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1、CHAPTER 6PRODUCTIONTEACHING NOTESChapter 6 is the first of the three chapters that present the basic theory of supply. It may be beneficial to first review, or summarize, the derivation of demand and present an overview of the theory of competitive supply. The review can be beneficial given the simi
2、larities between the theory of demand and the theory of supply. Students often find that the theory of supply is easier to understand because it is less abstract, and the concepts are more familiar. This in turn can improve the students understanding of the theory of demand when they go back and rev
3、iew it again.In this chapter it is important to take the time to carefully go through the definitions, as this will be the foundation for what is done in the next two chapters. While the concept of a production function is not difficult, the mathematical and graphical representation can sometimes be
4、 confusing. It helps to take the time to do as many examples as you have time for. When describing and graphing the production function with output on the vertical axis and one input on the horizontal axis, point out that the production function is the equation for the boundary of the production set
5、, and hence defines the highest level of output for any given level of inputs. Technical efficiency is assumed throughout the discussion of the theory of supply. At any time you can introduce a discussion of the importance of improving productivity and the concept of learning by doing. Examples 1 an
6、d 2 in the text are also good for discussion.Graphing the production function leads naturally to a discussion of marginal product and diminishing returns. Emphasize that diminishing returns exist because some factors are fixed by definition, and that diminishing returns does not mean negative return
7、s. If you have not discussed marginal utility, now is the time to make sure that the student knows the difference between average and marginal. An example that captures students attention is the relationship between average and marginal test scores. If their latest mid-term grade is greater than the
8、ir average grade to date, this will increase their average.Isoquants are defined and discussed in section 6.3 of the chapter. Rely on the students understanding of indifference curves when discussing isoquants, and point out that as with indifference curves, isoquants are a two-dimensional represent
9、ation of a three-dimensional production function. Key concepts in this section of the chapter are the marginal rate of technical substitution and returns to scale. Do as many concrete examples as you have time for to help explain these two important concepts. Examples 6.3 and 6.4 help to give concre
10、te meaning to MRTS and returns to scale. Section 6.4 discusses returns to scale.QUESTIONS FOR REVIEW1. What is a production function? How does a long-run production function differ from a short-run production function?A production function represents how inputs are transformed into outputs by a firm
11、. We focus on the firm with one output and aggregate all inputs or factors of production into one of several categories, such as labor, capital, and materials. In the short run, one or more factors of production cannot be changed. As time goes by, the firm has the opportunity to change the levels of
12、 all inputs. In the long-run production function, all inputs are variable.2. Why is the marginal product of labor likely to increase initially in the short run as more of the variable input is hired?The marginal product of labor is likely to increase initially because when there are more workers, ea
13、ch is able to specialize on an aspect of the production process in which he or she is particularly skilled. For example, think of the typical fast food restaurant. If there is only one worker, he will need to prepare the burgers, fries, and sodas, as well as take the orders. Only so many customers c
14、an be served in an hour. With two or three workers, each is able to specialize and the marginal product (number of customers served per hour) is likely to increase as we move from one to two to three workers. Eventually, there will be enough workers and there will be no more gains from specializatio
15、n. At this point, the marginal product will diminish.3. Why does production eventually experience diminishing marginal returns to labor in the short run?The marginal product of labor will eventually diminish because there will be at least one fixed factor of production, such as capital. With capital
16、 fixed, the workplace will eventually become so congested, that the productivity of additional workers will decline. Also, with capital fixed, as more workers are added, they will need to share the fixed capital, which will eventually cause the marginal product of labor to diminish as the capital is
17、 spread across too many workers. Think for example of an office where there are only three computers. As more and more employees must share the computers, the marginal product of each additional employee will diminish.4. You are an employer seeking to fill a vacant position on an assembly line. Are
18、you more concerned with the average product of labor or the marginal product of labor for the last person hired? If you observe that your average product is just beginning to decline, should you hire any more workers? What does this situation imply about the marginal product of your last worker hire
19、d?In filling a vacant position, you should be concerned with the marginal product of the last worker hired because the marginal product measures the effect on output, or total product, of hiring another worker. This in turn will help to determine the revenue generated by hiring another worker, which
20、 can then be compared to the cost of hiring another worker.The point at which the average product begins to decline is the point where average product is equal to marginal product. When average product declines, the marginal product of the last worker hired is lower than the average product of previ
21、ously hired workers.Although adding more workers results in a further decline in average product, total product continues to increase, so it may still be advantageous to hire another worker.5. What is the difference between a production function and an isoquant?A production function describes the ma
22、ximum output that can be achieved with any given combination of inputs. An isoquant identifies all of the different combinations of the inputs that can be used to produce one particular level of output.6. Faced with constantly changing conditions, why would a firm ever keep any factors fixed? What c
23、riteria determine whether a factor is fixed or variable?Whether a factor is fixed or variable depends on the time horizon in consideration: all factors are fixed in the very short run; all factors are variable in the long run. As stated in the text: “All fixed inputs in the short run represent outco
24、mes of previous long-run decisions based on firms estimates of what they could profitably produce and sell.” Some factors are fixed in the short run, whether the firm likes it or not, simply because it takes time to adjust the level of the variables. For example, the firm may be legally bound by a l
