Average Cost

Some definitions will enable us to examine costs more completely. Average total cost (ATC) is total cost incurred per unit of output, and is sometimes termed unit cost, or simplified to average cost.

Average costs equal total costs divided by output (TC/q).

Total costs are composed of fixed and variable costs, so average total cost (ATC) equals average fixed cost (AFC) plus average variable cost (AVC). [1]  After the cost data for excavating various amounts of earth have been collected, computing each type of average cost only requires dividing each by the output level.

Average fixed cost (AFC) is the fixed cost per unit of output, or (TFC/q).

Average variable cost (AVC) is the variable cost per unit, or (TVC/q).

Table 3 lists these costs for your sand-and-gravel operation. Let's explore all these averages in more detail to see how they are typically related to production.

Table 3  Average Total Costs, Average Fixed Costs, Average Variable Costs, and Marginal Cost

 (1)       Workers Per 8-hr Shift (L) (2) Tons of Sand and Gravel Removed Daily (q) (3)     Total Variable Cost (\$) (w´L) (TVC) (4)     Total Fixed Cost (\$) (TFC) (5)     Average Variable Cost (\$) (3)/(2) (AVC) (6)     Average Fixed Cost (\$) (4)/(2) (AFC) (7)     Average Total Cost (\$) (5)+(6) (ATC) (8)       Marginal Cost (\$) (D3)/(D2) (MC) 0 0 0 \$100 --- --- --- --- 1 10 50 100 5.00 10.00 15.00 5.00 2 22 100 100 4.54 4.55 9.09 4.17 3 36 150 100 4.17 2.78 6.95 3.57 4 52 200 100 3.85 1.92 5.77 3.13 5 70 250 100 3.57 1.43 5.00 2.78 6 86 300 100 3.49 1.16 4.65 3.13 7 100 350 100 3.50 1.00 4.50 3.57 8 112 400 100 3.57 0.89 4.46 4.17 9 122 450 100 3.69 0.82 4.51 5.00 10 130 500 100 3.85 0.77 4.62 6.25 11 137 550 100 4.01 0.73 4.74 7.14 12 143 600 100 4.20 0.70 4.90 8.33 13 148 650 100 4.39 0.68 5.07 10.00 14 152 700 100 4.60 0.66 5.26 12.50 15 155 750 100 4.84 0.65 5.49 16.67 16 157 800 100 5.10 0.64 5.74 25.00 17 158 850 100 5.38 0.63 6.01 50.00 18 158 900 100 5.69 0.63 6.32 --- 19 157 950 100 6.05 0.64 6.69 ---

### Average Fixed Costs

Just because total fixed costs do not vary with output does not make an AFC curve horizontal. AFC = TFC/q, where TFC is constant. Figure 3 shows how the AFC is related to the output of your operation, calculated in column 6 of Table 3. Total fixed costs are constant, so, as output increases, fixed costs per unit of output decline—a process that many managers describe as "spreading overhead" through high volume. [2]

### Average Variable Costs

Managers can control variable costs by changing the level of output. As output grows, the AVC initially tends to fall. But eventually, diminishing marginal returns will drive up average variable costs. Seeing why this occurs requires understanding a bit about marginal cost, which is the most important cost concept of all for business decision making.

[1]   Proof: Dividing both sides of TC= TFC+ TVC by output (q)

[2]   Notice that if we arbitrarily select any two points on the AFC curve (say, a and b), the rectangles formed by dropping horizontal and vertical lines to the axes have identical areas (\$100). (Since AFC = TFC/q, multiplication of AFC by q yields TFC: TFC/q´ q = TFC, which is constant.) Thus, the AFC curve is a rectangular hyperbola. Recall that unitary elastic demand curves are also rectangular hyperbolas.

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