Cost curve

In economics, a cost curve is a chart that shows production costs relative to the total quantity of output. In a free market, firms that are productively efficient minimize their costs for each possible production level, which results in a cost curve.

Businesses aiming to maximize profit rely on cost curves to determine how much to produce. Several types of cost curves exist, all interconnected, including total and average cost curves; marginal cost curves (for each extra unit), which are the derivative of total cost curves; and variable cost curves. Some apply to the short run, others to the long run.

Notation

Standard abbreviations are used for each cost concept, built from these descriptors: SR (short run—costs for non-reusable materials like raw materials), LR (long run—costs for renewable materials like equipment), A (average per unit), M (marginal per additional unit), F (fixed, unadjustable), V (variable, adjustable), T (total, fixed plus variable), and C (cost). These combine in various ways, often omitting SR or LR when clear: one from the first group (SR or LR); none or one from the second group (A, M, or none for “level”); none or one from the third group (F, V, or T); and the fourth item (C). This yields short-run curves like SRAFC, SRAC (or SRATC), AVC (or SRAVC), SRMC, FC (or SRFC), SRTC, and VC (or SRVC), and long-run curves like LRAC (or LRATC), LRMC, and LRTC.

Short-run total cost (SRTC) and long-run total cost (LRTC) curves

The short-run total cost (SRTC) and long-run total cost (LRTC) curves rise as output increases, because more output requires more labor in both time frames, and in the long run also more physical capital; using more of either input raises costs. In the short run, with only one variable input (labor), each output level needs a specific amount of labor, so SRTC is that labor quantity times the wage rate. In the long run, both labor and capital quantities can be chosen, and the total cost for a given output is the result of minimizing the sum of labor costs (wage rate times labor usage) and capital costs (unit cost of capital times capital usage), subject to the production function linking output to both inputs; the minimized total cost is then the cost of producing that output.

Short-run variable and fixed cost curves (SRVC and SRFC or VC and FC)

Short-run fixed cost (FC/SRFC) does not change with output, so its curve is horizontal. Short-run variable costs (VC/SRVC) increase with output, since more output requires more variable inputs and thus more payment.

Short-run average variable cost curve (AVC or SRAVC)

Average variable cost (AVC/SRAVC) is variable cost per unit: SRAVC = wL / Q, where w is the wage rate, L is labor quantity, and Q is output. The SRAVC curve is typically drawn as U-shaped, though this is convenient for theory but has little real-world support; estimates for manufacturing show only 5 to 11 percent of firms report a U-shaped cost curve. Short-run average fixed cost (SRAFC) falls as output rises, because fixed cost is spread over more units, producing a downward-sloping curve.

The average total cost curve shows the relationship between cost per unit and output, all else constant. A perfectly competitive, productively efficient firm arranges its factors of production to use as few as possible for a given output level. In the short run, with at least one fixed factor, this happens at the output where all possible average cost gains from increasing production have been realized—the minimum point on the curve. Short-run total cost is given by SRTC = PK * K + PL * L, where PK is the unit price of physical capital per time, PL is the unit price of labor per time, K is capital usage, and L is labor usage.