### Fixed, Variable, Marginal, and Average Costs: Examples.

For example, in a production environment fixed costs, such as those for factory floor space and equipment, remain the same even though production quantity, number of employees, and level ofwork-in-processmay vary.Labor costs are classified as a variable cost because they depend on the number of employees in the factory. Thus fixed costs are level or constant regardless of output or activity, and variable costs are changing and related to the level of output or activity.

As another example, many universities charge full-time students a fixed cost for 12 to 18 hours and a cost per credit hour for each credit hour over 18.Thus for full-time students who are taking an overload (> 18 hours), there is a variable cost that depends on the level of activity.

This example can also be used to distinguish between marginal and average costs. A marginal cost is the cost of one more unit. This will depend on how many credit hours the student is taking. If currently enrolled for 12 to 17 hours, adding one more is free. The marginal cost of an aditional credit hour is $0.However, if the student is taking 18 or more . ours, then the marginal cost equals the variable cost of one more hour.

To illustrate average costs, the fixed and variable costs need to be specified. Suppose the cost of 12 to 18 hours is $1800 per term and overload credits are $120/hour.If a student takes 12 hours, the average cost is $1800/12 = $150 per credit hour. If the student were to take 18 hours, the average cost decreases to $1800/18 = $100 per credit hour. If the student takes 21 hours, the average cost is $102.86 per credit hour [$1800 + (3 x $120) /21].

Average cost is thus calculated by dividing the total cost for all units by the total number of units. Decision makers use average cost to attain an overall cost picture of the investment on a per unit basis.

Marginal cost is used to decidew~~therthe additional unit should bemade, purchased, or enrolledin.For the full-time'studentatourexampleuniversity,themarginalcost of another credit is $0 or $120 depending on how many credits the student has already signed up for.

*EXAMPLE 1*An entrepreneur named DK was considering the money-making potential of chartering a bus to take people from his hometown to an event in a larger city. DK planned to provide transportation, tickets to the event,andrefreshmentsonthe bus forhis customers.He gathereddata andcategorized the predicted expenses as either fixed or variable.

Develop an expression of DK's total fixed and total variable costs for chartering this trip.

**SOLUTION**DK's fixed costs will be incurred regardless of howmany people sign up for the trip (even if only one person signs up!). These costs include bus rental, gas and fuel expense, apd the cost to hire a driver:

**Total fixed costs = 80 + 75 + 20 + 50 = $225**

DK's variable costs depend on how many people sign up for the charter, which is the level of activity.Thus for event tickets and refreshments, we would write

**Total variable costs = 12.50 + 7.50 = $20 per person.**

From Example 1 we see how it is possible to calculate total fixed and total variable costs. Furthennore, these values can be combined into a single total cost equation as follows:

**Total cost =Total fixed cost + Total variable cost (2-1)**

The relationship between total cost and fixedand variable costSare shownin Figure 2-1.

The fixed-costportion of $3000 is the same across the entire range of the output variable x.

Often, the variable costs are linear (y equals a constant times x); however, the variable costs can be nonlinear. For example, employees are often paid at 150%of their hourly rate for overtime hours, so that production levels requiring overtime have higher variable costs.

**FIGURE 2-1**Fixed, variable, and total costs.

Total cost in Figure2-1 is a fixed cost of $3000 plus a variable cost of $200 per unit for straight-time production of up to 10 units and $300 per unit for overtime production of up to 5 more units.

Figure 2-1 can also be used to illustrate marginal and average costs. At a volume of 5 units the marginal cost is $200 per unit, while at a volume of 12units the marginal cost is $300 per unit. The respective average costs are $800 per unit, or (3000 + 200 x 5)/5, and $467 per unit, or (3000 + 200 x 10 + 300 x 2)/12.

**EXAMPLE 2**In Example 1, DK develop~dap overall total cost equation for his business expenses.Now he

wants to evaluate the potential to make money from this chartered bus trip.

**SOLlJTION**

We use Equation 2-1 to findDK's total cost equation:

Using this relationship, DK can calculate the total cost for any number of people - up to the capacity of the bus. What he lacks is a revenue equatiQnto offset his costs. DK's total revenue from this trip can.be expressed as:

DK believes that he could attract 30 people at a charter ticket price of $35. Thus

So, if 30 people take the charter, DKwill net acprofit of $225. This somewhat simplastic.analysis ignores the value of DK's time-he would have to "pay himself" out of his $225 profit.

InExamples 1 and 2 DKdeveloped totalcost andtotal revenueequations to describe the charter bus proposal. These equations can be used to create what is called aprofit-loss breakeven chart (see Figure 2-2).Both the costs and revenuesassociatedwith various levels of output (activity) are placed on the same set of x-y axes. This allows one to illustrate a breakevenpoint (in terms of costs and revenue) and regions of profit and loss for some business activity.These terms can be defined as follows.

*The level of business activity at which the total costs to provide the product, good, or service are equal to the revenue (or savings) generated by providing the service. This is the level at which one "just breaks even."*

**Breakeven point:****The output levelof the variablex greater than the breakevenpoint,where total revenue is greater than total costs.**

*Profit region:**The output level of the variable x less than the breakeven point, where total costs are greater than total revenue. .*

**Loss region:**Notice in Figure 2-2 that the breakeven point for the number of persons on the charter trip is 15 people. For more than 15 people, DK will make a profit. If fewer than 15 sign up

**FIGURE 2-2**Profit-loss breakevenchart for Examples 1 and 2.

there will be a net loss. At the breakeven level the total cost to provide the charter equals the

revenue received fromthe 15passengers.Wecan solve for the breakevenpoint by settingthe

total costs and total revenue expressions equal to each other and solving for the unknown

value of x. From Examples 2-1 and 2-2:

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