Module 8: Cost Curves

 THE POLICY QUESTION

SHOULD THE FEDERAL GOVERNMENT PROMOTE THE DOMESTIC PRODUCTION OF STREETCARS?

In recent years, streetcars have enjoyed a bit of a renaissance in the United States. Streetcars are electric-powered public vehicles that ride on rails embedded into normal city streets and comingle with traffic. Once common in the United States and still common in many European cities, streetcars all but disappeared from US streets in the second half of the twentieth century. Portland, Oregon, is one city that revived the streetcar and subsequently expanded its system.

After initially buying streetcars from the German company Siemens, Portland’s transit authority and government, pushed by the federal government, which funds a large portion of urban transit projects, decided to contract with a local firm, Oregon Iron Works, to produce the streetcars locally. Oregon Iron Works had no experience in manufacturing streetcars but created a subsidiary firm to do so called United Streetcar. Other US cities that were introducing streetcars, such as Washington, DC, and Tucson, Arizona, contracted with Oregon Iron Works for their cars as well. In the end, the firm faced severe delays and cost overruns and eventually got very behind on its scheduled delivery. In addition, the expected boom in streetcars slowed considerably with the recession of 2008 and changing municipal priorities. In 2014, United Streetcar ceased production and laid off its workers.

EXPLORING THE POLICY QUESTION

Is the story of United Streetcar an example of a misguided effort to steer business domestically? Would it have succeeded if the market for streetcars in the United States had not dried up? To answer these questions, we need to think about the cost structure of the industry and whether there are aspects of it that would support the decision to start manufacturing streetcars domestically. Cost curves—the subject of this chapter—are critical tools for analyzing a company’s cost structure.

LEARNING OBJECTIVES

8.1 Short-Run Cost Curves

Learning Objective 8.1: Derive the seven short-run cost curves from the total cost function.

8.2 Long-Run Cost Curves

Learning Objective 8.2: Derive the three long-run cost curves from the total cost function.

8.3 Short-Run versus Long-Run Costs: The Advantage of Flexibility

Learning Objective 8.3: Explain why long-run costs are always as low as or lower than short-run costs and how more flexibility in choosing inputs is always better than less.

8.4 Multiproduct Firms, Learning Curves, and Learning by Doing

Learning Objective 8.4: Explain how making more than one product, learning over time, and learning by producing can lower costs.

8.5 Policy Example
Should the Federal Government Promote Domestic Production of Streetcars?

Learning Objective 8.5: Use a cost analysis to explain why building streetcars domestically in the United States is or is not a good policy.

8.1 SHORT-RUN COST CURVES

Learning Objective 8.1: Derive the seven short-run cost curves from the total cost function.

A cost curve represents the relationship between output and the different cost measures involved in producing the output. Cost curves are visual descriptions of the various costs of production. In order to maximize profits, firms need to know how costs vary with output, so cost curves are vital to the profit maximization decisions of firms.

There are two categories of cost curves: short run and long run. In this section, we focus on short-run cost curves.

The Seven Short-Run Cost Measures

The short run, as we learned in the previous chapter, is a time period short enough that some inputs are fixed while others are variable. There are seven cost curves in the short run: fixed cost, variable cost, total cost, average fixed cost, average variable cost, average total cost, and marginal cost.

The fixed cost ($FC$) of production is the cost of production that does not vary with output level. The fixed cost is the cost of the fixed inputs in production, such as the cost of a machine (capital) that costs the same to operate no matter how much production is happening. An example of such a machine is a conveyor belt in a factory that moves a streetcar chassis through various stages of an assembly line. The belt is either on or off, but the cost of running it does not change depending on how many streetcars it carries at any point in time.

Note that the fixed cost of a piece of capital equipment that the company owns includes the opportunity cost as well. In our example, the fixed cost includes the actual costs of running the conveyer belt, such as power and maintenance, as well as the opportunity cost of using it for the firm’s own production rather than renting it out to another company.

The variable cost ($VC$) of production is the cost of production that varies with output level. This is the cost of the variable inputs in production—for example, the cost of the workers that assemble the electronic devices along a conveyor belt. The number of workers might depend on how many devices the factory is trying to produce in a day. If its production target increases, it uses more labor. Thus the hourly wages it pays for these workers are a variable cost. Variable cost generally increases with the amount of output produced.

Like fixed cost of production, there is an opportunity cost associated with variable cost of production. In this case, the next best use of these workers is to go to another firm that will employ them. Thus the market wage for workers represents their opportunity cost, and as such, the wage cost of employing them is equivalent to their opportunity cost.

