Figure 112

of units. In other words, the relationship between total variable cost (VC), cost per unit of output (v), and total quantity of output (Q) can be written simply as:

Total variable cost = Total quantity of output X Cost per unit of output

For example, suppose variable costs (v) are $2 per unit. If total output (Q) is 1,000 units, what will total variable costs (VC) be?

Similarly, if Q is 5,000 units, then VC will be 5,000 X $2 = $10,000. Figure 11.2 illustrates the relationship between output level and variable costs in this case. In Figure 11.2, notice that increasing output by one unit results in variable costs rising by $2, so "the rise over the run" (the slope of the line) is given by $2/1 = $2.

Variable Costs

The Blume Corporation is a manufacturer of pencils. It has received an order for 5,000 pencils, and the company has to decide whether or not to accept the order. From recent experience, the

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358 PART FOUR Capital Budgeting company knows that each pencil requires 5 cents in raw materials and 50 cents in direct labor costs. These variable costs are expected to continue to apply in the future. What will Blume's total variable costs be if it accepts the order?

In this case, the cost per unit is 50 cents in labor plus 5 cents in material for a total of 55 cents per unit. At 5,000 units of output, we have:

Therefore, total variable costs will be $2,750.

fixed costs

Costs that do not change when the quantity of output changes during a particular time period.

Fixed Costs Fixed costs, by definition, do not change during a specified time period. So, unlike variable costs, they do not depend on the amount of goods or services produced during a period (at least within some range of production). For example, the lease payment on a production facility and the company president's salary are fixed costs, at least over some period.

Naturally, fixed costs are not fixed forever. They are only fixed during some particular time, say, a quarter or a year. Beyond that time, leases can be terminated and executives "retired." More to the point, any fixed cost can be modified or eliminated given enough time; so, in the long run, all costs are variable.

Notice that during the time that a cost is fixed, that cost is effectively a sunk cost because we are going to have to pay it no matter what.

Total Costs Total costs (TC) for a given level of output are the sum of variable costs (VC) and fixed costs (FC):

So, for example, if we have variable costs of $3 per unit and fixed costs of $8,000 per year, our total cost is:

If we produce 6,000 units, our total production cost will be $3 X 6,000 + 8,000 = $26,000. At other production levels, we have:

Quantity Produced

Total Variable Costs

Fixed Costs

Total Costs

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