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Graph used in economics
In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms optimize their production process by minimizing cost consistent with each possible level of production, and the result is a cost curve. Profit maximizing firms use cost curves to decide output quantities. There are various types of cost curves, all related to each other, including total and average cost curves; marginal ("for each additional unit") cost curves, which are equal to the differential of the total cost curves; and variable cost curves. Some are applicable to the short run, others to the long run.

The short run total cost (SRTC) and long run total cost (LRTC) curves are increasing in the quantity of output produced because producing more output requires more labor usage in both the short and long runs, and because in the long run producing more output involves using more of the physical capital input; and using more of either input involves incurring more input costs. With only one variable input (labor usage) in the short run, each possible quantity of output requires a specific quantity of usage of labor, and the short–run total cost as a function of the output level is this unique quantity of labor times the unit cost of labor. But in the long run, with the quantities of both labor and physical capital able to be chosen, the total cost of producing a particular output level is the result of an optimization problem: The sum of expenditures on labor (the wage rate times the chosen level of labor usage) and expenditures on capital (the unit cost of capital times the chosen level of physical capital usage) is minimized with respect to labor usage and capital usage, subject to the production function equality relating output to both input usages; then the (minimal) level of total cost is the total cost of producing the given quantity of output.

Since short run fixed cost (FC/SRFC) does not vary with the level of output, its curve is horizontal as shown here. Short run variable costs (VC/SRVC) increase with the level of output, since the more output is produced, the more of the variable input(s) needs to be used and paid for.

Average variable cost (AVC/SRAVC) (which is a short run concept) is the variable cost (typically labor cost) per unit of output: SRAVC = wL / Q where w is the wage rate, L is the quantity of labor used, and Q is the quantity of output produced. The SRAVC curve plots the short run average variable cost against the level of output and is typically drawn as U shaped. However, whilst this is convenient for economic theory, it has been argued that it bears little relationship to the real world. Some estimates show that, at least for manufacturing, the proportion of firms reporting a U shaped cost curve is in the range of 5 to 11 percent.

Since fixed cost by definition does not vary with output, short run average fixed cost (SRAFC) (that is, short run fixed cost per unit of output) is lower when output is higher, giving rise to the downward sloped curve shown.

A short run marginal cost (SRMC) curve graphically represents the relation between marginal (i. e., incremental) cost incurred by a firm in the short run production of a good or service and the quantity of output produced. This curve is constructed to capture the relation between marginal cost and the level of output, holding other variables, like technology and resource prices, constant. The marginal cost curve is usually U shaped. Marginal cost is relatively high at small quantities of output; then as production increases, marginal cost declines, reaches a minimum value, then rises. The marginal cost is shown in relation to marginal revenue (MR), the incremental amount of sales revenue that an additional unit of the product or service will bring to the firm. This shape of the marginal cost curve is directly attributable to increasing, then decreasing marginal returns (and the law of diminishing marginal returns). Marginal cost equals w/MPL.

The long run marginal cost (LRMC) curve shows for each unit of output the added total cost incurred in the long run, that is, the conceptual period when all factors of production are variable. Stated otherwise, LRMC is the minimum increase in total cost associated with an increase of one unit of output when all inputs are variable. The long run marginal cost curve is shaped by returns to scale, a long run concept, rather than the law of diminishing marginal returns, which is a short run concept. The long run marginal cost curve tends to be flatter than its short run counterpart due to increased input flexibility. The long run marginal cost curve intersects the long run average cost curve at the minimum point of the latter. Because the production function determines the variable cost function it necessarily determines the shape and properties of marginal cost curve and the average cost curves. Likewise, it has diseconomies of scale (is operating in an upward sloping region of the long run average cost curve) if and only if it has decreasing returns to scale, and has neither economies nor diseconomies of scale if it has constant returns to scale. In this case, with perfect competition in the output market the long run market equilibrium will involve all firms operating at the minimum point of their long run average cost curves (i. e., at the borderline between economies and diseconomies of scale). If, however, the firm is not a perfect competitor in the input markets, then the above conclusions are modified. For example, if there are increasing returns to scale in some range of output levels, but the firm is so big in one or more input markets that increasing its purchases of an input drives up the input's per unit cost, then the firm could have diseconomies of scale in that range of output levels. On the other hand, if the firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range.

For each quantity of output there is one cost–minimizing level of capital and a unique short–run average cost curve associated with producing the given quantity. The following statements assume that the firm is using the optimal level of capital for the quantity produced. If not, then the SRAC curve would lie "wholly above" the LRAC and would not be tangent at any point. Each STC curve can be tangent to the LRTC curve at only one point. The STC curve cannot cross (intersect) the LRTC curve. One STC curve is tangent to LRTC at the long–run cost–minimizing level of production. At the point of tangency LRTC = STC. At all other levels of production STC will exceed LRTC. Average cost functions are the total cost function divided by the level of output. Therefore, the SATC curve is also tangent to the LRATC curve at the cost minimizing level of output. At the point of tangency LRATC = SATC. At all other levels of production SATC > LRATC
The slope of the total cost curves equals marginal cost. Therefore, when STC is tangent to LTC, SMC = LRMC. At the long–run cost–minimizing level of output LRTC = STC; LRATC = SATC and LRMC = SMC,. With fixed unit costs of inputs, if the production function has constant returns to scale, then at the minimal level of the SATC curve we have SATC = LRATC = SMC = LRMC. With decreasing returns, minimum SRAC occurs at a lower production level than minimum LRAC because a firm could reduce average costs by simply decreasing the size or its operations. The minimum of a SRAC occurs when the slope is zero. Thus the points of tangency between the U shaped LRAC curve and the minimum of the SRAC curve would coincide only with that portion of the LRAC curve exhibiting constant economies of scale. For increasing returns to scale the point of tangency between the LRAC and the SRAC would have to occur at a level of output below level associated with the minimum of the SRAC curve.

Both the SRAC and LRAC curves are typically expressed as U shaped. while the upward slope is due to diminishing marginal returns to the variable input.