CFA® Program Curriculum, Volume 2, page 109 To increase output in the short run, firms must use more labor, which increases cost. The relationship between output and cost may be explained in terms of three cost concepts:
(1) total cost, (2) marginal cost, and (3) average cost.
Total fixed cost (TFC) is the cost of inputs that do not vary with the quantity of output and cannot be avoided over the period of analysis. Examples of fixed costs are property, plant, and equipment; normal profit; fixed interest costs on debt financing; and wages of management and finance employees who are not directly involved in the production of the firm’s product. Note that some of these costs will remain constant over some range of output but will increase if output is increased beyond some quantity (e.g., administrative salaries and utilities). These costs can be referred to as quasi-fixed costs. Because fixed costs must be paid (at least over the near term) even when demand for the firm’s product declines, they can result in significant losses during economic downturns or when industry competition is especially aggressive.
Total variable cost (TVC) is the cost of all inputs that vary with output over the period of analysis. The largest variable costs for most firms are wages, raw materials, or both.
Variable costs increase with greater output and can be reduced if a decrease in demand leads to a decrease in production.
Total cost (TC) is the sum of all costs (fixed or variable, explicit and implicit) of producing a specific level of output.
Once we determine total costs for various levels of output, we can calculate marginal costs (MCs) as the addition to total cost of producing one more unit. Given output levels that are several units of output apart, dividing the difference in total cost by the number of units will provide a measure of marginal cost per unit.
. change in total cost ATC
marginal cost = ---;--- , or MG = ---change in output AQ
average total costs (ATC) = total costs / total product average fixed costs (AFC) = total fixed costs / total product average variable costs (AVC) = total variable costs / total product
Figure 4 illustrates the components of total cost for Sam’s Shirts at various output levels.
Sam’s total fixed cost is $20 per day to rent one sewing machine. Labor is Sam’s only variable cost, and the wage rate is $20 per day.
Figure 4: Total Cost Curves
Cost per day
TC TVC
___________ __________ __________ _______ OutputTFC
0 10 20 30 (shirts Per da^
We can apply much of what we have learned so far to interpret the graph in Figure 4.
Total fixed costs do not change with output, and the vertical distance between TVC and TC is equal to TFC. As the variable cost per worker is $20, examining the points plotted on either the TC or the TVC curve, we can see the increase in output associated with each additional worker.
Just as our example of a production function was drawn to illustrate first increasing and
Study Session 4
Figure 5: Total, Marginal, and Average Costs for Sam’s Shirts
Output
(shirts) Labor
(workers!day) TFC
($/day) TVC TC M C
($/additional shirt)
($/shirt) AVC ATCAFC
0 0 20 0 20
----2.50----
8 1 20 20 40
-— 1.67-— 2.50 2.50 5.00
20 2 20 40 60
-— 3.33-— 1.00 2.00 3.00
26 3 20 60 80
----5.00--- 0.77 2.31 3.08
30 4 20 80 100
— 10.00---- 0.67 2.67 3.33
32 5 20 100 120 0.63 3.13 3.75
TFC = Total fixed cost TVC = Total variable cost TC = Total cost MC = Marginal cost
cost of fixed inputs; independent of output
cost of variable inputs;
changes with output
TC = TFC + TVC change in total cost for one unit MC = ATC / A Q increase in output
AFC = Average fixed cost AVC = Average variable cost ATC = Average total cost
AFC = TFC / Q AVC = TVC / Q ATC = AFC + AVC
Example: Marginal cost
Using the information for Sam’s Shirts presented in Figure 5, calculate the marginal cost per shirt when output increases from 8 to 20 shirts per day.
Answer:
In Figure 5, we see that the change in TC when output increases from 8 to 20 shirts is
$60 - $40 = $20. Because the change in output is 20 - 8 = 12 shirts, the marginal cost can be calculated as:
MC = $20 / 12 shirts = $1.67 per shirt
Average costs at the various output levels for Sam’s have been calculated and tabulated in Figure 5. The marginal cost (MC) and average cost curves (ATC, AVC, and AFC) for Sam’s Shirts are shown in Figure 6.
Figure 6: Average and Marginal Costs
Shirts per day
Important relationships among the marginal and average cost curves illustrated in Figure 6 are:
• AFC slopes downward. This is because fixed costs are constant but are distributed over a larger and larger number of products as output quantity increases.
• The vertical distance between the ATC andAVC curves is equal to AFC. This is indicated by the arrows marked x at an output of 20 shirts per day.
• MC declines initially, then increases. At low output quantities, efficiencies are realized from the specialization of labor. However, as more and more labor is added, marginal cost increases. This is due to diminishing returns, which means that at some point, each added worker contributes less to total output than the previously added worker.
• MC intersects AVC and ATC at their minimum points. The intersection comes from below, which implies that when MC is less than ATC or AVC, respectively, ATC or AVC are decreasing. This also implies that when MC exceeds ATC or AVC, respectively, ATC or AVC are increasing. The MC curve is considered to have a J-shape due to the declining MC over lower production quantities and because the minimum points of the ATC and the AVC curves are not the same.
• ATC andAVC are U-shaped. AVC decreases initially, but as output increases, the effect of diminishing returns sets in and AVC eventually slopes upward, giving the curve its U shape. However, because fixed costs are spread out over a larger and larger quantity of output, AFC decreases as output increases, and eventually flattens out. ATC gets its U shape because as output increases we are adding a curve that goes from downward sloping to flat (AFC) to a U-shaped curve (AVC), which results in a U-shaped ATC curve. Remember, ATC = AVC + AFC.
• Minimum point on the ATC curve represents the lowest cost per unit, but it is not necessarily the profit-maximizing point. It means the firm is maximizing profit per
Study Session 4
and average cost curves are presented in Panel (b). Figure 7 illustrates the following important links between a firm’s product curves (technology) and its cost curves.
• Over the initial increase in labor from zero to Lj in Panel (a), MP and AP increase and MP reaches its maximum. Over the corresponding output range in Panel (b), MC and AVC decrease to output quantity Qj where MC is at a minimum. Note that Ll is the labor required to produce Qr
• As labor increases from Zj to L2 and output increases from Qj to Q2, AP continues to increase to a maximum at Lv and AVC continues to fall to its minimum at Q2.
Over this same production range, MP is declining and MC is rising.
• As labor increases beyond L2 and output increases beyond Q2, MP and AP both decrease, and MC and AVC both increase.
Figure 7: Product and Cost Curves
(a) Marginal and Average Output per Product Curves unit of labor
/ > k ' V
^ M P
M P t , M C I A P t, A V C t
M P t . M C t A P t , A V C t
M P * , M C t A P t , A V C t
L i C
(b) Cost Curves Cost
--- Output, total
Qi Q2