# Short run and long cost relationship

### Long and short run cost functions

Short Run and Long Run Average Cost Curves: Relationship and Difference: Short Run Average Cost Curve: In the short run, the shape of the average total cost. Figure “Relationship Between Short-Run and Long-Run Average Total Costs” shows how a firm's LRAC curve is derived. Suppose Lifetime Disc Co. In this article we will discuss about the relation between Short-Run and Long- Run Costs. There is a close relation between short-run and long-run costs.

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 MRthe incremental amount of sales revenue that an additional unit of the product or service will bring to the firm.

## Cost curve

This shape of the marginal cost curve is directly attributable to increasing, then decreasing marginal returns and the law of diminishing marginal returns. Thus marginal cost initially falls, reaches a minimum value and then increases.

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.

### Short Run and Long Run Average Cost Curve

This relation holds regardless of whether the marginal curve is rising or falling. 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 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. Long-run marginal cost equals short run marginal-cost at the least-long-run-average-cost level of production. Graphing cost curves together[ edit ] Cost curves in perfect competition compared to marginal revenue Cost curves can be combined to provide information about firms.

In this diagram for example, firms are assumed to be in a perfectly competitive market. In a perfectly competitive market the price that firms are faced with would be the price at which the marginal cost curve cuts the average cost curve. Cost curves and production functions[ edit ] Assuming that factor prices are constant, the production function determines all cost functions.

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.

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.

Conversely, 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.

Suppose, for example, that the firm wants to increase its output from Q0 to Q1. If all inputs were variable, it could produce this new output at TCL.

### Cost curve - Wikipedia

Only at output Q0 are the two curves equal. Given the total cost curves in Figure 13, short-run average cost will be equal to long-run average cost only at an output of Q0. These are the short- run curves for the plant size designed to produce output QS optimally.

Since the short-run total cost curve would be tangent to the long-run total cost curve at this output, the two average cost curves are also tangent at this output. Since marginal cost is given by the slope of the total cost curve, long-run marginal cost equals short-run marginal cost at the output given by the point of tangency, QS. Thus, SRAC3 is increasing at this point also. Finally, SRAC2 is the short-run average cost curve corresponding to the output level — plant size — at which long-run average cost is at its minimum.

At output level Qm the two average cost curves are tangent. And, since both average cost curves attain their minimum at Qm, the two marginal cost curves must intersect the two average cost curves.

Thus, all four curves must intersect the two average cost curves, i. If the firm is limited to producing only with one of the three short-run cost structures shown in Fig.

- Short-Run and Long-Run Costs (With Diagram)
- Short Run and Long Run Average Cost Curve

This average cost curve lies below either of the other two for any output over this range.