The total cost ($C$) of production is the sum of fixed and variable costs of production:

$C=FC+VC$

There are three short-run average cost measures: average variable cost, average fixed cost, and average total cost.

Average variable cost ($AVC$) is the variable cost per unit of output. Mathematically, it is simply the variable cost divided by the output:

$AVC=VC/Q$

Note that since variable cost generally increases with the amount of output produced, the average variable cost can increase or decrease as output increases.

Average fixed cost ($AFC$) is the fixed cost per unit of output. Mathematically, it is simply the fixed cost divided by the output:

$AFC=FC/Q$

Because fixed cost does not change with the amount of output produced, the average fixed cost always decreases as output increases.

Average total cost ($AC$), or simply average cost, of production is total cost per unit of output. This is the same as the sum of the average fixed cost and the average variable cost:

$AC=AC/Q=AFC+AVC$

Because it is the sum of the average fixed cost, which is always declining with output, and the average variable cost, which may increase or decrease with output, the average total cost may increase or decrease with output.

Marginal cost ($MC$) is the additional cost incurred from the production of one more unit of output. Thus marginal cost is

$MC=\frac{\Delta C}{\Delta Q}$.

The only part of total cost that increases with an additional unit of output is the variable cost, so we can re-write the marginal cost as

$MC=\frac{\Delta VC}{\Delta Q}$.

Calculus

The marginal cost is the rate of change of the total cost as output increases, or the slope of the total cost function, $C\left(Q\right)$. To find this, we need to simply take the derivative of the total cost function:

$MC\left(Q\right)=\frac{dC\left(Q\right)}{dQ}$

Since $C\left(Q\right)=FC+VC\left(Q\right)$, we can rewrite this derivative as $MC\left(Q\right)=\frac{dFC}{dQ}+\frac{dVC\left(Q\right)}{dQ}$.

$FC$ is a constant, so $\frac{dFC}{dQ}=0$. Thus $MC\left(Q\right)=\frac{dVC\left(q\right)}{dQ}$.

Since fixed cost does not change as output increases, marginal cost depends only on the variable cost.

ixed Cost, Variable Cost, and Total Cost Curves

Table 8.1.1 summarizes a firm’s daily short-run costs. The firm has a fixed cost of $50 per day of production. This cost is incurred whether the firm produces or not, as we can see by the fact that $50 is still a cost when output is zero. The firm’s fixed cost of $50 does not change with the amount of output produced. The data in the first two columns of table 8.1.1 allow us to draw the firm’s fixed cost curve. It is a horizontal line at $50, as shown in figure 8.1.1.

Table 8.1.1 An example of the seven short-run cost measures, organized by total cost per unit of output.
Output (variable Q)	Fixed cost (variable FC)	Variable cost (variable VC)	Total cost (variable C)	Marginal cost (variable MC)	Average fixed cost (variable AFC)	Average variable cost (variable AVC)	Average cost (variable AC)
When Output(Q) equals 0…	FC=50	VC=0	C=50	MC=0	AFC=0	AVC=0	AC=0
When Output(Q) equals 1…	FC=50	VC=40	C=90	MC=40	AFC=50.0	AVC=40.0	AC=90.0
When Output(Q) equals 2…	FC=50	VC=70	C=120	MC=30	AFC=25.0	AVC=35.0	AC=60.0
When Output(Q) equals 3…	FC=50	VC=90	C=140	MC=20	AFC=16.7	AVC=30.0	AC=46.7
When Output(Q) equals 4…	FC=50	VC=100	C=150	MC=10	AFC=12.5	AVC=25.0	AC=37.5
When Output(Q) equals 5…	FC=50	VC=120	C=170	MC=20	AFC=10.0	AVC=24.0	AC=34.0
When Output(Q) equals 6…	FC=50	VC=150	C=200	MC=30	AFC=8.3	AVC=25.0	AC=33.3
When Output(Q) equals 7…	FC=50	VC=190	C=240	MC=40	AFC=7.1	AVC=27.1	AC=34.3
When Output(Q) equals 8…	FC=50	VC=240	C=290	MC=50	AFC=6.3	AVC=30.0	AC=36.3
When Output(Q) equals 9…	FC=50	VC=300	C=350	MC=60	AFC=5.6	AVC=33.3	AC=38.9
When Output(Q) equals 10…	FC=50	VC=370	C=420	MC=70	AFC=5.0	AVC=37.0	AC=42.0

