Section outline

  • The law of diminishing returns is an economic concept stating that at a certain point it is not financially sound to continue adding more resources to a company unless other factors change. For instance, it is not financially viable to keep hiring more workers unless other factors, like workspace, supplies, or materials, increase as well 1 . 
    ::收益减少法是一个经济概念,它指出,在某一时刻,除非其他因素发生变化,否则继续增加公司的资源在财政上是不健全的,例如,继续雇用更多的工人在财政上是不可行的,除非其他因素,如工作空间、用品或材料,也增加1。

    lesson content

    Say a business makes a product that can be assembled by workers according to the following data: 
    ::说企业根据以下数据生产一种可由工人组装的产品:

    Number of Workers Products Assembled
    0 0
    5 9
    10 20
    15 27
    20 23
    25 16

    1. Using a graphing utility, find and graph the quadratic function that models this situation. The videos below show how to do quadratic regression with Desmos or a TI-83/84. 
    ::1. 使用图形工具、查找和图表来模拟这种情况的二次函数,下面的视频显示如何用Desmos或TI-83/84来进行二次回归。

     

    2. According to the model, what is the maximum number of products that can be produced? How many workers are needed?
    ::2. 根据模型,可以生产的产品的最大数量是多少?需要多少工人?

    3. What does the larger zero of the function represent? 
    ::3. 该函数的大零代表什么?

      

    4. Looking at the table, find the marginal product, the additional number of products produced by the new number of workers. For example, the marginal product between 0 workers and 5 workers is 9 products, the marginal product between 5 and 10 workers is 11 products, etc. Notice the marginal product is the difference in the  y -values. 
    ::4. 从表中看,找到边际产品,找到新的工人数量所生产的更多产品,例如,0个工人和5个工人之间的边际产品是9个产品,5个工人和10个工人之间的边际产品是11个产品等等。

    5. For which numbers of workers are the marginal products increasing? 
    ::5. 边际产品在增加哪些工人?

    6. For which numbers of workers are the marginal products decreasing? This is when the law of diminishing returns shows its effect. 
    ::6. 边际产品对哪些人数的工人在减少?这是收益减少法显示出其效果的时候。

    7. For which numbers of workers are the marginal products negative? 
    ::7. 边缘产品对哪些数目的工人不利?

    8. Graph the marginal products and compare that graph to the graph you found in question 1. What trends do you observe? 
    ::8. 绘制边际产品图,并将该图与您在问题1中发现的图作比较。

    This video by Kyle McKeel shows a classroom activity demonstrating the law of diminishing returns. 
    ::这段影片由Kyle McKeel拍摄,

     

    References
    ::参考参考资料

    1. “Diminishing Returns,” last edited April 21, 2017,
    ::1. " 减少返回 " ,上次编辑于2017年4月21日、2017年4月21日、