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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 use these curves to find the optimal point of production, where they make the most profits. There are various types of cost curves, all related to each other.

**1. The Short-Run Average Variable Cost Curve (SAVC)****: **

Average variable cost (which is a short-run concept) is the variable cost (typically labour cost) per unit of output- SAVC = wL/Q where w is the wage rate, L is the quantity of labour used, and Q is the quantity of output produced.

The SAVC curve plots the short-run average variable cost against the level of output, and is typically U-shaped.

**Typical Short-Run Average Cost Curve: **

The average total cost curve is constructed to capture the relation between cost per unit of output and the level of output, ceteris paribus. A perfectly competitive and productively efficient firm organizes its factors of production in such a way that the average cost of production is at the lowest point.

In the short run, when at least one factor of production is fixed, this occurs at the output level where it has enjoyed all possible average cost gains from increasing production. This is at the minimum point in the diagram on the right.

**Short-run total cost is given by: **

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STC = P_{k}K+P_{l}L,

where P_{K} is the unit price of using physical capital per unit time, P_{L} is the unit price of labour per unit time (the wage rate), K is the quantity of physical capital used, and L is the quantity of labour used.

**From this we obtain short-run average cost, denoted either SATC or SAC as STC/Q: **

SATC or SAC = P_{k}K/Q + P_{L}L/Q = P_{K}/AP_{K} + P_{L}/AP_{L},

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where AP_{K} = Q/K is the average product of capital and AP_{L} = Q/L is the average product of labour.

Short run average cost equals average fixed costs plus average variable costs. Average fixed cost continuously falls as production increases in the short run, because K is fixed in the short run. The shape of the average variable cost curve is directly determined by increasing and then diminishing marginal returns to the variable input (conventionally labour).

**Typical Long-Run Average Cost Curve:**

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The long-run average cost curve depicts the cost per unit of output in the long ran—that is, when all productive inputs’ usage levels can be varied. The behavioural assumption underlying the curve is that the producer will select the combination of inputs that will produce a given output at the lowest possible cost.

Given that LRAC is an average quantity, one must not confuse it with the long-run marginal cost curve, which is the cost of one more unit. The LRAC curve is created as an envelope of an infinite number of short-run average total cost curves, each based on a particular fixed level of capital usage.

The typical LRAC curve is U-shaped, reflecting economies of scale where negatively-sloped and diseconomies of scale where positively sloped. Contrary to Viner the envelope is not created by the minimum point of each short-run average cost curve. This mistake is recognized as Viner’s Error.

In a long-run perfectly competitive environment, the equilibrium level of output corresponds to the minimum efficient scale, marked as Q2 in the diagram. This is due to the zero-profit requirement of a perfectly competitive equilibrium. This result, which implies production is at a level corresponding to the lowest possible average cost, does not imply that production levels other than that at the minimum point are not efficient. All points along the LRAC are productively efficient by definition, but not all are equilibrium points in a long-run perfectly competitive environment.

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In some industries, the LRAC is always declining (economies of scale exist indefinitely). This means that the largest firm tends to have a cost advantage, and the industry tends naturally to become a monopoly, and hence is called a natural monopoly. Natural monopolies tend to exist in industries with high capital costs in relation to variable costs, such as water supply and electricity supply.

**Typical Marginal 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 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, 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/MP_{L}. For most production processes the marginal product of labour 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.

The marginal cost curve intersects first the average variable cost curve then the 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.

**2. The Long-Run Marginal Cost Curve (LRMC)****: **

The long run marginal cost curve shows the minimum cost incurred per unit change in output when all factors of production are variable. The long run marginal cost curve is shaped by economies and diseconomies of 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.

When long run marginal costs are below long run average costs, long run average costs are falling. 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.

**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.

**Relationship between Short Run and Long Run Cost Curves****: **

1. The STC curve can be tangent to the LRTC curve at only one point. The STC curve cannot cross the LRTC curve. The STC curve can lie wholly “above” the LRTC curve with no tangency point.

2. One STC curve is tangent to LRTC at the long-run cost minimizing level of production. At the point of tangency LRTC = STC, the latter contingent on K being at its long-run optimal level. At all other levels of production STC will exceed LRTC. The difference is that SAC represents the effect of the law of diminishing marginal returns, which operates in the short run but does not apply in the long run.

3. Average cost functions are the total cost function divided by the level of output. Therefore the LRATC curve is also tangent to a SATC curve at the cost-minimizing level of output. At the point of tangency LRATC = SATC, the latter contingent on K being at its long- run optimal level. At all other levels of production SATC > LRATC.

4. The slope of the total cost curves equals marginal cost. Therefore when LRTC is tangent to STC, SMC = LRMC. “SMC intersects LMC at the output level… at which SAC is tangent to LAC.”

5. At the long run cost minimizing level of output LRTC = STC; LRATC = SATC and LRMC = SMC, the short-run cost curves being contingent on K being at its long-run optimal level.

6. The long run cost minimizing level of output may be different from minimum SATC, if the latter is drawn contingent on a level of K which is not long-run optimal.

7. 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.

8. With fixed unit costs of inputs, if the production function has increasing returns to scale, the minimum of the SATC curve is to the right of the point of tangency between the LRAC and the SATC curves. Where LRTC = STC, LRATC = SATC and LRMC = SMC. SMC does not equal LRMC and LRMC does not equal LRAC.

9. With fixed unit costs of inputs and decreasing returns the minimum of the SATC curve is to the left of the point of tangency between LRAC and SATC. Where LRTC = STC, LRATC = SATC and LRMC = SMC. SMC does not equal LRMC and LRMC does not equal LRAC.

10. With fixed unit input costs, a firm that is experiencing increasing (decreasing) returns to scale and is producing at its minimum SAC can always reduce average cost in the long run by expanding (reducing) the use of the fixed input.

11. LRATC will always equal to or be less than SATC.

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