Intermediate Microeconomics Module 8 Cost Curves

COST CURVES 153 CHAPTER COSE ' 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 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 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 , Portland 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 to do so called United Streetcar . Other US cities that were introducing streetcars , such as Washington , 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 subject of this critical tools for analyzing a company cost structure . LEARNING OBJECTIVES Cost Curves Learning Objective Derive the seven cost curves from the total cost function . 153

154 PATRICK EMERSON Cost Curves Learning Objective Derive the three cost curves from the total cost function . versus Costs The Advantage of Flexibility Learning Objective Explain why costs are always as low as or lower than costs and how more flexibility in choosing inputs is always better than less . Firms , Learning Curves , and Learning by Doing Learning Objective Explain how making more than one product , learning over time , and learning by producing can lower costs . Policy Example Should the Federal Government Promote Domestic Production of Streetcars ?

Learning Objective Use a cost analysis to explain why building streetcars domestically in the United States is or is not a good policy . COST CURVES Learning Objective Derive the seven 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 cost curves . The Seven 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 ( 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 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 own production rather than renting it out to another company .

COST CURVES 155 The variable cost ( of production is the cost of production that varies with output level . This is the cost of the variable inputs in example , the cost of the workers that assemble the 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 ( of production is the sum of fixed and variable costs of production There are three average cost measures average variable cost , average fixed cost , and age total cost . Average variable cost ( is the variable cost per unit of output . Mathematically , it is simply the variable cost divided by the output Note that since variable cost generally increases with the amount of output produced , the average able cost can increase or decrease as output increases . Average fixed cost ( is the fixed cost per unit of output . Mathematically , it is simply the fixed cost divided by the output 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 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 ( MO ) is the additional cost incurred from the production ofone more unit of output . Thus marginal cost Calculus The marginal cost is the rate of change of the total cost as output increases , AC or the slope of the total cost function , To this , we need to simply . take the derivative of the total cost function The only part of total cost that ( increases with an additional unit of put is the Variable cost so We can re Since we can rewrite this derivative write the marginal cost as , as (

156 constant , so Thus is a ( Since fixed cost does not change as output increases , marginal cost depends only on the variable cost . PATRICK EMERSON Fixed Cost , Variable Cost , and Total Cost Curves Table summarizes a firm daily 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 fixed cost of 50 does not change with the amount of output produced . The data in the first two columns of table allow us to draw the firm fixed cost curve . It is a horizontal line at 50 , as shown in . Table An of the seven cost measures Output Fixed cost Marginal cost Average fixed cost Average variable cost Average cost 50 40 90 40 50 70 120 30 50 90 140 20 50 100 150 10 50 120 170 20 50 150 200 30 50 190 240 40 50 240 290 50 50 300 350 60 10 50 370 420 70

COST CURVES 157 Cost 400 350 300 250 Cost , Cost , Total Cost , 200 150 100 50 Quantity Figure Three cost curves fixed , variable , and total costs Figure also shows variable and total cost curves plotted from data in table . 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 , increases . The variable cost curve is determined by and matches the shape ofthe production function , which we studied in chapter . The production function is the same as the total 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 assume a constant price of labor , say 10 an hour . Figure presents a typical production function , which leads to the shape of the variable cost curve in figure . 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 .

158 PATRICK EMERSON Labor I I I I 10 20 30 40 Lab Figure The total product of labor curve If we multiply the amount of labor at every level of output in figure by the wage rate of 10 per hour , we get the va cost curve from figure . Marginal , Average Fixed , Average Variable , and Average Total Cost Curves Figure presents the four remaining cost curves marginal cost ( average fixed cost ( average variable cost ( and average total cost ( AC ) Cost Per Unit , run con . Arc Variable con . man cost . AC Quantity Figure marginal cost , average fixed cost , average variable cost , and average total cost curves

COST CURVES 159 The marginal cost , average variable cost , and average total cost curves are derived from the total cost curve . From figure , 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 curve a . What the marginal cost curve ?

Wha ( COST CURVES Learning Objective Derive the three 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 cost cost , average cost , and marginal how to derive them . Total Cost Curve To determine the total cost ( for a firm , we must think about the cost minimization lem introduced in chapter . Remember that the cost minimization problem answers the question , What is the most 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 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 ofthe firm . Recall from chapter that the expansion path is the combination of inputs that minimize costs for every level of output , and it can be as a curve . Figure shows the expansion path for a firm that manufactures tablet ers .

