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marginal cost : ウィキペディア英語版
marginal cost

In economics, marginal cost is the change in the total cost that arises when the quantity produced is incremented by one unit, that is, it is the cost of producing one more unit of a good. In general terms, marginal cost at each level of production includes any additional costs required to produce the next unit. For example, if producing additional vehicles requires building a new factory, the marginal cost of the ''extra'' vehicles includes the cost of the new factory. In practice, this analysis is segregated into short and long-run cases, so that, over the longest run, all costs become marginal. At each level of production and time period being considered, marginal costs include all costs that vary with the level of production, whereas other costs that do not vary with production are considered fixed.
The graph is plotted with Price, Cost and Revenue on the Y-axis and Quantity on the X-axis.
If the good being produced is infinitely divisible, the size of a marginal cost will change with volume; so a non-linear and non-proportional cost function includes the following:
* variable terms dependent on volume,
* constant terms independent on volume and occurring with the respective lot size,
* jump fix cost increase or decrease dependent on 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 differential definition of marginal cost for virtually all non-linear functions. This is as the definition 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 differentially.
If the cost function is differentiable joining, the marginal cost is the cost of the next unit produced referring to the basic volume.
: \text(MC) = \frac
If the cost function is not differentiable, the marginal cost can be expressed as follows.
: MC = \frac
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, the presence of negative or positive externalities, transaction costs, price discrimination 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.
:ATC=\frac
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.〔Silberberg & Suen, The Structure of Economics, A Mathematical Analysis 3rd ed. (McGraw-Hill 2001) at 181.〕 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 of the diminishing marginal returns. 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.
Marginal costs can also be expressed as the cost per unit of labor divided by the marginal product of labor.〔See http://ocw.mit.edu/courses/economics/14-01-principles-of-microeconomics-fall-2007/lecture-notes/14_01_lec13.pdf.〕
: MC = \frac
: \Delta VC =
: MC = \frac
Because \frac is the change in quantity of labor that affects a one unit change in output, this implies that this equals \frac.
where MPL is ratio of increase in the quantity produced per unit increase in labour i.e. ΔQ/ΔL.
Therefore, MC = \frac 〔Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on (Sept 2009 ).〕 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).〔Note also that AVC = VC/Q=wL/Q = w/(Q/L) OR w/APL

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