Marginal Costs

The extra production costs incurred are vital for decisions about changing output levels.

Marginal cost (MC) is the change in total cost associated with producing an additional unit of output.

Since TC = TFC + TVC, any change in total cost reflects changes in variable costs, as fixed costs do not depend on the output level.[1] Thus, producing an extra unit of output incurs marginal cost that equals either (a) the change in the total cost, or (b) the change in the total variable cost. Marginal cost for your firm is listed in column 8 of Table 3.

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 ---

Figure 4 shows how average variable cost (AVC) and marginal cost (MC) change as you process various amounts of earth. Why are these curves U-shaped? Recall that the marginal physical product of labor (MPPL) initially rose as you hired more labor but then fell when diminishing marginal returns were encountered. This means that the labor costs of additional output (its MC, in this case) initially decline, but diminishing returns ultimately cause marginal costs to rise as additional workers add less and less to total output. Similarly, the average physical product of labor (APPL) initially rose, but then declined as more workers were employed, causing the U shape of average variable cost curves. These relationships between production levels and costs will be detailed in a moment.

figure 4

The average variable cost (AVC) curve falls when marginal cost (MC) is below it, and rises when MC exceeds AVC. Average variable cost is at its minimum when AVC = MC. Both curves are U-shaped because, initially, gains from specialization push AVC and MC down. But eventually, as output is expanded, diminishing returns are encountered and the MC and AVC both rise.

### Graphically Summing Average Costs

In Figure 5 we tack an average fixed cost (AFC) curve onto a graph with typical U-shaped marginal cost (MC) and average variable cost (AVC) curves. Summing vertically the AVC and AFC associated with each output level yields the average total cost (ATC) curve shown. Notice that as output increases, differences between the AVC and ATC curves shrink. The ATC and AVC converge, because their vertical differences equal AFC, which falls as output rises. We now take a quick look at how costs relate to production.

figure 5

[1]   Proof: Dividing DTC= DTFC+ DTVC by a small change in output (Dq) reveals that

But output does not affect fixed costs, so DTFC/Dq = 0 and

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