Table 8.1.1 An example of the seven short-run cost measures

Output	Fixed cost	Variable cost	Total cost	Marginal cost	Average fixed cost	Average variable cost	Average cost
$Q$	$FC$	$VC$	$C$	$MC$	$AFC$	$AVC$	$AC$
0	50	0	50	–	–	–	–
1	50	40	90	40	50.0	40.0	90.0
2	50	70	120	30	25.0	35.0	60.0
3	50	90	140	20	16.7	30.0	46.7
4	50	100	150	10	12.5	25.0	37.5
5	50	120	170	20	10.0	24.0	34.0
6	50	150	200	30	8.3	25.0	33.3
7	50	190	240	40	7.1	27.1	34.3
8	50	240	290	50	6.3	30.0	36.3
9	50	300	350	60	5.6	33.3	38.9
10	50	370	420	70	5.0	37.0	42.0

Figure 8.1.1 Three short-run cost curves: fixed, variable, and total costs

Figure 8.1.1 also shows variable and total cost curves plotted from data in table 8.1.1. The variable cost increases with output because extra output requires extra variable inputs. As we can see in the graph, the variable cost curve rises as output, $Q$, increases.

The short-run variable cost curve is determined by and matches the shape of the short-run production function, which we studied in chapter 6. The short-run production function is the same as the total product of labor curve when labor is the variable input in the short run, which we always assume it is. To go from the production function to the variable cost curve requires knowing the price of labor. Let’s assume a constant price of labor, say $10 an hour.

Figure 8.1.2 presents a typical short-run production function, which leads to the shape of the variable cost curve in figure 8.1.1. The production function exhibits increasing marginal returns to labor initially: as the labor input is increased from zero, the output increases at an increasing rate. Eventually, however, the addition of extra hours of labor leads to additional output at a decreasing rate. This happens as we increase labor input from ten hours of labor.

Figure 8.1.2 The total product of labor curve

If we multiply the amount of labor at every level of output in figure 8.1.2 by the wage rate of $10 per hour, we get the variable cost curve from figure 8.1.1.

Marginal, Average Fixed, Average Variable, and Average Total Cost Curves

Figure 8.1.3 presents the four remaining short-run cost curves: marginal cost ($MC$), average fixed cost ($AFC$), average variable cost ($AVC$), and average total cost ($AC$).

Figure 8.1.3 Short-run marginal cost, average fixed cost, average variable cost, and average total cost curves

The marginal cost, average variable cost, and average total cost curves are derived from the total cost curve.

From figure 8.1.3, we can see that the marginal cost curve crosses both the average variable cost curve and the average fixed cost curve at their minimum points. This is not random. Since the marginal cost indicates the extra cost incurred from the production of the next unit of output, if this cost is lower than the average, it must be bringing the average down. If this cost is higher than the average, it must pull the average up. Think of your own grade point average: if your average this term is higher than your overall average, your overall average will go up. If your average this term is lower than your overall average, your overall average will go down.

Calculus

1. If the total cost curve of a firm is $C\left(Q\right)=25+10Q^2$ 
   1. What is the marginal cost curve?
   2. What is marginal cost at $Q=125$?

8.2 LONG-RUN COST CURVES

Learning Objective 8.2: Derive the three long-run cost curves from the total cost function.

As we learned in previous chapters, in the long run, all inputs are variable, and there are no fixed costs. In this section, we look at the three long-run cost curves—total cost, average cost, and marginal cost—and how to derive them.

Long-Run Total Cost Curve

To determine the long-run total cost (LRTC) for a firm, we must think about the cost minimization problem introduced in chapter 7. Remember that the cost minimization problem answers the question, What is the most cost-effective way to produce a given amount of output? The total cost curve represents the cost associated with every possible level of output, so if we figure out the cost-minimizing choice of inputs for every possible level of output, we can determine the cost of producing each level of output.

When we do this exercise, we are looking for the expansion path of the firm. Recall from chapter 7 that the expansion path is the combination of inputs that minimize costs for every level of output, and it can be graphed as a curve. Figure 8.2.1 shows the expansion path for a firm that manufactures tablet computers.

Figure 8.2.1 Expansion path

Each point on the expansion path is the solution to the cost minimization problem for that particular output. Recall from chapter 7 that $r$ is the rental rate or price of capital and $w$ is the wage rate or price of labor. Consider point X: here the output quantity is set at ten million, and the tangency of the isocost and isoquant at this point establishes the optimal combination of the inputs. To go from this point to the cost, we have only to know the combined cost of the inputs. Fortunately, the isocost line tells us exactly that; the total cost here is $C_1$. Now consider point Y, where the output quantity has increased to twenty million. With this, the new production level is associated with a new isocost curve, with total cost at $C_2$. Finally, point Z indicates that for an output quantity of thirty million, the total cost is $C_3$.

