Marginal cost

Marginal cost

Overview
In economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

 and finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...

, marginal cost is the change in total cost
Total cost
In economics, and cost accounting, total cost describes the total economic cost of production and is made up of variable costs, which vary according to the quantity of a good produced and include inputs such as labor and raw materials, plus fixed costs, which are independent of the quantity of a...

 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.


In practice the above definition of marginal cost as the change in total cost as a result of an increase in output of one unit is inconsistent with the calculation of marginal cost as MC=dTC/dQ for virtually all non-linear functions.
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Encyclopedia
In economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

 and finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...

, marginal cost is the change in total cost
Total cost
In economics, and cost accounting, total cost describes the total economic cost of production and is made up of variable costs, which vary according to the quantity of a good produced and include inputs such as labor and raw materials, plus fixed costs, which are independent of the quantity of a...

 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.


In practice the above definition of marginal cost as the change in total cost as a result of an increase in output of one unit is inconsistent with the calculation of marginal cost as MC=dTC/dQ for virtually all non-linear functions. This is as the definition MC=dTC/dQ finds the tangent to the total cost curve at the point q which assumes that costs increase at the same rate as they were at q. A new definition may be useful for marginal unit cost (MUC) using the current definition of the change in total cost as a result of an increase of one unit of output defined as: TC(q+1)-TC(q) and re-defining marginal cost to be the change in total as a result of an infinitesimally small increase in q which is consistent with its use in economic literature and can be calculated as dTC/dQ.

In general terms, marginal cost at each level of production includes any additional costs required to produce the next unit. If producing additional vehicles requires, for example, building a new factory, the marginal cost of those extra vehicles includes the cost of the new factory. In practice, the analysis is segregated into short and long-run cases, and over the longest run, all costs are marginal. At each level of production and time period being considered, marginal costs include all costs that vary with the level of production, and other costs are considered fixed costs.

If the cost function is differentiable, 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 number of other factors can affect marginal cost and its applicability to real world problems. Some of these may be considered market failures. These may include information asymmetries
Information asymmetry
In economics and contract theory, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. This creates an imbalance of power in transactions which can sometimes cause the transactions to go awry, a kind of market failure...

, the presence of negative or positive externalities
Externality
In economics, an externality is a cost or benefit, not transmitted through prices, incurred by a party who did not agree to the action causing the cost or benefit...

, transaction costs, price discrimination
Price discrimination
Price discrimination or price differentiation exists when sales of identical goods or services are transacted at different prices from the same provider...

 and others.

Cost functions and relationship to average cost


In the simplest case, the total cost function and its derivative are expressed as follows, where Q represents the production quantity, VC represents variable costs, FC represents fixed costs and TC represents total costs.



Since (by definition) fixed costs do not vary with production quantity, it drops out of the equation when it is differentiated. The important conclusion is that marginal cost is not related to fixed costs. This can be compared with average total cost or ATC, which is the total cost divided by the number of units produced and does include fixed costs.



For discrete calculation without calculus, marginal cost equals the change in total (or variable) cost that comes with each additional unit produced. In contrast, incremental cost is the composition of total cost from the surrogate of contributions, where any increment is determined by the contribution of the cost factors, not necessarily by single units.

For instance, suppose the total cost of making 1 shoe is $30 and the total cost of making 2 shoes is $40. The marginal cost of producing the second shoe is $40 - $30 = $10.

Marginal cost is not the cost of producing the "next" or "last" unit. As Silberberg and Suen note the cost of the last unit is the same as the cost of the first unit and every other unit. In the short run increasing production requires using more of the variable input - conventionally assumed to be labor. Adding more labor to a fixed capital stock reduces the marginal product of labor because of the diminishing marginal returns
Diminishing returns
In economics, diminishing returns is the decrease in the marginal output of a production process as the amount of a single factor of production is increased, while the amounts of all other factors of production stay constant.The law of diminishing returns In economics, diminishing returns (also...

