing the relationship between marginal factor cost (MFC) and the value of marginal product (VMP) for a given firm, it is essential to understand these concepts in the context of firm production and profit maximization. If the MFC is constant regardless of the quantity of the factor purchased, this implies a perfectly elastic supply of the factor.
In a perfectly competitive market, firms are price takers both for the inputs they purchase and the products they sell. Therefore, to maximize profit, a firm will hire factors of production up to the point where the value of the marginal product (VMP) of the factor equals the marginal factor cost (MFC). This condition is described as MFC = VMP (Answer 'b'). Utilizing factors beyond this point would mean the cost of the additional factor is greater than the revenue it generates, leading to decreased profits.
Another important point to consider is that if a firm is producing at a quantity where marginal costs exceed marginal revenue, then each marginal unit is costing more than the revenue it brings in, reducing profits. Therefore, the firm will adjust its output until marginal revenue (MR) equals marginal cost (MC).