Long-run Cost Curves
The Long Run
• In the short run, with a predetermined output level and
only one factor variable, there is only one technically
possible way of achieving that output.
• In the long run, all factors are variable. There is an
additional decision to make regarding how to produce
the predetermined output level.
• The firm has to make a choice from the many
technically possible methods by which the desired
output level will be produced.
• The firm has to decide to adopt a technique that uses
much capital and little labour or one that uses less
capital but more labour.
• Firms make such decisions using the simple rule of cost
minimization- where the firm chooses the least costly
method of production from the alternatives open to it.
The Principle of Substitution
• A firm producing with two inputs ( labour and
capital) will minimize the cost of producing
any given output when the following
condition is satisfied:
•
𝑀𝑃𝑘
𝑝𝑘
𝑀𝑃𝑙
=
𝑝𝑙
• Whenever the two sides of the equation
above are not equal, there are factor
substitutions that will reduce the cost of
producing any given output.
• If the LHS is greater than the RHS, then the
firm will substitute more capital units for
labour units since and additional cedi spent on
capital produces more output than labour
• For example: What substitution would the
firm make if capital costs ghc10 a unit and
has a marginal product of 40 units of output
while labour costs ghc 2 a unit and has a
marginal product of 4 units of output.
Discuss.
Discussion Question
• Suppose that a firm is producing where the
cost minimizing condition is met but the cost
of labour increases while the cost of capital
remains unchanged. What will the firm decide
in terms of substituting one input for the
other.
• The least cost method of producing any
output will now use less labour and more
capital than was required before the factor
prices changed.
Making Long-Run Production Decisions
• To make their long-run decisions:
– Firms look at costs of various inputs and the
technologies available for combining these inputs.
– Then decide which combination offers the lowest
cost.
• The firm makes long-run decisions on the basis of
the expected costs and expected usefulness of
inputs.
• To make long run decisions, the firm considers two
main types of efficiencies- technical and economic
• Technical efficiency – as few inputs as possible
are used to produce a given output.
• Technical efficiency is efficiency that does not
consider cost of inputs.
• Economically efficient – the method that
produces a given level of output at the lowest
possible cost.
• It is the least-cost technically efficient process.
The Long Run Cost Curves
• In the long run, a firm has many sizes to
choose from.
• The short run requires that scale be fixed—
only one or a few resources can be changed.
The Shape of the LRAC
• The law of diminishing marginal productivity
does not hold in the long run.
• All inputs are variable in the long run.
• The shape of the long-run cost curve is due to
the existence of economies and diseconomies
of scale.
Economics of Scale
• Scale means size.
• Economies of scale: the decrease in per unit costs as the quantity
of production increases and all resources are variable
– Gains from specialization: output increases by a greater
proportion than cost
– Spreading cost of lumpy inputs
• Diseconomies of scale: the increase in per unit costs as the
quantity of production increases and all resources are variable
– Increased layers of management→ communication and decision making
become more time consuming etc.
– Difficulty to screen misfits among employees etc.
• Constant returns to scale: unit costs remain constant as the
quantity of production is increased and all resources are variable.
What is the difference between
decreasing economies of scale and
diminishing marginal returns?
• Most industries experience both economies
and diseconomies of scale.
• The minimum efficient scale (MES) is the
minimum point of the long-run average-cost
curve
• the output level at which the cost per unit of
output is the lowest.
Long-Run Average Total Cost
Total Costs of
Labor
Quantity
11
12
13
14
15
16
17
18
19
20
$381
390
402
420
450
480
510
549
600
666
Total Cost of
Machines
$254
260
268
280
300
320
340
366
400
444
Total Costs =
TCL + TCM
Average Total
Costs = TC/Q
$635
650
670
700
750
800
850
915
1,000
1,110
$58
54
52
50
50
50
50
51
53
56
Costs per unit
Long-Run Average Total Cost Curve
$64
62
60
58
56
54
52
50
48
Average
total cost
Minimum efficient
level of production
11 12 13 14 15 16 17 18 19 20 Quantity
Costs per unit
Economies and Diseconomies of Scale
$64
62
60
58
56
54
52
50
48
Economies of
Scale
Constant
returns to
Scale
Diseconomies
of Scale
Average
total cost
11 12 13 14 15 16 17 18 19 20 Quantity
Graphing the LRATC Curve
Figure 5 Long-Run Average Total Cost
Dollars
ATC1
$4.00
ATC0
ATC2
3.00
C
D
B
A
2.00
LRATC
ATC3
E
1.00
0
30
Use 0
automated
lines
17
90
130
160 184
175 196
Use 1
automated
lines
250
Use 2
automated
lines
300
Use 3
automated
lines
Units of Output
The Shape of LRATC
• Economies of scale - LRATC decreases as
output increases
– LRATC curve slopes downward
• More likely to occur at lower levels of output
• Spreading costs of Lumpy inputs
• Diseconomies of scale - LRATC increases as
output increases
– LRATC curve slopes upward
• More likely at higher output levels
18
The Shape of LRATC
• Constant returns to scale - LRATC is unchanged as
output increases
– LRATC curve is flat
• U-shape of LRATC curve
– Economies of scale at relatively low levels of output
– Constant returns to scale at some intermediate levels
of output
– Diseconomies of scale at relatively high levels of
output
– The long-run and the short-run average cost curves
have the same U-shape, but the underlying causes of
these shapes differ.
19
The Shape Of LRATC
Figure 6 The Shape Of LRATC
Dollars
$4.00
3.00
LRATC
2.00
1.00
130
0
Economies of Scale
20
184
Constant
Returns to
Scale
Diseconomies of Scale
Units of Output
The Envelope Relationship
• Long-run costs are always less than or equal to short-run costs
because:
• In the long run, all inputs are flexible
• In the short run, some inputs are fixed
• There is an envelope relationship between
long-run and short-run average total costs.
Each short-run cost curve touches the longrun cost curve at only one point.
SRAC and LRAC
Technology and Innovation
• In the long run, technology is assumed to be
fixed. In the very long run however, technology
may change.
• Changes in Technology is as a result of inventions
and innovations.
• Invention and Innovation of new and improved
ways of production increases the productivity of
inputs which also leads to reduced cost of
production.
• The increased productivity of inputs imply that
the same quantities of inputs may then produce a
different quantity of output than before.
Reading Assignment
• Read on Technology and Innovation
• Urge to merge…