# Average versus Marginal Costs

Average cost measures the cost per unit of output, and marginal cost is the additional cost of producing an additional unit of output.
Average cost is the cost per unit of output. The average fixed cost, average variable cost, and average total cost can be measured in the short run. Average fixed cost (AFC) is fixed cost (FC) divided by the quantity of output (Q).
$\text{AFC} = \frac{\text{FC}}{\text{Q}}$
Because fixed cost is constant across output, average fixed cost starts at a high level, quickly decreases, and goes toward zero as output rises.
Average variable cost (AVC) is variable cost (VC) divided by the quantity output (Q).
$\text{AVC} =\frac{\text{VC}}{\text{Q}}$
Average variable cost may fall initially as output rises, but then it begins to rise because of diminishing marginal returns. (In the example of Belva's Beauty Shop, Belva's average variable cost rises throughout the output levels.) Per-unit variable costs (AVC) become large when output is high.
Average total cost (ATC) is total cost (TC) divided by the quantity of output (Q).
$\text{ATC}=\frac{\text{TC}}{\text{Q}}$
Average total cost can also be calculated as the sum of average fixed cost and average variable cost.
$\text{ATC} = \text{AFC} + \text{AVC}$
An average total cost (ATC) curve is generally U-shaped. At low levels of output, the average total cost (ATC) and average variable cost (AVC) decrease. As output rises from four to eight styling sessions per day, the fixed cost is $100 and the variable cost increases from$80 to $100. This means that the average fixed cost (AFC) decreases by$12.50 (from $25 to$12.50), the average variable cost (AVC) decreases by $7.50 (from$20 to $12.50), and the average total cost (ATC) decreases by$20 (from $45 to$25). At a higher level of output, the average variable cost (AVC) continues to increase, but the increases in the output aren’t growing as fast, which indicates the beginning of diminishing marginal returns.

As output rises from 14 to 18 hairstyles per day, the fixed cost is still $100, and the variable cost increases from$200 to $300. At this point, average fixed cost (AFC) decreases by more than a dollar (from$7.14 to $5.55), but average total cost (ATC) increases by less than a dollar (from$21.43 to $22.22). This is the minimum area for average total costs, represented by the lowest point on the ATC curve on a graph. When output rises from 14 to 18 hairstyles per day, the fixed cost is still$100, and the variable cost increases from $200 to$300, but this results the average variable cost (AVC) increasing (from $14.29 to$16.67). As a result, the average total cost (ATC) increases from $21.43 to$22.22, reflecting the diminishing marginal returns because the increase in average variable cost (AVC) overshadows the decrease in average fixed cost (AFC).

### Average Costs for Belva's Beauty Shop

Quantity of Styling Sessions (Q) Fixed Cost (FC) Average Fixed Cost (AFC) Variable Cost (VC) Average Variable Cost (AVC) Total Cost ( $\text{FC}+\text{VC}$ ) Average Total Cost (ATC)
$0$
$\100.00$
$\0.00$
$\100.00$
$4$
$\100.00$
$\frac{\100}{4} = \25.00$
$\80.00$
$\frac{\80}{4} = \20.00$
$\180.00$
$\frac{\180}{4} = \45.00$
$8$
$\100.00$
$\frac{\100}{8} = \12.50$
$\100.00$
$\frac{\100}{8} = \12.50$
$\200.00$
$\frac{\200}{8} = \25.00$
$14$
$\100.00$
$\frac{\100}{14} = \7.14$
$\200.00$
$\frac{\200}{14} = \14.29$
$\300.00$
$\frac{\300}{14} = \21.43$
$16$
$\100.00$
$\frac{\100}{16} = \6.25$
$\242.86$
$\frac{\242.86}{16} = \15.18$
$\342.86$
$\frac{\342.86}{16} = \21.43$
$18$
$\100.00$
$\frac{\100}{18} = \5.56$
$\300.00$
$\frac{\300}{18} = \16.67$
$\400.00$
$\frac{\400}{18} = \22.22$
$20$
$\100.00$
$\frac{\100}{20} = \5.00$
$\400.00$
$\frac{\400}{20} = \20.00$
$\500.00$
$\frac{\500}{20} = \25.00$
$21$
$\100.00$
$\frac{\100}{21} = \4.76$
$\500.00$
$\frac{\500}{21} = \23.81$
$\600.00$
$\frac{\600}{21} = \28.57$

The average fixed cost (AFC) is the fixed cost divided by the number of styling sessions. The average variable cost (AVC) is the variable cost divided by the number of styling sessions. The average total cost (ATC) is the total cost divided by the number of styling sessions.

Although average costs provide some information on how costs change with output, they do not indicate how much it will cost a firm to increase its output by one unit. This is a critical understanding because, although average costs indicates what has happened historically on the average, due to decreasing marginal returns they tell us nothing about what the next unit of production will cost. Marginal cost (MC) is the additional cost that a firm incurs by producing an additional unit of output, which must be covered in order to remain operational in the short run. Marginal cost is calculated by dividing the change in total cost (TC) by the change in output (Q).
$\text{MC}=\frac{\Delta \text{TC}}{\Delta \text{Q}}$

### Marginal Cost for Belva's Beauty Shop

Quantity of Styling Sessions (Q) Change in Quantity (ΔQ) Fixed Cost (FC) Variable Cost (VC) Change in Variable Cost (ΔVC) Average Variable Cost (AVC) Total Cost (TC) Change in TC Average Total Cost (ATC) Marginal Cost (MC)
0 $100.00$0.00 $100.00 4 4$100.00 $80.00$80.00 $20.00$180.00 $80.00$45.00 $20.00 8 4$100.00 $100.00$20.00 $12.50$200.00 $20.00$25.00 $5.00 14 6$100.00 $200.00$100.00 $14.29$300.00 $100.00$21.43 $16.67 16 2$100.00 $242.86$42.86 $15.18$342.86 $42.86$21.43 $21.43 18 2$100.00 $300.00$57.14 $16.67$400.00 $57.14$22.22 $28.57 20 2$100.00 $400.00$100.00 $20.00$500.00 $100.00$25.00 $50.00 21 1$100.00 $500.00$100.00 $23.81$600.00 $100.00$28.57 $100.00 Marginal cost (MC) is the change in total cost divided by the change in quantity. Notice that marginal cost starts to rise dramatically as Belva's Beauty Shop increases the number of hairstyles done per day. This occurs because there is a fixed input (the size of the shop) in the short run, leading to diminishing marginal returns. The 21st hairstyle costs more because space gets tight when Belva adds additional stylists. The marginal cost curve for Belva's Beauty Shop can be shown on a graph. There is a special relationship between average and marginal product, as well as average and marginal cost. Specifically, whenever marginal cost (product) is below average cost (product), the average cost (product) is increasing. The opposite case also holds; average cost (product) increases when marginal cost (product) is higher than average cost (product). This is made clear by placing the marginal cost curve on the same diagram as the average variable and average total cost curves. The relationship between average and marginal costs is clarified by examining the average total cost and marginal cost curves. Up to an output of 16 styling sessions, the marginal cost curve lies below the average total cost curve, and average total cost is falling. When the last unit produced costs less than the average, it pulls the average down. Beyond 16 styling sessions, however, marginal cost is larger than average total cost, and average total cost is rising. When the last unit produced costs more than the average, it causes the average to rise. It is important to note that at an output level of 16 styling sessions, average total cost and marginal cost are equal to$21.43, and average total cost is at its minimum.