Long run cost

Long run cost

Lessons

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.

  • Introduction
    Short Run Cost Overview:
    a)
    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

    b)
    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

    c)
    Long-Run Average Cost
    • LRAC: Long Run Average Cost
    • Lowest attainable cost across all ATC curves
    • What it looks like

    d)
    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