From the expansion path, we can draw the total cost curve. We have three points already, X, Y, and Z. Point X describes a quantity of ten million tablets and a total cost of $C_1$. Point Y describes a quantity of twenty million tablets and a total cost of $C_2$. Point Z describes a quantity of thirty million tablets and a total cost of $C_3$. These three cost-quantity pairs are three points on the long-run total cost curve illustrated in figure 8.2.2.

Figure 8.2.2 The long-run total cost curve

Remember from chapter 7 that the total cost is the sum of the input costs, $LRTC=wL+rK$. As we expand output, we must use more inputs, and the increase in labor and capital results in increasing overall cost of production.

A firm’s long-run average cost (LRAC) is the cost per unit of output. In other words, it is the total cost, LRTC, divided by output, $Q$:

$LRAC\left(Q\right)=\frac{LRTC\left(Q\right)}{Q}$

A firm’s long-run marginal cost (LRMC) is the increase in total cost from an increase in an additional unit of output:

$LRMC\left(Q\right)=\frac{\Delta LRTC\left(Q\right)}{\Delta Q}$

where $\Delta LRTC\left(Q\right)$ is the change in total cost and $\Delta Q$ is the change in output. This is the same thing as the slope of the total cost curve, $LRTC\left(Q\right)$.

Calculus

The long-run marginal cost is the rate of change of the total cost as output increases, or the slope of the total cost function, $LRTC\left(Q\right)$. To find this, we need to simply take the derivative of the total cost function:

$LRMC\left(Q\right)=\frac{dLRTC\left(Q\right)}{dQ}$

trates the relationship between the total cost curve (panel a) and erage and marginal cost curves (panel b).

Figure 8.2.3 Deriving long-run average and marginal cost curves from the long-run total cost curve

To see how long-run total and average costs are related, take point A on the total cost curve in figure 8.2.3. At this point, we can derive the average cost by dividing the vertical distance, which gives us the total cost, by the horizontal distance, which gives us quantity. This is the same thing as the slope of the ray from the origin that connects to point A: it is the “rise” over the “run.” So in panel b, we have the same quantity on the horizontal axis but the slope of the ray connecting to point A, or the average cost, on the vertical axis. Point A is, therefore, a point on the average cost curve. Note that as we move out along the total cost curve, the ray from the origin to the total cost curve becomes less and less steep until point B, after which the slope gets steeper. Thus point B is the point of minimum average cost, as illustrated in panel b.

To understand the relationship between long-run total cost and marginal cost, let’s go back to point A in panel a. The marginal cost is the same as the slope of the total cost curve, and we can illustrate the slope by using a tangent line: a straight line that passes through point A and has the same slope as the curve at that point. This slope gives us the marginal cost. Note that this slope is not as steep as the ray from the origin that defined average cost at this point. Therefore, in panel b, the marginal cost is lower than the average. We can also observe that as we move along the total cost curve, the slope continues to decrease until point C, after which the slope begins to increase. Thus point C is the minimum marginal cost, as illustrated on the marginal cost curve in panel b.

Finally, note that at point B on the total cost curve, the slope of the ray from the origin and the slope of the total cost curve are identical. At this point, the marginal and the average costs are the same, as seen by the intersection of the two curves in panel b.

This relationship between average and marginal costs is not a coincidence; it is always true. When average cost is above marginal cost, average cost must be decreasing. When average cost is lower than marginal cost, average cost must be increasing. And when average and marginal costs are equal, average cost is not changing. This relationship is described in table 8.2.1 and illustrated in figure 8.2.4.

Table 8.2.1 The relationship between long-run average and marginal costs
Relationship between AC and MC	Resulting change in AC
$AC\left(Q\right)<MC\left(Q\right)$	$AC\left(Q\right)$ increasing
$AC\left(Q\right)>MC\left(Q\right)$	$AC\left(Q\right)$ decreasing
$AC\left(Q\right)=MC\left(Q\right)$	$AC\left(Q\right)$ constant

Table 8.2.1 The relationship between long-run average and marginal costs

Relationship between AC and MC	Resulting change in AC
$AC\left(Q\right)<MC\left(Q\right)$	$AC\left(Q\right)$ increasing
$AC\left(Q\right)>MC\left(Q\right)$	$AC\left(Q\right)$ decreasing
$AC\left(Q\right)=MC\left(Q\right)$	$AC\left(Q\right)$ constant

Figure 8.2.4 Relationship between the long-run average and marginal cost curves

On the left half of figure 8.2.4, the average cost is above the marginal cost, and thus the average cost is falling. In the right half of figure 8.2.4, the average cost is below the marginal cost, and thus the average cost is rising. At the intersection of the two curves, the average cost is at its minimum, and the slope of the average cost curve is zero.

