Average Variable Cost

Average variable cost (AVC) is a firm’s total variable cost divided by the quantity of output produced. In microeconomics, it measures the average expenditure on inputs whose use changes with production, excluding fixed costs that remain unchanged over the relevant output range. It is a central component of short-run cost analysis and helps explain why a firm may continue producing despite making a loss. (openstax.org)

Definition and measurement

For a positive quantity of output $Q$,

where $VC(Q)$ denotes total variable cost. Examples include materials, production-related electricity, and labor that can be adjusted as output changes. Classification depends on the decision horizon: a contractual payment may be fixed over one period but adjustable over another. The economic short run is defined by the presence of at least one fixed input, rather than by a particular number of months or years. (open.oregonstate.education)

AVC is measured in currency per unit of output, whereas total variable cost is measured in currency. At zero output, the quotient is undefined, even when variable cost is zero; a graph may nevertheless show a limiting value as output approaches zero. Economic cost measurement also includes relevant opportunity costs, not merely recorded cash expenditures. Resources supplied by the owner can therefore carry an economic cost. (openstax.org)

Relationship to other costs

Total cost is the sum of fixed and variable costs:

Dividing by output gives

where $ATC$ is average total cost and $AFC=FC/Q$ is average fixed cost. With positive fixed cost, ATC exceeds AVC at every positive output. Their vertical separation narrows as output rises because fixed cost is spread across more units. This does not imply that AVC itself must decline. (openstax.org)

For an illustrative calculation, suppose production of 100 units incurs variable cost of $600 and fixed cost of $400. AVC is $6, AFC is $4, and ATC is $10 per unit. If variable cost rises to $1,400 at 200 units, AVC becomes $7. Thus, increasing total variable cost can accompany either rising or falling AVC, depending on how rapidly output increases. (open.oregonstate.education)

Marginal cost and the AVC curve

Marginal cost (MC) measures the additional cost associated with an increase in output. Because fixed cost does not change, marginal total cost equals marginal variable cost. For a differentiable cost function,

Applying the derivative to AVC yields

Consequently, AVC decreases when MC is below AVC and increases when MC is above it. At a smooth interior minimum, MC equals AVC. Under the conventional U-shaped specification, the marginal-cost curve crosses the AVC curve from below at that minimum. Equality alone, however, does not establish that a stationary point is a minimum. These relationships follow directly from the definitions. (open.oregonstate.education)

Production and curve shape

Textbooks commonly depict AVC as U-shaped. At low output, specialization and better use of a fixed facility can improve productivity. As production expands, diminishing returns to variable inputs may eventually increase unit costs: additional workers, for example, share a fixed amount of equipment or workspace. The U-shape is a model-dependent pattern, not a necessary property of every production process. (open.oregonstate.education)

A simple relationship illustrates this mechanism. If labor $L$ is the only variable input and its wage $w$ is constant, then $VC=wL$. Writing average product of labor as $AP_L=Q/L$ gives

Thus, higher average labor productivity corresponds to lower AVC, holding the wage constant. A production process with constant output per worker would instead generate constant AVC in this simplified model. This result is an algebraic consequence of the labor-cost and average-product definitions. (open.oregonstate.education)

Shutdown decisions and supply

Under perfect competition, a firm takes the market price $P$ as given. Conditional on operating, standard profit maximization selects output where price equals marginal revenue and marginal cost, subject to the appropriate maximizing conditions. The firm must also compare operating with producing nothing. (openstax.org)

When all fixed costs remain payable during shutdown and variable costs are avoidable, the operating contribution is

The shutdown price is therefore minimum AVC. Below it, no positive output covers variable cost. Above it, operating can cover variable cost and contribute toward fixed cost. At exactly minimum AVC, shutdown and production at the minimizing quantity yield the same profit under these assumptions. The conventional rising marginal-cost curve above this threshold forms the firm’s short-run supply curve. (openstax.org)

Covering AVC does not guarantee positive economic profit. At the chosen output, a price between AVC and ATC produces a loss smaller than the loss from shutdown. Temporary shutdown must also be distinguished from long-run exit: persistent inability to cover total economic cost motivates exit in the standard competitive model. (openstax.org)

Scope and limitations

Fixed cost and sunk cost are distinct: fixed describes responsiveness to output, whereas sunk describes irrecoverability. If stopping production avoids some nominally fixed expenses, the shutdown comparison must include those savings rather than mechanically applying AVC. Cost classification must match the actual alternatives available. (open.oregonstate.education)

In the long run, all inputs can be adjusted, so analysis generally uses long-run average total cost. A decline in short-run AVC should not automatically be called economies of scale, which concerns average cost as the scale of all inputs changes. (open.oregonstate.education)