Marginal Cost

In economics and finance, marginal cost is the change in the total cost that arises when the quantity produced has an increment by unit. That is, it is the cost of producing one more unit of a good. [1] 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.

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 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.

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, 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.

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.[2] 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. 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. 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 labour.[3]

Because   is the change in quantity of labor that affects a one unit

change in output, this implies that this equals  .

Therefore   [4] 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).[5]

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 0.

How to Calculate Marginal Cost

Marginal cost is a figure calculated from production costs for a short period of time. It takes into account the output and the total cost. To properly plot marginal cost, you will need to chart the output and costs on a spreadsheet and then use a formula to calculate the marginal cost. Follow these steps to calculate marginal cost.

Part 1 of 4: Preparation

1.

1Gather the data related to your production for a given period.

You will need inventory statistics like total output. You will also need the fixed costs, variable costs and total costs for a given quantity production (output).

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Part 2 of 4: Chart Production

1.

1Chart the total cost and output on a spreadsheet. Consider the following columns in your spreadsheet:

Use the header "Output" in your first column. You can fill the rows with single unit increases in output or larger jumps. For instance, it may be numbered 1,2,3, etc. or it can be numbered in larger increments, such as 1000, 2000, 3000, etc.

Consider whether you want to simply add "Total Cost" or add 3 columns for "Fixed Cost," "Variable Cost" and "Total Cost." If you do not want to include the numbers for fixed and variable cost, make sure both these figures are calculated in the total cost.

Type the correct "Total Cost" figures for each rise in output. You will be able to figure out marginal cost for each increase in output based on these figures.

2.

2Save your spreadsheet frequently while entering data.

Part 3 of 4: Calculate Marginal Cost

1.

1Add a column next to Total Cost labeled "Marginal Cost." You will figure out the marginal cost for each level of output separately.

Keep in mind that marginal cost is based on the changes in cost as you produce more. The figures will plot change in output and cost throughout your chart.

2.

2Write down the formula. To calculate marginal cost, you will need to take the change in total cost divided by the change in total output.

3.

3Take the first 2 rows of your chart. Subtract the total cost of the first row (after headings) by the total cost of the second row. This is your change in total cost.

4.

4Subtract the total output of the first row by the total output of the second row.This is your change in total output.

5.

5Enter the data into your formula.

For example, if your first row of data shows total output of 1,000 for a cost of $8,000 and the second row of data shows a total output of 2,000 for a cost of $12,000, your formula would be marginal cost=$12,000-$8,000)/(2,000-1,000).

6.

6Simplify to solve the problem.

In our example, we simplify to get marginal cost=$4,000/1,000 or marginal cost=$4.

Part 4 of 4: Chart Marginal Cost

1.

1Enter your marginal cost into the row next to your second set of data. The first row of data will not have a marginal cost, because marginal cost cannot be calculated based on an output of zero.

2.

2Continue to calculate the marginal cost between each row of data and the set above it.

If you are using Microsoft Excel, you can include a formula to automatically calculate the data. Enter an equals sign in the blank box under your marginal cost column, then replace the data numbers with cell numbers. For example, "=(F4-F3)/(G4-G3)." Then click "Enter." Drag the formula down the column to reproduce it in each row.