. This reduction in productivity is not limited to the additional labor needed to produce the marginal unit - the productivity of every unit of labor is reduced. Thus the costs of producing the marginal unit of output has two components:
the cost associated with producing the marginal unit
and the increase in average costs for all units produced due to the “damage” to the entire productive process (∂AC/∂q)q.
The first component is the per unit or average cost. The second unit is the small increase in costs due to the law of diminishing marginal returns which increases the costs of all units of sold.[1]
Therefore, the precise formula is:

MC = AC + (∂AC/∂q)q.


Marginal costs can also be expressed as the cost per unit of labor divided by the marginal product of labor.
MC = ∆VC∕∆q;
∆VC = w∆L;
MC = w∆L;/∆q;
∆L∕∆q the change in quantity of labor to affect a one unit change in output = 1∕MPL.
Therefore MC = w∕MPL Since the wage rate is assumed constant marginal cost and marginal product of labor have an inverse relationship - if marginal cost is increasing (decreasing) the marginal product of labor is decreasing (increasing).

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
Economies of scale
Economies of scale, in microeconomics, refers to the cost advantages that an enterprise obtains due to expansion. There are factors that cause a producer’s average cost per unit to fall as the scale of output is increased. "Economies of scale" is a long run concept and refers to reductions in unit...

 (or diseconomies of scale
Diseconomies of scale
Diseconomies of scale are the forces that cause larger firms and governments to produce goods and services at increased per-unit costs. The concept is less well known than economies of scale.-Communication costs:...

). 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.

Perfectly competitive supply curve


The portion of the marginal cost curve above its intersection with the average variable cost curve is the supply curve for a firm operating in a perfectly competitive market
Perfect competition
In economic theory, perfect competition describes markets such that no participants are large enough to have the market power to set the price of a homogeneous product. Because the conditions for perfect competition are strict, there are few if any perfectly competitive markets...

. (the portion of the MC curve below its intersection with the AVC curve is not part of the supply curve because a firm would not operate at price below the shut down point) This is not true for firms operating in other market structures. For example, while a monopoly "has" an MC curve it does not have a supply curve. In a perfectly competitive market, a supply curve shows the quantity a seller's willing and able to supply at each price - for each price there is a unique quantity that would be supplied. The one-to-one relationship simply is absent in the case of a monopoly. With a monopoly there could be an infinite number of prices associated with a given quantity. It all depends on the shape and position of the demand curve and its accompanying marginal revenue curve.

Decisions taken based on marginal costs


Firms decide the quantity to be produced based on marginal costs and sale price. If the sale price is higher than the marginal cost, then they supply the unit and sell it. If the marginal cost is higher than the price, it would not be profitable to produce it. So the production will be carried out until the marginal cost is equal to the sale price. In other words, firms refuse to sell if the marginal cost is higher than the market price.

Relationship to fixed costs


Marginal Costs are not affected by changes in fixed cost. Marginal costs can be expressed as ∆C(q)∕∆Q. Since fixed costs do not vary with (depend on) changes in quantity, MC is ∆VC∕∆Q. Thus if fixed cost were to double MC would not be affected and consequently the profit maximizing quantity and price would not change. This can be illustrated by graphing the short run total cost curve and the short run variable cost curve. The shape of the curves are identical. Each curve initially increases at a decreasing rate, reaches an inflection point, then increases at a decreasing rate. The only difference between the curves is that the SRVC curve begins from the origin while the SRTC curve originates on the y-axis. The distance of the origin of the SRTC above the origin represents the fixed cost - the vertical distance between the curves. This distance remains constant as the quantity produced, Q, increases. MC is the slope of the SRVC curve. A change in fixed cost would be reflected by a change in the vertical distance between the SRTC and SRVC curve. Any such change would have no effect on the shape of the SRVC curve and therefore its slope at any point - MC.

Externalities


Externalities are costs (or benefits) that are not borne by the parties to the economic transaction
Financial transaction
A financial transaction is an event or condition under the contract between a buyer and a seller to exchange an asset for payment. It involves a change in the status of the finances of two or more businesses or individuals.-History:...

