Relation of AC & MC

By Deepak Kumar

RELATIONSHIP BETWEEN AC AND MC

Average cost

In economics, average cost or unit cost is equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q). Average costs may be dependent on the time period considered (increasing production may be expensive or impossible in the short term, for example). Average costs affect the supply curve and are a fundamental component of supply and demand.

Short-run average cost

Short-run average cost will vary in relation to the quantity produced unless fixed costs are zero and variable costs constant. A cost curve can be plotted, with cost on the y-axis and quantity on the x-axis. Marginal costs are often shown on these graphs, with marginal cost representing the cost of the last unit produced at each point; marginal costs are the first derivative of total or variable costs.

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-utilised equipment, while above that level, production bottlenecks increase the average cost.

Long-run average cost

The long run is a time frame in which the firm can vary the quantities used of all inputs, even physical capital. A long-run average cost curve can be upward sloping, downward sloping, or downward sloping at relatively low levels of output and upward sloping at relatively high levels of output, with an in-between level of output at which the slope of long-run average cost is zero. The typical long-run average cost curve is U-shaped, by definition reflecting increasing returns to scale where negatively-sloped and decreasing returns to scale where positively sloped

Marginal cost

In economics and finance, marginal cost is the change in total cost that arises when the quantity produced changes by one unit. That is, it is the cost of producing one more unit of a good. If the good being produced is infinitely divisible, so the size of a marginal cost will change with volume, as a non-linear and non-proportional cost function includes the following:

• variable terms dependent to volume,
• constant terms independent to volume and occurring with the respective lot size,
• jump fix cost increase or decrease dependent to steps of volume increase.

If the cost function is differentiable joining, the marginal cost is the cost of the next unit produced referring to the basic volume.

If the cost function is not differentiable, the marginal cost can be expressed as follows.

 

A typical marginal cost curve with marginal revenue overlaid

Relationship to marginal cost

When average cost is declining as output increases, marginal cost is less than average cost. When average cost is rising, marginal cost is greater than average cost. When average cost is neither rising nor falling (at a minimum or maximum), marginal cost equals average cost.

               Other special cases for average cost and marginal cost appear frequently:

• Constant marginal cost/high fixed costs: each additional unit of production is produced at constant additional expense per unit. The average cost curve slopes down continuously, approaching marginal cost. An example may be hydroelectric generation, which has no fuel expense, limited maintenance expenses and a high up-front fixed cost (ignoring irregular maintenance costs or useful lifespan). Industries where fixed marginal costs obtain, such as electrical transmission networks, may meet the conditions for a natural monopoly, because once capacity is built, the marginal cost to the incumbent of serving an additional customer is always lower than the average cost for a potential competitor. The high fixed capital costs are a barrier to entry.
• Minimum efficient scale / maximum efficient scale: marginal or average costs may be non-linear, or have discontinuities. Average cost curves may therefore only be shown over a limited scale of production for a given technology. For example, a nuclear plant would be extremely inefficient (very high average cost) for production in small quantities; similarly, its maximum output for any given time period may essentially be fixed, and production above that level may be technically impossible, dangerous or extremely costly. The long run elasticity of supply will be higher, as new plants could be built and brought on-line.
• Zero fixed costs (long-run analysis) / constant marginal cost: since there are no economies of scale, average cost will be equal to the constant marginal cost.

Negative externalities of production

Negative Externalities of Production

Much of the time, private and social costs do not diverge from one another, but at times social costs may be either greater or less than private costs. When marginal social costs of production are greater than that of the private cost function, we see the occurrence of a negative externality of production. Productive processes that result in pollution are a textbook example of production that creates negative externalities.

Such externalities are a result of firms externalising their costs onto a third party in order to reduce their own total cost. As a result of externalising such costs we see that members of society will be negatively affected by such behavior of the firm. In this case, we see that an increased cost of production on society creates a social cost curve that depicts a greater cost than the private cost curve.

Positive externalities of production

Positive Externalities of Production

When marginal social costs of production are less than that of the private cost function, we see the occurrence of a positive externality of production. Production of public goods are a textbook example of production that create positive externalities. An example of such a public good, which creates a divergence in social and private costs, includes the production of education. It is often seen that education is a positive for any whole society, as well as a positive for those directly involved in the market.

Examining the relevant diagram we see that such production creates a social cost curve that is less than that of the private curve. In an equilibrium state we see that markets creating positive externalities of production will under produce that good. As a result, the socially optimal production level would be greater than that observed.

Economies of scale

Economies of scale is a concept that applies to the long run, a span of time in which all inputs can be varied by the firm so that there are no fixed inputs or fixed costs. Production may be subject to economies of scale (or diseconomies of scale). Economies of scale are said to exist if an additional unit of output can be produced for less than the average of all previous units— that is, if long-run marginal cost is below long-run average cost, so the latter is falling. Conversely, there may be levels of production where marginal cost is higher than average cost, and average cost is an increasing function of output. For this generic case, minimum average cost occurs at the point where average cost and marginal cost are equal (when plotted, the marginal cost curve intersects the average cost curve from below); this point will not be at the minimum for marginal cost if fixed costs are greater than zero.