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Chapter 8

Producers in the Long Run

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Learning Objectives

1. Discuss why profit maximization requires firms to equate the marginal product per dollar spent for all factors. (We skip this—saving it for intermediate micro.)

2. Explain why firms will use more of the factors the prices of which have fallen, and less of the factors the prices of which have increased.

3. Describe the relationship between short-run and long-run cost curves.

4. Explain the importance of technological change and why firms are often motivated to innovate to improve their production methods. [We will skip this]

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8.1 The Long Run: No Fixed Factors

In the long run, uses of ALL inputs are variable, and there are numerous ways to produce any given output.

How does a firm choose how to produce?

In the short run, the only way to produce a given level of output is to adjust the input of the variable factors.

Two objectives:

1. Don’t waste society’s scarce resources, and

2. Produce the chosen output at least cost.

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Technological Efficiency & Economic Efficiency

• The decision of “how to produce” is made on the basis of what economists call “economic efficiency” –production at least cost

• This is not the same as “technological efficiency,” but a process cannot be economically efficient unless it is also technologically efficient.

• A process is technologically efficient if there is no other known way of producing– (a) the same output with less of at least one input and no more

of any other, or equivalently– (b) more output using the same quantities of all inputs

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Technological Efficiency

• Three ways of producing 100 units of output

• Method “A” uses same capital, less labour than “B” – “B” is not efficient (wastes resources)

• Method “A” uses same labour, less capital than “C” – “C” is not efficient (wastes resources)

• Method “A” dominates Methods “B” and “C”

Method Labour Capital

A 75 5

B 80 5

C 75 6

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When No Method is Dominated?

• Technological efficiency is necessary for economic efficiency, but this criterion is not sufficient in all cases

• If production takes place using more than a single input, there can be alternative input combinations (technologies) for producing the same output, none of which are dominated in a technological efficiency sense.

• How would a firm choose in such a situation?

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Three Methods of Producing 100 Units

Labour Input

Capital Input

Method I Method II Method III

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100 75

5 20

25

How does the firm choose which method to use?

What other information does the firm need?

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Need Factor Prices, Compute Total Cost

Price of Capital

Price of Labour

Labour Input

Capital Input

Method I Method II Method III

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100 75

5 20

25

$2,150$950$900

$1,120 $950 $1,050

$850$900$30 $1,090

$40

$100

$10

$10

$6

3*$100+100*$6

3*$30 + 100*$10

20*$40 + 25*$10

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The principle of substitution implies that a firm’s method of production will change if the relative prices of factors change. Relatively more of the cheaper factor and relatively less of the more expensive factor will be used.

Substitution plays a central role in resource allocation because it describes how individual firms respond to changes in relative factor prices that are caused, in turn, by the changing scarcities of factors in the economy as a whole.

Holding output constant, if it is possible to reduce total cost by substituting one factor for another, then the firm is not using the least costly combination of factors.

Principle of Substitution

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Long-Run Cost Curves

When all factors of production can be varied, there exists a least average-cost method of producing any level of output.

The long-run average cost (LRAC) curve is the boundary between cost levels that are attainable (with given technology and factor prices) and those that are unattainable...

even when the use of ALL inputs (plant size, equipment, machinery [capital in general], as well as labour) can be varied by the firm.

To illustrate…

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Long-Run Cost Curves

More capital means higher average and marginal product of labour (labour cost per unit of output falls), but…

Consider production using various plant sizes or various amounts of machinery (amounts of capital).

More capital means higher total fixed cost.

For LOW rates of output, it makes little sense to use a lot of capital (very high average fixed cost), but...