Economies and Diseconomies of Scale

An important economic concept associated with the long-run average cost curve is economies of scale. Economies of scale occur when the average cost of production falls as output increases. Similarly, diseconomies of scale occur when the average cost of production rises as output increases. In a typical long-run average cost curve, there are sections of both economies of scale and diseconomies of scale. There is also a point or region of minimum efficient scale where average cost is at its minimum. This is the point where economies of scale are used up and no longer benefit the firm. Figure 8.2.5 illustrates these points.

Figure 8.2.5 Economies, diseconomies, and minimum efficient scale

8.3 SHORT-RUN VERSUS LONG-RUN COSTS: THE ADVANTAGE OF FLEXIBILITY

Learning Objective 8.3: Explain why long-run costs are always as low as or lower than short-run costs and how more flexibility in choosing inputs is always better than less.

Short-run average costs are constrained by the presence of a fixed input. So in the long run, we can always do at least as well as, and often better than, what we do in the short run with respect to cost. We can see this is true by comparing the long-run and short-run average cost curves.

The long-run average cost curve is a type of lower boundary of the short-run cost curves. This can be understood most easily by thinking of a series of short-run average total cost curves, each one for a different level of the fixed input, capital, as shown in figure 8.3.1.

Figure 8.3.1 The long-run average cost curve as the lower boundary of short-run average cost curves

Since capital is variable in the long run, the long-run average cost is essentially the same as picking among the short-run average total cost curves and combining the capital with the optimal level of labor, or in other words, the minimum ATC.

The long-run average cost curve illustrates the benefit of flexibility: by being able to choose both inputs, the firm can ensure that the efficient mix of the inputs is being used at all times, which keeps costs at their minimum points for all output levels. This flexibility means that we can expect that in the long run, the average cost of production is at least as low as, and generally lower than, what it is in the short run.

8.4 MULTIPRODUCT FIRMS, LEARNING CURVES, AND LEARNING BY DOING

Learning Objective 8.4: Explain how making more than one product, learning over time, and learning by producing can lower costs.

A number of other factors matter in a firm’s ability to lower costs. In this section, we look at two of them.

Multiproduct Firms

Often, a firm will make more than one product. This raises the interesting question, When is it better for the same firm to make multiple products than for multiple firms to each make one product? One answer lies in the concept of economies of scope: an economy of scope exists when the average cost of one product falls as the production of another product increases.

Take, for example, a firm that makes large LCD televisions. One expensive component of these displays is the flat glass panels needed for the screen. To make these large screens, very large pieces of glass are manufactured and then cut into individual rectangular pieces for the televisions. Often there are smaller glass pieces left over. Rather than discard these pieces, the same company can make smaller LCD displays for computers, cars, appliances, and so on. Since a lot of the other materials, technical know-how, skilled labor, and the like can be shared across the two types of products, the average cost of both declines when the production of smaller LCD displays for computers is increased.

More formally, we can think of a multiproduct firm as having a cost function that depends on the output of two goods: $Q_1$ and $Q_2$. Such a cost function can be expressed as $C(Q_1,Q+2)$. We say the economies of scope are present if

$C(Q_1,Q_2)<C(Q_1,0)+C(0,Q_2)$.

This equation makes intuitive sense. The left-hand side of the inequality is the cost of a single firm that produced positive quantities of both goods. The right-hand side is the total cost of producing only $Q_1$ added to the total cost of producing only $Q_2$. If it is cheaper to produce the two together, then the inequality holds.

Learning Curves

Sometimes firms get better at making things over time, as they gain experience. Economists call this learning by doing. Learning by doing means that as the cumulative output—the total output ever produced—of the firm increases, the average cost falls.

Learning by doing can take different forms:

• Over time, workers become more efficient at specific tasks they perform repeatedly.
• Managers can observe production and adjust task assignments and other aspects of the production process.
• Engineers can optimize product and plant design to increase efficiency.
• Firms can get better at handling inputs, materials, and inventories.

These and other instances of learning by doing often lower firms’ average costs and make them more efficient over time.

The idea of learning by doing can be graphed as a learning curve (figure 8.4.1) where average cost is plotted as a function of either time or cumulative output. The learning curve is different from the typical average cost curve, which represents the total cost divided by current output.

Figure 8.4.1 The learning curve

This temporal view of average costs makes firms’ decisions about operating and investing in the business more complicated. If a firm that is considering shutting down in the face of negative economic profits expects that it will be able to produce more efficiently in the future, it might be willing to accept near-term losses in the expectation of future profits.