. A producer may, for example, pollute
Pollution
Pollution is the introduction of contaminants into a natural environment that causes instability, disorder, harm or discomfort to the ecosystem i.e. physical systems or living organisms. Pollution can take the form of chemical substances or energy, such as noise, heat or light...

 the environment, and others may bear those costs. A consumer may consume a good which produces benefits for society, such as education; because the individual does not receive all of the benefits, he may consume less than efficiency would suggest. Alternatively, an individual may be a smoker or alcoholic and impose costs on others. In these cases, production or consumption of the good in question may differ from the optimum level.

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
Pollution
Pollution is the introduction of contaminants into a natural environment that causes instability, disorder, harm or discomfort to the ecosystem i.e. physical systems or living organisms. Pollution can take the form of chemical substances or energy, such as noise, heat or light...

 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.

In an equilibrium , state we see that markets creating negative externalities of production will overproduce that good. As a result, the socially optimal production level would be lower than that observed.

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 good
Public good
In economics, a public good is a good that is non-rival and non-excludable. Non-rivalry means that consumption of the good by one individual does not reduce availability of the good for consumption by others; and non-excludability means that no one can be effectively excluded from using the good...

s 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
Education
Education in its broadest, general sense is the means through which the aims and habits of a group of people lives on from one generation to the next. Generally, it occurs through any experience that has a formative effect on the way one thinks, feels, or acts...

. 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.

Social costs


Of great importance in the theory of marginal cost is the distinction between the marginal private and social costs. The marginal private cost shows the cost associated to the firm in question. It is the marginal private cost that is used by business decision makers in their profit maximization goals, and by individuals in their purchasing and consumption choices. Marginal social cost is similar to private cost in that it includes the cost functions of private enterprise but also that of society as a whole, including parties that have no direct association with the private costs of production. It incorporates all negative and positive externalities, of both production and consumption.

Hence, when deciding whether or how much to buy, buyers take account of the cost to society of their actions if private and social marginal cost coincide. The equality of price with social marginal cost, by aligning the interest of the buyer with the interest of the community as a whole is a necessary condition for economically efficient resource allocation.

See also

  • Cost
    Cost
    In production, research, retail, and accounting, a cost is the value of money that has been used up to produce something, and hence is not available for use anymore. In business, the cost may be one of acquisition, in which case the amount of money expended to acquire it is counted as cost. In this...

  • Cost curve
    Cost curve
    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 , and profit maximizing firms can use them to decide output quantities to...

  • Average cost
    Average cost
    In economics, average cost or unit cost is equal to total cost divided by the number of goods produced . It is also equal to the sum of average variable costs plus average fixed costs...

  • Economic surplus
    Economic surplus
    In mainstream economics, economic surplus refers to two related quantities. Consumer surplus or consumers' surplus is the monetary gain obtained by consumers because they are able to purchase a product for a price that is less than the highest price that they would be willing to pay...

  • Marginal concepts
    Marginal concepts
    In economics, marginal concepts are associated with a specific change in the quantity used of a good or service, as opposed to some notion of the over-all significance of that class of good or service, or of some total quantity thereof.- Marginality :...

  • Marginal revenue
    Marginal revenue
    In microeconomics, marginal revenue is the extra revenue that an additional unit of product will bring. It is the additional income from selling one more unit of a good; sometimes equal to price...

  • Marginal product of labor
    Marginal product of labor
    In economics, the marginal product of labor also known as MPL is the change in output that result from employing an added unit of labor. More generally, in defining marginal product, other inputs to production are held constant...

  • Externality
    Externality
    In economics, an externality is a cost or benefit, not transmitted through prices, incurred by a party who did not agree to the action causing the cost or benefit...

  • Merit good
    Merit good
    The concept of a merit good introduced in economics by Richard Musgrave is a commodity which is judged that an individual or society should have on the basis of some concept of need, rather than ability and willingness to pay...

    s
  • Cost-Volume-Profit Analysis
    Cost-Volume-Profit Analysis
    Coon-Volume-profit , in managerial economics is a form of cost accounting. It is a simplified model, useful for elementary instruction and for short-run decisions....

  • Break even analysis