For HIGHER rates of output, fixed cost of larger amounts of capital can be spread (averaged) over more units, and

Lower labour cost per unit (from higher labour productivity) outweighs the increase in fixed cost

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Various Short-Run Total Cost Curves

Co

st

($/U

nit)

TC-K1

TC-K2

TC-K3

TC-K4

TC-K5

K1 < K2 < K3 < K4 < K5

Output per PeriodUse K1 Use K2 Use K3

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SRAC-K1

SRAC-K2 SRAC-K3

SRAC-K4

SRAC-K5

Co

st (

$/U

nit)

K1 < K2 < K3 < K4 < K5

LRAC

Short-Run and Long-Run Average Cost Curves

Output per Period

Use K1 Use K2 Use K3 Use K4 Use K5

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Co

st (

$/U

nit)

LRAC

Long-Run Average Cost Curve

Output per Period

Attainable (High) Levels of Cost

Unattainable (Low) Levels of Cost

The Long Run Average Cost Curve serves to divide Attainable from Unattainable Levels of Cost (Can Do Worse, Cannot Do Better)

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SRATC2SRATC1 SRATC3SRATC4 SRATC5

LRAC

Co

st p

er U

nit

No short-run cost curve can fall below the long-run curve because the LRAC curve shows the lowest attainable cost for each possible level of output.

Note that the LRAC does NOT pass through the minimum point of a Short Run Average Cost if the tangency lies on the downward or upward sloping portion of LRAC

Output per Period

Each SRATC curve is tangent to the LRAC curve at the level of output for which the quantity of the fixed factor is optimal, and lies above it for all other levels of output.

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Over the range from zero to qM, the firm has falling unit costs.

This implies economies of scale (increasing returns to scale).

Long-Run Cost Curves

$/Unit

qM

Over the range from zero to qM to qD the firm has constant unit costs.

This implies constant returns to scale.

Inc. Ret. to Sc. Const. Ret. to Sc.

qD

LRAC

Such a decreasing-cost firm is said to have increasing returns, which typically result from greater specialization made possible by the division of labour.

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$/Unit

qM

For output rates greater than qD the firm has rising unit costs.

This implies diseconomies of scale (decreasing returns to scale).

Inc. Ret. to Sc. Const. Ret. to Sc. Decr. Ret. to Sc.

qD

LRAC

This typically results from difficulties in managing and controlling an enterprise as its size increases (increasing costs of control).

18Returns to Scale & LRAC

$/Unit

qM

What is it that is increasing, constant, or decreasing?

Output per unit of (composite) input, certainly, but also profit per unit

Inc. Ret. to Sc. Const. Ret. to Sc. Decr. Ret. to Sc.

qD

P

LRAC

FOR ANY FIXED PRICE,

decreasing LRAC implies increasing profit per unit…

constant LRAC implies constant profit per unit…

increasing LRAC implies decreasing profit per unit.

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Difference Between “Returns to Scale”

and “Diminishing Marginal Product”

• When the use of ALL inputs changes in the SAME proportion, we examine the resulting change in output

• If the change in output is proportionally LESS than the change in the use of ALL inputs, we have decreasing returns to scale…

• If the change in output is proportionally MORE than the change in the use of ALL inputs, we have increasing returns to scale…

• “Returns to Scale” relates to the change in output that results from changing ALL inputs by the same proportion (multiplying by the SAME positive number)

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Difference Between “Returns to Scale”

and “Diminishing Marginal Product”

• By contrast, “diminishing marginal product” refers to the change in output associated with changing the use of ONE input…

holding the amounts of other input(s) FIXED

• It is possible for a firm’s technology to exhibit increasing returns to scale at or around some level of output, while simultaneously experiencing diminishing marginal product of one input

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SRAC-K1 SRAC-K2

Co

st (

$/U

nit)

LRAC

“Returns to Scale” vs. “Diminishing Marginal Product”

Output per Period

Over the range q1 to q2, the firm experiences increasing returns to scale (falling LRAC) if ALL inputs are increased in the same proportion.

q1 q2

Over the same range q1 to q2, the firm experiences diminishing marginal product of the variable factor (labour), as shown by the rising SRAC-K1 curve FOR FIXED K = K1.

Short run cost rises as output is increased to q2 because K1 is the wrong amount of capital for producing q2 (should use K2 to minimize cost).