160 PATRICK EMERSON , Capital Expansion Path IO 99203 , Lab or Figure Expansion path Each point on the expansion path is the solution to the cost minimization problem for that particular output . Recall from chapter that ' is the rental rate or price of capital and is the wage rate or price of labor . Consider point here the output quantity is set at ten million , and the tangency of the and at this point establishes the optimal combination ofthe inputs . To go from this point to the cost , we have only to know the combined cost of the inputs . Fortunately , the line tells us exactly that the total cost here is . Now consider point , where the output quantity has increased to twenty million . With this , the new production level is associated with a new curve , with total cost at . Finally , point indicates that for an output quantity million , the total cost is . From the expansion path , we can draw the total cost curve . We have three points already , and . Point describes a quantity of ten million tablets and a total cost of . Point describes a quantity of twenty million tablets and a total cost of . Point describes a quantity of thirty million tablets and a total cost of . These three pairs are three points on the total cost curve in figure .

COST CURVES 161 Cost Quantity Figure The total cost curve Remember from chapter that the total cost is the sum of the input costs , 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 average cost ( is the cost per unit of output . In other words , it is the total cost , divided by output , A firm marginal cost ( is the increase in total cost from an increase in an additional unit of output ( where ' is the change in total cost and is the change in output . This is the same thing as the slope of the total cost curve , Figure illustrates the relationship between the total cost curve ( panel a ) and the average and marginal cost curves ( panel ) Calculus The marginal cost is the rate of change of the total cost as output increases , or the slope of the

162 PATRICK EMERSON total cost function , To find this , we need to simply take the derivative of the total cost function ( Cost ) min min Quantity Figure Deriving average and marginal ( ost curves from the total cost ( COST CURVES 163 To see how total and average costs are related , take point A on the total cost curve in figure . 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 , 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 , after which the slope gets steeper . Thus point is the point of minimum average cost , as illustrated in panel . To understand the relationship between total cost and marginal cost , let 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 , 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 , after which the slope begins to increase . Thus point is the minimum marginal cost , as illustrated on the marginal cost curve in panel . Finally , note that at point on the total cost curve , the slope ofthe 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 . This relationship between average and marginal costs is not a coincidence it is always true . When age cost is above marginal cost , average cost must be decreasing . When average cost is lower than 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 and illustrated in figure . Table The between and costs Relationship between AC and Resulting change in AC increasing decreasing ( a

164 PATRICK EMERSON Cost Quantity Figure Relationship between the average and cost On the left half of figure , the average cost is above the marginal cost , and thus the average cost is falling . In the right half of figure , 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 of Scale An important economic concept associated with the average cost curve is economies of scale . Economies of scale occur when the average cost of production falls as output increases . Similarly , economies of scale occur when the average cost of production rises as output increases . In a typical average cost curve , there are sections of both economies of scale and 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 illustrates these points .

COST CURVES 165 of Scale increasing Economies of Scale decreasing Cost Minimum efficient scale at minimum Quantity Figure Economies , and minimum ' SH VERSUS COSTS THE ADVANTAGE OF FLEXIBILITY Learning Objective Explain why costs are always as low as or lower than costs and how more flexibility in choosing inputs is always better than less . 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 and average cost curves . The average cost curve is a type of lower boundary of the cost curves . This can be understood most easily by thinking of a series of average total cost curves , each one for a level of the fixed input , capital , as shown in figure .

166 PATRICK EMERSON Cost Quantity Figure The average cost curve as the lower boundary of average cost curves Since capital is variable in the long run , the average cost is essentially the same as picking among the average total cost curves and combining the capital with the optimal level of labor , or in other words , the minimum ATC . The average cost curve illustrates the benefit 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 . 84 FIRMS , LEARNING CURVES , AND LEARNING BY DOING Learning Objective 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 ability to lower costs . In this section , we look at two of them . 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 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 displays for computers , cars , appliances , and so on . Since a lot of the other materials , technical

COST CURVES 167 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 displays for computers is increased . More formally , we can think of a firm as having a cost function that depends on the put of two goods and . Such a cost function can be expressed as ( We say the economies of scope are present if ( This equation makes intuitive sense . The side of the inequality is the cost of a single firm that produced positive quantities of both goods . The side is the total cost of producing only added to the total cost of producing only . 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 total output ever 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 ofthe tion 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 as a learning curve ( figure ) 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 .

168 PATRICK EMERSON Average Cost AC Cumulative output over time Figure 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 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 duction costs decrease significantly as they produce more and more streetcars . So although the 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 . 85 POLICY EXAMPLE SHOULD THE FEDERAL GOVERNMENT PROMOTE DOMESTIC PRODUCTION OF STREETCARS ?

