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Understanding Long Run Average Cost (LRAC) in Economics
Dive into the essential concept of Long Run Average Cost. Learn how to analyze firm behavior, optimize production levels, and identify economies of scale for long-term business strategy and growth.

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Now Playing:Long run cost – Example 0a
Intros
  1. Short Run Cost Overview:
  2. Short Run Cost Overview:
    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 Cost Overview:
    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
Examples
  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

    Short run product curve
    Jump to:NotesConceptFAQsPrerequisites
    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.

    Concept

    Introduction to Long Run Average Cost

    The long run average cost (LRAC) curve, also known as the long run average total cost, is a fundamental concept in economics that plays a crucial role in understanding firm behavior and cost structures. Our introduction video provides an essential overview of this concept, serving as a valuable starting point for students and professionals alike. The LRAC curve represents the lowest possible average cost a firm can achieve for any given level of output in the long run, when all factors of production are variable. It is derived from the envelope of short-run average cost curves and illustrates how a firm's average costs change as it scales its operations. Understanding the LRAC is vital for firms to analyze their cost structure in the long term, make informed decisions about production levels, and optimize their scale of operations. By studying the LRAC curve, businesses can identify economies and diseconomies of scale, determine the most efficient production size, and strategize for long-term growth and competitiveness in their respective markets.

    FAQs

    Here are some frequently asked questions about long run average cost:

    1. Why is the long run average cost curve U-shaped?

    The long run average cost (LRAC) curve is typically U-shaped due to the interplay between economies and diseconomies of scale. Initially, as production increases, the firm experiences economies of scale, causing average costs to decrease. However, beyond a certain point, diseconomies of scale set in, leading to rising average costs. This creates the characteristic U-shape of the LRAC curve.

    2. How do you calculate average total cost in the long run?

    To calculate the long run average total cost (LRATC), divide the total cost of production by the quantity produced when all inputs are variable. The LRATC is derived from the envelope of short-run average total cost curves, representing the lowest possible average cost for each level of output when the firm has time to adjust all factors of production.

    3. What is the difference between short run and long run average total cost?

    The main difference is that short run average total cost (SRATC) assumes at least one factor of production is fixed, while long run average total cost (LRATC) assumes all factors are variable. SRATC represents costs for a specific plant size, while LRATC shows the lowest possible average cost for each output level when the firm can adjust all inputs, including plant size.

    4. What happens to average cost in the long run?

    In the long run, average cost typically decreases initially due to economies of scale, reaches a minimum at the optimal scale of production, and then may increase due to diseconomies of scale. This pattern creates the U-shaped LRAC curve. The firm can adjust all inputs to find the most efficient scale of operation for each level of output.

    5. How do you find the long run total cost?

    To find the long run total cost, multiply the long run average total cost by the quantity produced at each output level. Alternatively, sum all the variable and fixed costs associated with production when all inputs are adjustable. The long run total cost curve is derived from the envelope of short-run total cost curves, representing the most cost-effective way to produce each output level.

    Prerequisites

    Understanding the concept of long run cost in economics is crucial, but it's equally important to grasp the foundational knowledge that supports this topic. One of the most essential prerequisite topics is short run cost. This concept is fundamental to comprehending the broader implications of long run cost analysis and decision-making in business and economics.

    Short run cost serves as a stepping stone to understanding long run cost dynamics. In the short run, firms face constraints that limit their ability to adjust all factors of production. This time frame is characterized by the presence of both fixed and variable costs. By mastering the principles of short run cost curves, students can more easily grasp how these concepts evolve in the long run scenario.

    The relationship between short run and long run costs is intricate and vital for a comprehensive understanding of economic theory. While short run costs deal with immediate production decisions, long run costs consider all factors of production as variable. This shift in perspective allows firms to make more comprehensive decisions about their production processes, scale, and overall efficiency.

    Students who have a solid grasp of short run cost concepts will find it easier to navigate the complexities of long run cost analysis. They will be better equipped to understand how firms can adjust their scale of operations over time, leading to economies or diseconomies of scale. This knowledge is crucial for analyzing business strategies and market structures in various economic scenarios.

    Moreover, the transition from short run to long run cost analysis helps in understanding how firms make decisions about entering or exiting markets. It provides insights into how businesses plan for future growth, adapt to changing market conditions, and strive for optimal efficiency in their operations.

    By thoroughly studying short run cost principles, students build a strong foundation for exploring more advanced economic concepts. This knowledge enables them to better comprehend the factors influencing long-term business decisions, industry dynamics, and overall market equilibrium. The ability to connect short run and long run cost analyses is a valuable skill in both academic economics and real-world business applications.

    In conclusion, mastering the prerequisite topic of short run cost is essential for a comprehensive understanding of long run cost. It provides the necessary context and analytical tools to explore more complex economic scenarios and business strategies. Students who invest time in solidifying their knowledge of short run costs will find themselves better prepared to tackle the challenges and nuances of long run cost analysis, ultimately enhancing their overall grasp of economic principles and their practical applications.