Marginal Cost

Marginal cost is the additional cost incurred when production increases by one unit, or the change in total cost per unit of additional output. In microeconomics, it distinguishes the cost of expanding production from the average cost of existing production. It is central to explanations of firms’ output decisions, competitive supply, and the allocation of resources. Marginal cost depends on the output level and the production conditions being considered; it is not necessarily constant. (openstax.org)

Definition and calculation

Let $C(q)$ denote total cost at output $q$. For a discrete increase in production, marginal cost is calculated as

If output rises by exactly one unit, the incremental cost is $C(q+1)-C(q)$. If output rises by several units, the quotient measures the average incremental cost across that interval, rather than necessarily the cost of its final unit. Costs and quantities must refer to comparable production conditions and the same accounting period. (openstax.org)

When output is modeled as continuous and the cost function is differentiable, marginal cost is its derivative:

This calculus formulation measures the instantaneous rate at which cost changes with output. The derivative approximates the cost of a small discrete increase but need not equal the exact cost of producing one additional indivisible unit. (openstax.org)

For illustration, suppose total daily cost rises from $1,000 at 100 units to $1,060 at 110 units. The average incremental cost over those ten units is $6 per unit. By contrast, average total cost at 110 units is approximately $9.64. These hypothetical figures show why marginal and average costs answer different questions.

Which costs are included?

In economic analysis, cost includes both explicit payments and opportunity costs: the value of resources in their next-best alternative use. Additional production can therefore have an economic cost even when it requires no new cash payment, as when an owner devotes additional unpaid time to the business. Marginal economic cost and marginal accounting expenditure need not coincide. (openstax.org)

In the standard short-run model, total cost consists of fixed cost and variable cost:

Because $F$ does not change with output within the relevant range, marginal cost equals the change in variable cost per additional unit—not variable cost itself. Sunk costs, which have already been incurred and cannot be recovered, do not change with a prospective production decision. Fixed costs and sunk costs are related but distinct concepts: “fixed” describes responsiveness to output, whereas “sunk” describes recoverability. (openstax.org)

Relationship to average cost

Average total cost is $AC(q)=C(q)/q$. Marginal cost determines whether increasing output raises or lowers this average. When marginal cost is below average cost, additional production lowers average cost; when it is above average cost, additional production raises it. (openstax.org)

For a differentiable cost function and positive output, differentiation gives

Thus, at a smooth interior minimum of average cost, marginal and average cost are equal. The same relationship applies to average variable cost. In conventional U-shaped diagrams, marginal cost crosses each average-cost curve at its minimum. These relationships follow from marginal-versus-average arithmetic, rather than requiring every actual cost curve to be U-shaped. (openstax.org)

Production conditions and time horizons

Short-run marginal cost reflects production with at least one input held fixed. It may initially fall as workers specialize or equipment is used more effectively. It often subsequently rises because of diminishing marginal returns: additional variable inputs generate progressively smaller increments of output when combined with fixed capacity. With unchanged input prices, producing each further unit then requires more expenditure. (openstax.org)

In the long run, all inputs can be adjusted, including plant and equipment. Long-run cost therefore reflects choices unavailable under an existing capacity constraint. Economies of scale describe declining long-run average cost as production expands; they are not synonymous with declining marginal cost. Marginal cost can rise while remaining below average cost, so average cost continues to fall. (assets.openstax.org)

Output decisions and market structure

Marginal cost is compared with marginal revenue, the additional revenue generated by selling more output. In the standard differentiable model of profit maximization, an interior optimum satisfies

Equality alone is not sufficient: a profit maximum requires appropriate curvature or a change from marginal revenue exceeding marginal cost to marginal cost exceeding marginal revenue. Boundary choices and discontinuous production possibilities also require consideration. (openstax.org)

Under perfect competition, a firm takes the market price as given, so marginal revenue equals price. In the conventional short-run model, its supply curve is the rising portion of marginal cost above minimum average variable cost; below that threshold, shutting down avoids greater losses. This connects marginal cost to supply and demand. (openstax.org)

A single-price monopolist instead faces downward-sloping demand. It selects output using the marginal-revenue–marginal-cost comparison and obtains its price from the demand curve. Consequently, its profit-maximizing price generally exceeds marginal cost. (openstax.org)

Private and social marginal cost

Private marginal cost measures the additional cost borne by the producer. Social marginal cost also includes costs imposed on others through an externality, such as pollution. With a negative production externality,

where $MEC$ is marginal external cost. In welfare economics, efficient output balances marginal social benefit against marginal social cost. A market responding only to private costs can therefore produce more than the socially efficient quantity, an instance of market failure. (openstax.org)