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

COST CURVES 169 To understand the business of building streetcars , we must first think about the cost structure . cars 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 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 ofthis , the minimum efficient scale is probably far beyond any one current scale . What this means is that the more streetcars a manufacturer produces , the lower the cost per car . Because ofthe complexity , there are likely to be large cost savings over time as a result of ing 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 , have considerable cost advantages over new firms because of their current production level , which allows them to take of economies of scale , and because they are much farther along the learning curve ( see figures and ) Any new firm likely would take a very long time to reach the current manufacturer scale and cost efficiencies from learning by doing . However , ifthe demand for streetcars was expected to grow and be sustained for a long period of time , a reasonable case could be made that the tic industry could mature into a reliable and supplier of streetcars to the United States and even the international market . United Streetcar Cost Quantity Figure . 77 Streetcar manufacturers on the average cost curve

170 PATRICK EMERSON United Streetcar Average Cost Quantity Cumulative output over time Figure . 72 Streetcar manufacturers on the learning curve Unfortunately , the projections of the level of demand for streetcars appear to have been far too mistic . 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 . Because of their size and weight , shipping streetcars internationally is costly . How would you include transportation costs in your analysis of the policy question ?

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 . REVIEW TOPICS AND RELATED LEARNING OUTCOMES Cost Curves Learning Objective Derive the seven cost curves from the total cost function . Cost Curves Learning Objective Derive the three cost curves from the total cost function .

COST CURVES 171 versus Costs The Advantage of Flexibility Learning Objective Explain why costs are always as low as or lower than costs and how more in choosing inputs is always better than less . Firms , Learning Curves , and Learning by Doing Learning Objective Explain how making more than one product , learning over time , and learning by producing can lower costs . Policy Example Should the Federal Government Promote Domestic Production of Streetcars ?

Learning Objective Use a cost analysis to explain why building streetcars domestically in the United States is or is not a good policy . LEARN KEY TOPICS Terms Fixed cost The cost of production that does not vary with output level . The cost is the cost of the inputs in production , such as the cost of a machine ( capital ) that costs the same to operate no matter how much production is happening , ie , 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 . Variable cost The cost of production that varies with output level . This is the cost of the variable inputs in , 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 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 . Total cost The sum of and variable costs of production . Average cost The fixed cost per unit of output . Average variable cost The total cost per unit of output . This is the same as the sum of the average cost and the average variable cost . Average total cost The total cost per unit of output . This is the same as the sum of the average cost and the average variable cost . Marginal cost The additional cost incurred from the production of one more unit of output . total cost In the , all costs are variable . This represents the total cost of all previously and variable inputs . average cost

The cost per unit of output . In other words , it is the total cost , divided by output , marginal cost The increase in total cost from an increase in an additional unit of output . Expansion path A curve that shows the amount of each input for every level of output . Economies of scale When the average cost of production falls as output increases , of scale When the average cost of production rises as output increases . Minimum scale PATRICK EMERSON The point on a cost curve where average cost is at its minimum . This is the point where economies of scale are used up and no longer the . Economies of scope When the average cost of one product falls as the production of another product increases . Learning by doing As the cumulative total output ever the increases , the average cost falls . Learning curve The graph of a process of learning by doing . Differs from the typical average cost curve this is plotted as a function of time or cumulative output . Graphs Three cost curves , variable , and total costs Cost 450 ' 350 300 250 200 150 100 50 400 Cost , Cost , Total Cost , Quantity Figure Three cost , variable , and total costs The total product of labor curve

COST CURVES 173 ) 10 Product of Labor . 10 20 30 40 Figure The total product of labor curve Marginal cost , average cost , average variable cost , and average total cost mo so Aw ?

mam . so arc ' an Quantity Expansion path Figure marginal cost , average fixed cost , average variable cost , and average total cost 174 PATRICK EMERSON , Capital HO Expansion Path LO ?

Labor Figure path The total cost curve Cost Quantity Figure The oral ( Deriving average and marginal costs curves from the total cost curve COST CURVES 175 ) Cost ) min min Quantity average and marginal ( curves from the rural cost curve Relationship between the average and marginal cost curves Cost Quantity Figure . Relationship between the average and marginal cost curves The average cost curve as the lower boundary of average cost curves

176 PATRICK EMERSON Quantity Figure The average cost curve as the lower boundary average cost curves The learning curve United Streetcar Average Cost Quantity Cumulative output over time Figure . 72 Streetcar manufacturers an the learning curve Equations Short Run Cost Equations Fixed Cost Lacks an exact equation the cost in the context of 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 .

COST CURVES 177 Total cost The sum of and variable costs of production . Average cost The cost per unit of output . Average variable cost The variable cost per unit of output . Average total cost The total cost per unit of output . The sum of the average cost and average variable cost AC Marginal cost The additional cost incurred from the production of one more unit of output . Because the only part of total cost that increases with an additional unit of output is the variable cost , we can rewrite the marginal cost as Cost Equations cost minimization problem , review cost minimization problem The slope of the is the , and the slope of the is ' So the solution to the cost minimization problem is

178 PATRICK EMERSON ) This formula has many different calculus derived conclusions that can be reviewed in chapter . Total Cost The sum of the all input costs ' average cost ) The cost per unit of output . Because there is no in the , it is the total cost by output ' marginal cost The increase in total cost from an increase in an additional unit of output .