The learning curve is potentially important in the policy question. If there is substantial learning involved in the production of a streetcar, then the domestic manufacturer of streetcars might see its production costs decrease significantly as they produce more and more streetcars. So although the short-run costs of production might suggest that domestic promotion is a bad idea, if there is good reason to believe that in the long run, average costs will decrease significantly, a reasonable case could be made for such promotion.

8.5 POLICY EXAMPLE
SHOULD THE FEDERAL GOVERNMENT PROMOTE DOMESTIC PRODUCTION OF STREETCARS?

Learning Objective 8.5: Use a cost analysis to explain why building streetcars domestically in the United States is or is not a good policy.

To understand the business of building streetcars, we must first think about the cost structure. Streetcars are large, heavy, and loaded with specific and sophisticated technology, such as electric propulsion engines, car electronics and controls, and passenger controls. Their manufacture takes a factory of considerable size, and yet they are produced in small quantities. This suggests a few things about their costs:

• There are very large fixed costs because of the machinery and the plant required for constructing these cars. Because of this, the minimum efficient scale is probably far beyond any one manufacturer’s current scale. What this means is that the more streetcars a manufacturer produces, the lower the cost per car.
• Because of the complexity, there are likely to be large cost savings over time as a result of learning by doing.
• The complexity of the streetcar itself suggests that the quality of the product from new firms might suffer because they have not had the experience that longtime suppliers have had.

These observations suggest that current suppliers of streetcars, like Siemens, have considerable cost advantages over new firms because of their current production level, which allows them to take advantage of economies of scale, and because they are much farther along the learning curve (see figures 8.5.1 and 8.5.2). Any new firm likely would take a very long time to reach the current manufacturer’s scale efficiencies and cost efficiencies from learning by doing. However, if the demand for streetcars was expected to grow and be sustained for a long period of time, a reasonable case could be made that the domestic industry could mature into a reliable and cost-efficient supplier of streetcars to the United States and even the international market.

Figure 8.5.1 Streetcar manufacturers on the long-run average cost curve

Figure 8.5.2 Streetcar manufacturers on the learning curve

Unfortunately, the projections of the level of demand for streetcars appear to have been far too optimistic. It seems unlikely that the domestic streetcar industry will have a chance to grow and learn, so we may never know if it would have become cost competitive over time.

EXPLORING THE POLICY QUESTION

1. Because of their size and weight, shipping streetcars internationally is costly. How would you include transportation costs in your analysis of the policy question?
2. If the market had not dried up, do you think United Streetcar would have succeeded in the long run? Why or why not? Use economic reasoning in your answer.

LEARN: KEY TOPICS

Terms

Fixed cost

Variable cost

Total cost

Average fixed cost

Average variable cost

Average total cost

Marginal cost

Long-run total cost

Long-run average cost

Long-run marginal cost

Expansion path

Economies of scale

Diseconomies of scale

Minimum efficient scale

Economies of scope

Learning by doing

Learning curve

Graphs

Three short-run cost curves: fixed, variable, and total costs

The total product of labor curve

Marginal cost, average fixed cost, average variable cost, and average total cost

Expansion path

The long-run total cost curve

Deriving long-run average and marginal costs curves from the long-run total cost curve

Relationship between the long-run average and marginal cost curves

The long-run average cost curve as the lower boundary of short-run average cost curves

The learning curve

Equations

Short Run Cost Equations

Fixed Cost

Lacks an exact equation: the fixed cost in the context of short-run curves is the cost even when the output is at zero.

Variable cost

Variable cost varies with output level. Variable costs generally increase with the amount of output produced.

Total cost

The sum of fixed and variable costs of production.

$C=FC+VC$

Average fixed cost

The fixed cost per unit of output.

$AFC=FC/Q$

Average variable cost

The variable cost per unit of output.

$AVC=VC/Q$

Average total cost

The total cost per unit of output. The sum of the average fixed cost and average variable cost

$AC=AC/Q=AFC+AVC$

Marginal cost

The additional cost incurred from the production of one more unit of output.

$MC=\frac{\Delta C}{\Delta Q}$

Because the only part of total cost that increases with an additional unit of output is the variable cost, we can re-write the marginal cost as

$MC=\frac{\Delta VC}{\Delta Q}$

Long-run Cost Equations

Long-run cost minimization problem, review.

Long-run Total Cost

The sum of the all input costs

$LTRC=wL+rK$

Long-run average cost (LRAC)

The cost per unit of output. Because there is no fixedcost in the Long-run, it is the total cost $LRTC$, divdied by output $Q$.

