# "Marginal cost is never equal to variable cost." Please explain why this is false.

Marginal cost will be equal to variable cost when the number of units produced is 1. Thus, the statement "marginal cost is never equal to variable cost" is false.

Almost all of the time marginal cost and variable cost are not equal. Marginal cost refers to the amount of money a business has to pay to produce more of something. Variable cost connects to the way in which the cost of production will change depending on how much, or how little, a thing is produced.

Pretend that the business in question is a lemonade stand. When the lemonade stand makes its first lemonade, the marginal cost and the variable cost will be equal. There is no additional product, which means there is no change of cost to record.

Of course, to make a profit and grow, the lemonade stand will have to produce additional cups of lemonade. Once the additional lemonade products come to be, the marginal cost and the variable cost will go in different directions. The marginal cost will have to account for how much money it takes to keep making more lemonade. The variable cost will have to measure the cost of the vacillating output.

As most businesses exist to produce more than one of something, it could seem rather insignificant that there is a point at which marginal cost and variable cost are the same. Nonetheless, when the first item is made, the two are equal, which is why the statement in the question is false.

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To understand why this statement is true for every situation after the first unit is produced, it is necessary to understand exactly what variable cost is. As the name implies, variable cost varies with the level of output produced. For instance, in a bakery, to produce one incremental unit of bread requires some additional flour, eggs and water. Thus, the total costs of these items will vary with each additional production of units, or loaves of bread.

Let’s say the unitary variable cost of these ingredients for the production of one loaf is \$1.00. If the entire bag of flour costs \$10 and each bag has enough flour to produce 20 loaves, then the flour component of each unitary cost of production is \$0.50 (\$10 divided by 20 loaves). The \$1.00 variable cost covers the cost of all of these ingredients together plus any other ingredient (salt, for example) required to produce one unit.

Variable cost does not include costs such as rental of the bakery facilities, as that is a fixed amount that will not change regardless of whether the bakery produces 10 loaves or 1,000 loaves. Variable costs or VC is derived by multiplying total output by the unitary cost of production.

The incremental cost is the cost of each incremental or additional unit. Essentially, it is the unitary cost of \$1.00 in the bakery example. Therefore, incremental cost equals total VC when the output is one unit.

To produce 1 unit, VC would be 1 x \$1.00 (from our example) = \$1.00, which is also the incremental cost.

At all levels above one unit, total VC is greater than incremental cost, as illustrated below.

To produce 10 units, VC would be 10 x \$1.00 (from our example) = \$10

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The marginal cost of production is calculated by dividing the change in the total cost by a one-unit change in the production output level. The calculation determines the cost of production for an additional unit of the good. Hence,

##### Marginal Cost = (Change in Costs) / (Change in Quantity)

Marginal costs are a function of the total cost of production, which includes fixed and variable costs. Fixed costs of production are constant, occur regularly, and do not change in the short-term with changes in production such as administration, overhead, and selling expenses.

Variable costs, however, tend to increase with expanded capacity, adding to marginal cost due to the law of diminishing marginal returns. The usual variable costs included in the calculation are labor and materials.

Marginal cost is usually less than the Variable cost because it only relates to the Variable costs incurred with production of one unit.

However, the only time when the Marginal cost and Variable cost will be equal is when the first unit is produced.

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The trick to understanding why the statement "marginal cost is never equal to variable cost" is false is to understand the relationship between the two. Variable cost refers to costs that change as the total level of output changes. Marginal cost refers to the additional cost incurred for producing each additional unit of the product. Therefore,

Marginal cost (nth unit) = Variable cost (n units) - Variable cost (n-1 units).

Thus, the marginal cost will always be less than the variable cost as long as n > 1. When the number of units produced is 1, the variable cost (n-1 units) will be 0. Thus, when n=1,

Marginal cost (1 unit) = variable cost (1 unit) - 0.

In this instance, marginal cost = variable cost.

Thus, the statement "marginal cost is never equal to variable cost" is false.

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Usually, this statement would be true.  Marginal cost refers to the cost of producing the next unit of output.  By contrast, variable costs are all the variable costs associated with all the output up to and including the last unit.  So the marginal cost will usually be smaller than the variable cost because it only refers to the variable costs associated with making the *last* unit.

However, there is one time when the two things will be equal.  That is for the *first* unit produced.  When you go from 0 units produced to 1 unit produced, the marginal cost of the 1st unit will be equal to the total variable costs.

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