25、ease on a building, some employees may have contracts that must be upheld, or construction of a new facility may take some number of months. Recall that the short run is not defined as a specific number of months or years, but as that period of time where some inputs cannot be changed for reasons su
26、ch as those given above.7. Isoquants can be convex, linear, or L-shaped. What does each of these shapes tell you about the nature of the production function? What does each of these shapes tell you about the MRTS?Convex isoquants imply that within some range, some number of units of one input can be
27、 substituted for a unit of the other input, and output can be maintained at the same level. In this case, the MRTS is diminishing as we move down along the isoquant. Linear isoquants imply that the slope, or the MRTS, is constant. This means that the same number of units of one input can always be e
28、xchanged for a unit of the other input and output can be maintained. The inputs are perfect substitutes. L-shaped isoquants imply that the inputs are perfect complements, or that the firm is producing under a fixed proportions type of technology. In this case the firm cannot give up one input in exc
29、hange for the other and still maintain the same level of output. For example, the firm may require exactly 4 units of capital for each unit of labor, in which case one input cannot be substituted for the other.8. Can an isoquant ever slope upwards? Explain.No. This would mean that if you increased b
30、oth inputs then output would stay the same. As a general rule, if the firm has more of all the inputs they can produce more output.9. Explain the term “marginal rate of technical substitution”? What does a MRTS=4 mean?MRTS is the amount by which the quantity of one input can be reduced when the othe
31、r input is increased by one unit, while maintaining the same level of output. If the MRTS is 4 then the one input can be reduced by 4 units as the other is increased by one unit and output will be the same.10. Explain why the marginal rate of technical substitution is likely to diminish as more and
32、more labor is substituted for capital.As the quantities of the inputs are changed the marginal product of each input will change. As more and more labor is added, the marginal product of labor is likely to diminish. Because capital has been reduced, each unit of capital remaining is likely to be mor
33、e productive. Therefore, more units of labor will be required to replace each unit of capital. Alternatively, as we move down and to the right along an isoquant along which the MRTS is diminishing, we have to give up less capital for each unit of labor added to keep output constant. 11. Diminishing
34、returns to a single factor of production and constant returns to scale are not inconsistent. Discuss.Diminishing returns to a single factor are observable in all production processes at some level of inputs. This fact is so pervasive that economists have named it the “law of diminishing marginal pro
35、ductivity.” By definition, the marginal product of an input is the additional output generated by employing one more unit of the input, all other inputs held fixed. The extra output, or returns, to the single input diminish because all other inputs are held fixed. For example, when holding the level
36、 of capital constant, each additional unit of labor has less capital to work with.Unlike the returns to a single factor, returns to scale are proportional increases in all inputs. While each factor by itself exhibits diminishing returns, output may more than double, less than double, or exactly doub
37、le when all the inputs are doubled. The distinction again is that with returns to scale, all inputs are increased in the same proportion and no input is held fixed.12. Can a firm have a production function that exhibits increasing returns to scale, constant returns to scale, and decreasing returns t
38、o scale as output increases? Discuss.Most firms have production functions that exhibit first increasing, then constant, and ultimately decreasing returns to scale. At low levels of output, a proportional increase in all inputs may lead to a larger-than-proportional increase in output, based on an in
39、crease in the opportunity for each factor to specialize. For example, if there are now two people and two computers, each person can specialize by completing those tasks that they are best at, which allows output to more than double. As the firm grows, the opportunities for specialization may dimini
40、sh and a doubling of all inputs will lead to only a doubling of output. When there are constant returns to scale, the firm is replicating what it is already doing. At some level of production, the firm will be so large that when inputs are doubled, output will less than double, a situation that can
41、arise from management diseconomies.13. Give an example of a production process in which the short run involves a day or a week and the long run any period longer than a week.Any small business where one input requires more than a week to change would be an example. The process of hiring more labor,
42、which requires announcing the position, interviewing applicants, and negotiating terms of employment, can take a day, if done through a temporary employment agency. Usually, however, the process takes a week or more. Expansion, requiring a larger location, will also take longer than a week.EXERCISES
43、1. The menu at Joes coffee shop consists of a variety of coffee drinks, pastries, and sandwiches. The marginal product of an additional worker can be defined as the number of customers that can be served by that worker in a given time period. Joe has been employing one worker, but is considering hir
44、ing a second and a third. Explain why the marginal product of the second and third workers might be higher than the first. Why might you expect the marginal product of additional workers to eventually diminish? The marginal product could well increase for the second and third workers, since each of
45、the first 2 or 3 workers would be able to specialize in a different task. If there is only 1 worker, then that worker will have to take orders and prepare all the food. Eventually, however, the marginal product would diminish because there would be too many people behind the counter trying to accomp
46、lish a limited number of tasks.2. Suppose a chair manufacturer is producing in the short run (with its existing plant and equipment). The manufacturer has observed the following levels of production corresponding to different numbers of workers:Number of chairsNumber of workers1102183244285306287 25
47、a.Calculate the marginal and average product of labor for this production function.The average product of labor, APL, is equal to . The marginal product of labor, MPL, is equal to , the change in output divided by the change in labor input. For this production process we have:LQAPLMPL00_110101021898
48、3248642874530626284.7-27253.6-3b.Does this production function exhibit diminishing returns to labor? Explain.This production process exhibits diminishing returns to labor. The marginal product of labor, the extra output produced by each additional worker, diminishes as workers are added, and is actually negative for the sixth and seventh workers.c.Explain intuitively what might cause the marginal product of labor to become negative.Labors negative marginal product for L 5 may arise from congestion in the chair manufacturers factory.
