There are several ways to calculate marginal cost without total cost. It depends on the information given.
a) If we are given the total revenue function of a profit maximizing firm, then marginal cost is found by applying the profit maximizing rule that MC = MR. In this case, total revenue function is differentiated to get the marginal revenue and the marginal revenue is also the marginal cost, since the firm is maximizing profit.
If marginal revenue is already given explicitly, then it is also the marginal cost, given the firm is maximizing profit.
If given average revenue, the average revenue is multiplied by quantity to convert it to total revenue, and derive the marginal revenue, which is also the marginal cost.
b) if given average cost, the cost function is multiplied by quantity to convert it to total cost, and deduce marginal cost after.
Therefore, the calculation depends on information provided.
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