Exam Focus

This review is primarily focused on the components of total cost. Be able to describe relationship between short-run costs diminishing returns to labor and capital, and output. You should know how total, and understand the long-run conditions marginal, and average product relate to the that lead to economies of scale.

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The short run is defined as a time period tor which quantities of some resources are fixed. A firm has chosen its production methods and, if it is a manufacturer, the machinery it will use to produce its products. In the long run, a firm can adjust its input quantities, production methods, and plant size.

So the technology of production is fixed in the short run and is a constraint on a firm's ability to it.crease production. Typically, economists treat labor and raw materials as variable in the short run, holding plant size, capital equipment, and technology constant. All of these factors become variable in the long run.

Short-run decisions, such as adjusting labor and raw materials inputs, are easier to reverse than long-run decisions, such as investing in new technology or capital assets. Capital that has been spent on a long-run project is typically a sunk cost which (as we will see in the Study Session on Corporate Finance) managers should not consider when making investment decisions.

' O.S VJ ; '"VC-nU'-- :.uk; cjijvlajfs mt veiatioiu; among total product of laboi> marginal pmiiucf •:>•' lufroi. ¡."'era«!.' product of labor, and describe

In what follows, we will examine output in the short run, allowing only the quantity of labor employed to vary.

The table in Figure I contains output information for a hypothetical maker of shirts, Sam's Shirts. The first column of the table lists different quantities of workers per day that can be employed. The second column lists the total number of shirts per day that Sam's can produce with different numbers of workers, holding plant and equipment constant. This total output of shirts is called the total product. The third column has the number of additional shirts per day from adding each successive worker. This is the marginal product of labor, the additional output from adding one more unit (in this case one worker-day) of labor. The fourth column lists the average number of shirts per worker that are produced for each quantity of workers. This is the average product of labor. Note that the units of total, marginal, and average product are units of the good produced per unit of the input under consideration, in this case, shirts per worker day.

Figure 1: Short-Run Output as a Function of Labor Employed

Workers Total Product

1

8

2

20

3

26

4

30

5

32

Workers Total Product

Marginal

Average

Product

Product

8

8

12

10

6

8.7

4

7.5

2

6.4

1

5.5

Panel (a) and panel (b) of Figure 2 show the total product curve and marginal product curve, respectively, for Sam s Shirts. The total and marginal product curves in Figure 2 have been "smoothed" to account for fractional worker days. The total product curve can be viewed as a production possibilities frontier. The area above the curve represents output that cannot be produced by the given number of workers. The area below the curve represents technologically inefficient production because more labor than necessary is being used to produce each level of output.

Note that the marginal product curve shown in panel (b) of Figure 2 initially increases, reaches a peak, and then begins to decline. This behavior is typical. The marginal product curve for an input typically shows increasing marginal returns initially, and decreasing marginal returns at some point. Decreasing marginal returns describes a situation where the marginal product of an input decreases as additional units of that input are employed.

Figure 2: Total Product and Marginal Product

(b) Marginal product (MP)

Labor (workers per day)

12

/

\

/'

i

k

H

Workers per day

Figure 3 shows the relation between the average product curve for Sam's Shirts and the marginal product curve. Note in Figure 3 that average product is at its maximum at the point where the marginal product curve intersects it from above. For Sam's Shirts, this intersection occurs between two and three workers per day. Note that for the second worker, MP is greater than AP, but with three workers, MP is less than AP. This relationship is not unique to Sam's Shirts. Typically, marginal product exceeds average product up to some input quantity where they are equal. Beyond that point, marginal product is less than average product.

Figure 3: Average Product and Marginal Product of Labor

LOS 1 7.c: Distinguish amone, total cosí (including both fixed cost and variable cost), marginal cost, and average cost., and explain the relations among the various cost curves.

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 cost, TC, is the sum of all costs associated with the generation of output. Total cost is made up of total fixed cost and total variable cost.

Total fixed cost, TFC, is the cost of fixed inputs, such as property, plant, and equipment, plus normal profit, i.e., the value of the entrepreneurial abilitv of the firm's owners or managers. Total fixed cost is independent of the level of the firm's output in the short run.

Total variable cost, TVC, is the cost of all variable production inputs. Total variable cost increases as output increases. The single biggest variable cost for most firms is the cost of labor (and raw materials for manufacturing firms).

total cost = total fixed cost + total variable cost

Figure 4 illustrates the components of total cost for Sam's Shirts at different output levels. We will assume that Sam's fixed cost is $20 per day to rent one sewing machine. This amount will not change regardless of the quantity of shirts produced. So, the TFC curve is a horizontal line at $20 per day.

For simplicity, assume that labor is the only variable cost, and that Sam pays his workers $20 per day. So total variable cost will increase by $20 as each additional worker is required to increase output. Notice in Figure 4 that the vertical distance between the TVC and the TC curves is total fixed cost. It is also important to note that both TVC andTC are increasing. This is because TVC increases as output increases.

Figure 4: Total Cost Curves

Cost per day

Cost per day

Notice that the TC and TVC' curves in Figure 4 increase at increasing rates. This can be explained through a discussion of the concept of marginal cost.