$LRAC\left(Q\right)=\frac{LRTC\left(Q\right)}{Q}$

Long-run marginal cost

The increase in total cost from an increase in an additional unit of output.

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Consumption II: Laspeyres and Paasche price indices

 

Summary

This Learning Path is a bit more of a mixed bag than the previous one, finishing off our consumer choice problem, looking at the some useful implications of this in demand theory before moving on to other types of demand theories.

Price indices are used to monitor changes in prices levels over time. This is useful when separating real income from nominal income, as inflation is a drain on purchasing power. The two most basic indices are the Laspeyres index (named after Etienne Laspeyres) and the Paasche index (named after Hermann Paasche).

Both indices are very similar:

Laspeyres index:

Paasche index:

 

They work by dividing expense on a specific basket in the current period (the sum of p*q for each product in the basket considered when calculating the index) by how much the same basket would cost in the base period (period 0). The main difference is the quantities used: the Laspeyres index uses q0 quantities, whereas the Paasche index uses period n quantities.

What this translates to is that a Laspeyres index of 1 means that, as the nominator is the same as the denominator, an individual can afford the same basket of goods in the current period as he did in the base period. As the quantities are the same, this just leaves price as a variable, which must remain unchanged. This translates to the concept of compensated variation (CV): by how much do we need to increase an individual’s income in order to offset inflation? This is, at the new level of prices, how much is required to compensate the effect of the price increase? In the top diagram, we see that an increase in the price of good x1 means a move to a lower utility curve. The compensated variation is the theoretical amount of money the individual would need to maintain their level of utility, putting them back on their original utility curve.

What we can also see is that the Laspeyres index overestimates this CV: it assumes that inflation has a greater effect than it does. This can be more clearly seen in the bottom diagram. The change in price from P0 to P1 leads to a change in the quantity of X consumed from X0 to X1. The green rectangle shows the Laspeyres effect associated with this, which is greater than the CV effect. The CS effect, the dark blue trapezoid, shows the loss of consumer surplus associated with the price variation.

A Paasche index of 1 means that the consumer could have afforded the same bundle of goods in the base period as they can now. This can be translated to the concept of equivalent variation (EV): how much income would we have to take away from an individual, at the base price level, to have the same impact on their utility as the inflation between the base period and period 1? That is, if we took the individual’s utility in 2009 at that price level, how much would we have to take away from it to have the same utility as a person on the same income with 2012’s level of prices? Applying the same dynamic we applied to the Laspeyres index, we can see from the top diagram that the Paasche index underestimates the equivalent variation.

We can see this more clearly in the bottom diagram: the consumer surplus is greater than the variation effect, which is in turn greater than the Paasche effect.

If we put this all together, it may be easier to understand each of the effects and understand their downisdes:

These diagramas are simply a combination of the two we saw individually. They help us, however see the differences between both indices. The main downside to these indices is the fact that they do not take into effect substitution effects. When the price of something rises, we tend to consume less of it. Because the Laspeyres index uses base period quantities, it tends to overestimate inflation by assuming that individuals’ income expense is still distributed in the same way. The opposite is true of the Paasche index: because it uses current period quantities, it underestimates inflation.

Therefore, for normal goods, if inflation exists:

L > CV > CS > EV > P

 

Video – Laspeyres index:

Video – Paasche index:

So far, we have looked at consumer theory as individuals choosing one good over another. However, newer theories examine the possibility of consumers maximising utility by choosing characteristics of particular goods (not ‘music’ over ‘reading’, but ‘progressive rock’ over ‘Dickens’- leaving open ‘crime novels’ over ‘heavy metal’). Let’s explore how this changes demand functions.

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The Pros and Cons of Printed Marketing Materials

 Many marketers say they value that printed marketing materials such as brochures enable them to provide a physical copy of information, but they also say they worry that people simply throw those materials away, according to recent research from RRD and Finn Partners.

The report was based on data from a survey conducted in November 2022 among 300 marketing professionals in the United States who have insight into the decision-making processes at their organizations.

When asked what benefits print marketing has over digital marketing, respondents cite that it enables them to provide a physical copy of information (41% say is a benefit), that it provides an offline channel for consideration (39%), and that it provides a tactile, interactive, and memorable experience (34%).

When asked what challenges print marketing has compared with digital marketing, respondents cite the fear that people just throw printed materials away (47% cite as a challenge), that they can't track response rates effectively (38%), and that printed materials become out of date too quickly (34%).

Some 63% of marketers surveyed say digital marketing generally has a higher ROI than print marketing, 14% say print has a higher ROI, 20% say the ROI is equal, and 3% say they don't know because they don't use print marketing.

