Marginal cost is the additional cost attributed to an additional unit produced. Marginal product is the increase in the total product due to an additional resource allocation. The marginal cost and marginal return have an inverse relationship and can almost be represented as mirror images of each other.

The peak of the marginal product corresponds with the lowest point of the marginal cost. Thus as marginal product increases, the marginal cost decreases and vice versa. The relationship can be attributed to the law of diminishing returns. As we start adding labor, the output per additional labor increases and this means that the marginal product increases, and thereby the marginal costs decrease; however, if we continue adding more labor, they may get in each other’s way, may become inefficient and thereby reduce the marginal product and this in turn will increase the marginal cost.

The formula explains the relationship between marginal cost and marginal product MC= P /MPL

(Where MC is the marginal cost, P is the wage rate of labor and MPL is the marginal product).

Consider that marginal product is 5 additional units per unit labor and the wage rate of labor as $15. Hence the marginal cost is 15/5 = $3.

Now say we employ more labor and the marginal product is 10 additional units per labor, then the marginal cost is 15/10= $1.5.

We observe that as the marginal product increases from 5 to 10 units, the marginal cost decreases from $3 to $1.5. This proves the inverse relationship between marginal cost and marginal cost.