Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. Short Run Cost Overview:
  2. Long-Run Production Function
    • Both labour and capital vary
    • Table for Production Function
    • Diminishing returns of marginal product of labour
    • Diminishing returns of marginal product of capital
  3. Short-Run Costs & Total Average Costs
    • All ATC curves are U-shaped
    • More machines = bigger output at minimum average cost
    • Planned output \, \, find the lowest possible cost
  4. Long-Run Average Cost
    • LRAC: Long Run Average Cost
    • Lowest attainable cost across all ATC curves
    • What it looks like
  5. Economies & Diseconomies of Scale
    • Economies of Scale: \downarrow average cost as output \uparrow , falling LRAC
    • Diseconomies of Scale: \uparrow average cost as output \uparrow , rising LRAC
    • Constant Returns to Scale: average cost unchanged as output \uparrow , horizontal LRAC
    • Minimum Efficient Scale
?
Examples
Lessons
  1. Finding the Average Total Costs
    Suppose the cost of each machine is $50, and the cost of each worker per week is $50. Using the following table to calculate and graph the ATC curves for factories 1 and 2.

    Labour (workers per week)

    Output (Clothes per week)

    Factory 1

    (1 machine)

    Factory 2

    (2 machines)

    Factory 3

    (3 machines)

    Factory 4

    (4 machines)

    1

    10

    30

    45

    55

    2

    30

    50

    65

    75

    3

    45

    65

    80

    90

    4

    55

    75

    90

    100

    5

    60

    80

    95

    105

    1. Suppose the cost of each machine is $50, and the cost of each worker per week is $50. Using the following table to calculate and graph the ATC curves for factories 3 and 4.

      Labour (workers per week)

      Output (Clothes per week)

      Factory 1

      (1 machine)

      Factory 2

      (2 machines)

      Factory 3

      (3 machines)

      Factory 4

      (4 machines)

      1

      10

      30

      45

      55

      2

      30

      50

      65

      75

      3

      45

      65

      80

      90

      4

      55

      75

      90

      100

      5

      60

      80

      95

      105

      1. Understanding the Long-Run Cost Curve
        Suppose you are given 4 ATC curves on the following graph.
        Long run cost curve
        1. Draw the LRAC.
        2. For what output does the minimum efficient scale happen?
        3. Identify the regions with economies of scale, economies of descale.
      2. Suppose you are given 4 ATC curves on the following graph.
        Long run cost curve
        1. Draw the LRAC.
        2. For what output does the minimum efficient scale happen?
        3. Identify the regions with economies of scale, economies of descale.
      Free to Join!
      StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
      • Easily See Your Progress

        We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
      • Make Use of Our Learning Aids

        Last Viewed
        Practice Accuracy
        Suggested Tasks

        Get quick access to the topic you're currently learning.

        See how well your practice sessions are going over time.

        Stay on track with our daily recommendations.

      • Earn Achievements as You Learn

        Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
      • Create and Customize Your Avatar

        Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
      Topic Notes
      ?
      Long-Run Production Function

      In the long run, all inputs and costs are variables.


      Long-run Production Function: the relationship between the output and the quantities of both capital and labour.


      The function is not graphable in a 2D graph, but it can be shown in a table.


      Labour (workers per week)

      Output (Cars per week)

      Factory 1

      (1 machine)

      Factory 2

      (2 machines)

      Factory 3

      (3 machines)

      Factory 4

      (4 machines)

      1

      9

      14

      17

      19

      2

      14

      19

      22

      24

      3

      17

      22

      25

      27

      4

      19

      24

      27

      29

      5

      20

      25

      28

      30



      Marginal Product of Capital: the additional total product from a one-unit increase of capital.


      Diminishing Returns of Labour: can be shown by allowing labour to vary and keeping capital constant.


      Diminishing Returns of Capital: can be shown by allowing capital to vary and keeping labour constant.


      Each column of the table could be graphed as a total product curve for each factory.



      Short-Run Costs & Total Average Cost

      Recall that the total average cost is:


      ATC = TCQ\frac{TC}{Q}

      We can use this formula to calculate the short-run average total cost for each factory. Suppose the cost for each worker is $10, and the cost for each machine is 10$.


      Then for factory 1 and 2, you get the following table,

      # of Machines & Labour

      TC

      Q

      ATC1

      1 machine, 1 worker

      20

      9

      $2.22

      1 machine, 2 workers

      30

      14

      $2.14

      1 machine, 3 workers

      40

      17

      $2.35

      1 machine, 4 workers

      50

      19

      $2.63

      1 machine, 5 workers

      60

      20

      $3.00

      # of Machines & Labour

      TC

      Q

      ATC2

      2 machine, 1 worker

      30

      14

      $2.14

      2 machine, 2 workers

      40

      19

      $2.11

      2 machine, 3 workers

      50

      22

      $2.27

      2 machine, 4 workers

      60

      24

      $2.50

      2 machine, 5 workers

      70

      25

      $2.80


      Then for factory 3 and 4, we will get

      # of Machines & Labour

      TC

      Q

      ATC3

      3 machine, 1 worker

      40

      17

      $2.35

      3 machine, 2 workers

      50

      22

      $2.27

      3 machine, 3 workers

      60

      25

      $2.40

      3 machine, 4 workers

      70

      27

      $2.59

      3 machine, 5 workers

      80

      28

      $2.86

      # of Machines & Labour

      TC

      Q

      ATC4

      4 machine, 1 worker

      50

      19

      $2.63

      4 machine, 2 workers

      60

      24

      $2.50

      4 machine, 3 workers

      70

      27

      $2.59

      4 machine, 4 workers

      80

      29

      $2.76

      4 machine, 5 workers

      90

      30

      $3.00



      We can now graph all the ATC curves into one graph.

      Average total cost curve

      Note 1: All ATC curves are U shaped.

      Note 2: The more machines there are, the bigger the output is at which average total cost is at a minimum.


      Long Run Average Cost


      Long-Run Average Cost (LRAC) is the relationship between the lowest average total cost attainable and output when the firm can change both the factories and the number of labours it employs.

      To draw the LRAC, we draw a curve that is tangent to all ATC's.


      Economies & Diseconomies of Scale


      Economies of Scale: the area in which the LRAC decreases as output increases.

      Diseconomies of Scale: the area in which LRAC increases as output increases.

      Constant Returns to Scale: the area in which LRAC is horizontal as output increases.


      Economies & diseconomies of scale curve

      Minimum Efficient Scale: the point in the LRAC curve where the lowest possible cost is attained.