About the research: The report was based on data from a survey conducted in November 2022 among 300 marketing professionals in the United States who have insight into the decision-making processes at their organizations.

https://cutt.ly/h9NWtFE

55 Business Model Patterns. #11 Digitization

 

This pattern relies on the ability to turn existing products or services into digital variants, and thus offer advantages over tangible products, e.g., easier and faster distribution. Ideally, the digitization of a product or service is realized without harnessing the value proposition which is offered to the customer. In other words: efficiency and multiplication by means of digitization does not reduce the perceived customer value.

How they do it: Cewe digitized the process of creating and ordering individualized products, utilizing your own fotos. Through their website, customers can create their products remotely at anytime and have them shipped to their home.

Top Industries

Pattern Co-Occurrence

Below, the pattern "Digitization" is analyzed based on co-occurrence, in order to get insights into how this business model pattern is applied in combination with other patterns within the firms we studied.

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A digital transformation business model for innovation (chapter)

4 Results

Figure 1 The Digitization business model framework.

In  Figure  1,  we  present  a  first  graphical  version  of  the  digitization  business  model

innovation framework. The model is depicted as a directed graph whose components are

causally linked. The nodes represent components of the business model framework and

contain descriptions of typical effects resulting from digitization. 

The way to read this model is to start with a node that is affected by digitization, e.g.

shifting from products  to digital  features will  typically create  new  value  propositions,

such as real-time data, a potential for data analytics, remote access, etc. Often, this will

generate new digital,  bidirectional channels,  etc. As such, the  model is an explanatory

model of current changes in businesses. However, it is also possible to exploit the model

structure for the study of the consequences of going digital.  The model then should be

read in sense that a change in a component will naturally imply a predicted change in the

connected  components.  Importantly,  such  a  causally  connected  business  model  thus

naturally  supports  a  more  general  analysis  of  the  consequences  of  going  digital  for

previously unseen cases and can be tested and further improved. Of course, it is possible

to  describe the  model in  more detail,  e.g. going  back to  individual  case studies.  For

reasons of legibility this information is not include in the Figure above.

In this model, there is an important link from the channels component to customer

relations and back to activities (with a potential added circle from channels to customer

segments to customer relation for the case where the new digital channels also open new

customer groups). These links are built from the consideration of hybrid value creation

(Reichwald & Piller 06, Velamuri 10) often triggered by digitisation. Although the joint

value creation of businesses and their customers does not rely on being digital, it is

particulary widespread in the digital world and has been labelled co-creation, open

innovation, crowdsourcing etc.

The model clarifies that – as products or services shift towards digital, it can be

expected that the associated channels become digital. This is direct consequence of the

underlying technology characteristics – low-cost, direct and bidirectional. This in turn

induces a change in the customer relationship and will often naturally lead to open

innovation approaches that exploit the bidirectional communication for the design of

products/services. For the innovation practitioner this suggests to include hybrid value

creation approaches whenever a product is equipped with a digital component.

5 Discussion

The  model  presented  here  aims  to  represent  both  empirical  objects  and  empirical

characteristics  of  phenomena  businesses  experience  when  going digital.  It  models  in

particular  components of  business models and  assumes an  underlying causality  in the

linkages between components following changes in any given component. The model is

both descriptive  of a set of  cases described in literature, structured using technical and

economic  characteristics  of  information  and  communication  technology,  but  also

predictive with respect to yet  unseen cases of  digitization. Causality is  modelled using

directed  links  that  suggest  consequences  in  a  component  resulting  from  changes  in

another.

The underlying motivation behind this paper is to provide such causal linkages as a

central element in improved economic models of innovation processes. It has previously

been argued for the theory of innovation management research  that innovation research

(and management research in general) exhibits a lack of causal models. This lack often

unnecessarily opens  the whole  field to  severe criticism as it  makes it very hard,  if not

impossible, to test and validate research results. The model presented here is only a first

step and should be tested with novel cases of digitization and, where necessary, refined

further. 

Secondly, the model offers a systematic approach to the study of effects on business

models  of  going  digital.  We  have  already  seen  how  the  change  in  one  component

(products)  generates  consequential  changes  through  a  range  of  components  (up  to

‘activities’).  In  order  to  model  this  change,  it  was indeed  necessary to  introduce added

causal links (not present in the Schallmo and Brecht (10) framework). It is to be expected

that more  such links  will be  identified when studying a large number  or perhaps  more

detailed case examples.

Thirdly, from a practical perspective, the model can be used to develop  or to refine

new  digital business  models.  It offers  an opportunity  to study  the whole  spectrum of

potential  changes  induced  by  digital  technologies  starting  from  an  existing  business

model.

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