Marginal cost, MC, is the increase in total cost for one additional unit of output. Since the addition of each worker results in multiple additional shirts, we divide the change in total cost by the increase in output to get the marginal cost amounts in Figure 5. That is:

change in total cost ATC

change in output AQ

The relationships among TFC, TVC, MC, AFC, AVC, and ATC are shown for increasing amounts of labor and output in Figure 5.

Figure 5: Total, Marginal, and Average Costs for Sam's Shirts

MC

Output (Shtrts)

Labor (workers!day)

TFC (S/day)

TVC

TC

($/additional shirt)

AFC ($/shirt)

AVC

ATC

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 cost of fixed inputs; independent -----5.00

of output

TFC = Total fixed cost cost of fixed inputs; independent -----5.00

of output

TVC - Total variable cost cost oi variable inputs;

changes with output

iMC = Marginal cost change in total cost for one unit MC = ATC / AQ

increase in output

AVC = Average variable cost AVC = TVC / Q

ATC = Average total cost 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 eight to 20 shirts is $60 - $40 = $20. Since the change in output is 20 - 8 = 12 shirts, the marginal cost can be calculated as:

Average cost is the average cost per unit of output at a given level of output. Since there are three types of costs, there are three corresponding average costs. These are:

• Average fixed cost, AFC, total fixed cost per unit of output.

• Average variable cost, AVC, total variable cost per unit of output.

• Average total cost, ATC, total cost per unit of output.

The individual average costs are calculated by dividing the total costs at a given level of output, Q, by that level of output. Mathematically, we have:

TC TFC TVC

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 (ATC, AVC, and AFC) curves 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 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 and AVC curves is ecjual 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.

• ATC and AVC 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, since 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.

The relationship between product curves and cost curves is illustrated in Figure 7, where average and marginal product curves for a firm are presented in panel (a), and marginal 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 Lj is the labor required to produce Q,.

• As labor increases from Lj to L,, and output increases from Qt to Q2, AP continues to increase to a maximum at L2 and AVC continues to fall to its minimum at Q-,. Over this same production range, MP is declining and MC is rising.

• As labor increases beyond L2 and output increases beyond Q-,, MP and AP both decrease, and MC and AVC both increase.

Figure 7: Product and Cost Curves

Output pet-unit ol labor

Product (..urve.s

Output pet-unit ol labor

Product (..urve.s

Cos:

Labor

Qi

Output, total

LOS 17.d: Explain the firm's production function, its properties of diminishing returns and diminishing marginal product of capital, the relation between short-run and long-run costs, and how economies and diseconomies of scale affect long-run costs.

A firm's production function is the relationship between its inputs of capital and labor and the quantity of output it can produce. Figure 8 shows a possible production function for Sam's Shirts. Notice that as the firm adds more units of labor or capital, the resulting increase in output reaches a maximum and then starts to get smaller. This illustrates the fact that productive inputs exhibit diminishing returns.

Study Session 4

Cross-Reference to CFA Institute Assigned Reading #17 - Output and Costs Figure 8: Production Function for Sam's Shirts

Capital (sewing machines used)

Labor (hours/day)

1

2

3

4

5

6

40

6

9

12

14

16

17

48

8

12

16

20

23

25

56

11

15

20

24

27

30

6 4

13

18

23

27

31

34

80

15

20

25

30

34

37

88

16

21

27

32

36

39

1 lie law of diminishing returns states that at some point, as more and more of one resource (e.g., labor) is added to the production process, holding the quantitv of other inputs constant, the output continues to increase, but at a decreasing rare. For example, if an acre of corn needs to be picked, the addition of a second and third worker is highly productive. If vou already have 300 workers in the field, the additional output from adding the 301st worker is lower than that of the second worker.

I he marginal product nj capital is the increase in output from using one additional unit of capital, holding the quantitv of labor constant. Diminishing marginal product of capital refers to the fact that at a constant level of labor, output increases as capital is added, but at some point, the increase in output from adding one more unit of capital begins to decrease.

Short-Run and Long-Run Costs

Short-run cost curves apply to a plant of a given size. In the long run, everything is variable, including technology, plant size, and equipment. Long-run cost curves arc known as planning curves. There is often a trade-off between the size of the* firm and unit costs in the long run.

Three reasons unit cost may decline as output or plant size increase are:

1. Savings due to mass production.

2. Specialization oflabor and machinery.

3. Experience.

The downward sloping segment of the long-run average total cost curve presented in Figure 9 indicates that economies of scale are present. In this range increasing the scale (size) of the firm results in lower average unit costs. I'he upward sloping segment of this long-run average total cost curve indicates that diseconomies of scale are present when average unit costs rise as the scale of the business increases. The flat portion of the long-run average total costs curve in Figure 9 represents constant returns to scale. As shown, the firm's minimum efficient scale (the firm size that will minimize average unit costs) is one which will produce Q* units of output.

Figure 9: Long-Run Average Total Cost

Average Unit Costs economies of scale diseconomies of scale economies of scale diseconomies of scale

-1- Output

Q* = minimum efficient scale (firm size)

Diseconomies of scale ma}' result as the increasing bureaucracy of larger firms leads to inefficiency, as well as from problems of motivating a larger work force, greater barriers to innovation and entrepreneurial activity, and increased principal-agent problems.

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