Average Cost

Average cost is the cost per unit of output, calculated by dividing total production cost by the quantity produced. In microeconomics, “average cost” generally means average total cost, encompassing both fixed and variable costs. It differs from marginal cost, which measures the additional cost of increasing output. Average cost is central to the analysis of production efficiency, profitability, and the relationship between firm size and production costs. (openstax.org)

Definition and measurement

For a positive output quantity $Q$, average cost is

where $TC(Q)$ denotes total cost. Its units are monetary units per unit of output: dollars per haircut, for example. Average cost is undefined at zero output because the calculation would require division by zero. Total cost and output must refer to the same production period and activity. (openstax.org)

In economic analysis, total cost includes explicit expenditures and implicit opportunity costs. The latter represent the value of alternatives forgone when a business uses resources it owns, such as an owner’s time or premises. Consequently, average economic cost can exceed a unit-cost figure based only on recorded expenditures. This distinction matters when measuring economic profit: covering all economic costs includes compensating owner-supplied resources at their opportunity costs. (openstax.org)

Fixed and variable components

In the short run, total cost can be decomposed into fixed cost $FC$, which does not change with output over the relevant range, and variable cost $VC(Q)$, which changes as production changes:

Dividing by output yields

Here, $AFC$ is average fixed cost, while $AVC$ is average variable cost. If fixed cost is positive, average fixed cost falls as output expands. The vertical gap between the average total and average variable cost curves therefore narrows with increasing output. (openstax.org)

As a hypothetical illustration, suppose fixed cost is $1,000 per production period and variable cost is $10 per unit. Producing 100 units gives total cost of $2,000 and average cost of $20. Producing 200 units gives total cost of $3,000 and average cost of $15. In this example, marginal cost remains $10: the decline in average cost comes entirely from spreading fixed cost over more units.

Relationship to marginal cost

When total cost is differentiable, marginal cost is its derivative with respect to output. Differentiating the average-cost formula gives

Thus, marginal cost below average cost lowers the average, while marginal cost above average cost raises it. At a differentiable interior minimum of average cost, $MC=AC$. Equality alone does not establish a minimum; the direction of change around the point must also be considered. The same averaging principle explains the relationship between marginal cost and average variable cost. (openstax.org)

This distinction separates unit-cost measurement from optimization of production. Average cost indicates whether revenue covers costs at a particular output. Marginal cost, compared with marginal revenue, helps determine whether changing output increases profit. Minimizing average cost and maximizing profit are therefore different problems. (pressbooks-dev.oer.hawaii.edu)

Short-run and long-run curves

The short run is a period in which at least one production input is fixed. Average total cost is often represented by a U-shaped curve. Initially, spreading fixed expenses over additional output can reduce unit cost. At higher output, diminishing returns to variable inputs can increase marginal cost sufficiently to raise average cost. This is a common model rather than a universal requirement for every production process. (openstax.org)

In the long run, all production inputs can be adjusted. The long-run average cost curve shows the lowest attainable average cost at each output, given available technology and input prices. It forms the lower envelope of the short-run average-cost curves associated with alternative plant sizes and production arrangements; it is not obtained simply by joining their minimum points. (openstax.org)

Declining long-run average cost indicates economies of scale; rising long-run average cost indicates diseconomies of scale. A flat segment indicates constant average cost. These patterns describe adjustments in production scale, unlike short-run diminishing returns, which concern increasing a variable input while another input remains fixed. (openstax.org)

Profitability and market structure

If all output is sold at a single price $P$, total revenue is $PQ$, and profit can be expressed as

Price above average economic cost implies positive economic profit; equality implies zero economic profit; price below it implies a loss. (pressbooks-dev.oer.hawaii.edu)

A loss does not necessarily imply immediate shutdown. In the standard short-run model of perfect competition, a firm can reduce its losses by producing when revenue covers variable costs and contributes toward unavoidable fixed costs. Below minimum average variable cost, shutdown avoids additional operating losses. A sunk cost is already incurred and unrecoverable, so it does not change with the production decision. (openstax.org)

Under the textbook assumptions of identical firms and free entry and exit, long-run competitive market equilibrium places price at minimum average cost, with zero economic profit. Average-cost behavior also helps explain natural monopoly: when economies of scale persist across the relevant market demand, one supplier may serve that demand at lower cost than multiple suppliers. In economic regulation, average-cost pricing can permit cost recovery, whereas marginal-cost pricing can leave a deficit when marginal cost lies below average cost. (openstax.org)