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“Returns to Scale” and LRAC Examples

• If output increases by a SMALLER proportion than does input use, output increases at a Decreasing rate, and LRAC rises

• If output increases by the SAME proportion as does input use, output increases at a Constant rate, and LRAC is unchanging (horizontal)

• If output increases by a LARGER proportion than does input use, output increases at an Increasing rate, and LRAC falls

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Capital UsedLabour Used

OutputCapital CostLabour CostTotal Cost

Average Cost $30 $90 $120 $150$60

111

$20$10$30

442

$80$40

$120

94

2.45$180$90

$270

$320$160$480 $750

$250$500

993 4

1616

4.47

1625

25255

Capital, Labour Output Quantity

Ou

tput

Qua

ntit

y $/Unit

PC = r = $20 PL = w = $10

1

2

3

4

5

5 10 15 20 25 1 2 3 4 5

$30

$60

$90

$120

$150

Decreasing Returns to Scale, Rising LRAC

LRAC

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“Returns to Scale” and LRAC Examples

• If output increases by a SMALLER proportion than does input use, output increases at a Decreasing rate, and LRAC rises

• If output increases by the SAME proportion as does input use, output increases at a Constant rate, and LRAC is unchanging (horizontal)

• If output increases by a LARGER proportion than does input use, output increases at an Increasing rate, and LRAC falls

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Capital UsedLabour Used

OutputCapital CostLabour CostTotal Cost

Average Cost $30 $30 $30 $30$30

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$20$10$30

444

$80$40

$120

946

$180$90

$270

$320$160$480 $750

$250$500

999 16

1616

20

1625

252525

Capital, Labour Output Quantity

Ou

tput

Qua

ntit

y $/Unit

PC = r = $20 PL = w = $10

5

10

15

20

25

5 10 15 20 25 5 10 15 20 25

$10

$20

$30

$40

$50

Constant Returns to Scale, Constant LRAC

1

LRAC

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“Returns to Scale” and LRAC Examples

• If output increases by a SMALLER proportion than does input use, output increases at a Decreasing rate, and LRAC rises

• If output increases by the SAME proportion as does input use, output increases at a Constant rate, and LRAC is unchanging (horizontal)

• If output increases by a LARGER proportion than does input use, output increases at an Increasing rate, and LRAC falls

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Capital UsedLabour Used

OutputCapital CostLabour CostTotal Cost

Average Cost $30 $3.33 $0.47 $0.05$15

111

$20$10$30

224

$40$20$60

329

$60$30$90

$80$40

$120 $150$50

$100

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27 256

44

1024

45

55

3125

Capital, Labour Output Quantity

Ou

tput

Qua

ntit

y $/Unit

PC = r = $20 PL = w = $10

50

100

150

200

250

1 2 3 4 5 50 100 150 200 250

$3

$6

$9

$12

$15

LRAC

Increasing Returns to Scale, Falling LRAC

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To recap:

• falling LRAC ==> increasing returns to scale;

• constant LRAC ==> constant returns to scale;

• rising LRAC ==> decreasing returns to scale.

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If there is a range over which the firm experiences Constant Returns to Scale (the Long Run Average Cost is constant)…

and if, over that range, the LRAC is at its minimum, then there are many output levels satisfying the definition of Efficient Scale

Efficient Scale, MINIMUM Efficient Scale, Capacity

Any output level that can be produced at the LOWEST Long Run Average Cost is characterized as an Efficient Scale of output.

The SMALLEST of these flow rates of output at which the firm attains minimum LRAC is called the firm’s Minimum Efficient Scale of output.

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Minimum Efficient Scale

$/Unit

Output per Period

Efficient ScaleOutput Rates

LRAC

Minimum Efficient Scale

qMES

The SMALLEST of these flow rates of output at which the firm attains minimum LRAC is called the firm’s Minimum Efficient Scale of output.

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Shifts in LRAC Curves

We saw in Chapter 7 how changes in either technology or factor prices cause the entire family of short-run costs curves to shift. The same is true for long-run cost curves.

A rise in factor prices shifts short-run and long-run average cost curves upward.

A fall in factor prices or a technological improvement shifts short-run and long-run average cost curves downward.

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