relationship between average total cost curve and marginal cost curve
Cost curve A short-run marginal cost 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.[3]:191 For most production processes the marginal product of labor initially rises, reaches a maximum value and then continuously falls as production increases. Thus marginal cost initially falls, reaches a minimum value and then increases.[4]:209 The marginal cost curve intersects both the average variable cost curve and (short-run) average total cost curve at their minimum points. When the marginal cost curve is above an average cost curve the average curve is rising. When the marginal costs curve is below an average curve the average curve is falling. This relation holds regardless of whether the marginal curve is rising or falling.[5]:226
Cost curve 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 as to cost minimization. The long-run marginal cost curve intersects the long-run average cost curve at the minimum point of the latter.[3]:208 When long-run marginal costs are below long-run average costs, long-run average costs are falling (as to additional units of output).[3]:207 When long-run marginal costs are above long run average costs, average costs are rising. Long-run marginal cost equals short run marginal-cost at the least-long-run-average-cost level of production. LRMC is the slope of the LR total-cost function.
Average cost A typical average cost curve will have a U-shape, because fixed costs are all incurred before any production takes place and marginal costs are typically increasing, because of diminishing marginal productivity. In this "typical" case, for low levels of production marginal costs are below average costs, so average costs are decreasing as quantity increases. An increasing marginal cost curve will intersect a U-shaped average cost curve at its minimum, after which point the average cost curve begins to slope upward. For further increases in production beyond this minimum, marginal cost is above average costs, so average costs are increasing as quantity increases. An example of this typical case would be a factory designed to produce a specific quantity of widgets per period: below a certain production level, average cost is higher due to under-utilized equipment, while above that level, production bottlenecks increase the average cost.
Capability Maturity Model Integration Maturity Level 5 - Optimizing