Long Run Cost Curves

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Lecture 10 Long Run Cost Curves
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Cost Minimization in the Long Run

• In the last lecture we showed that the firm
  minimizes cost by equating the slope of the
  isoquant with the slope of the cost line
• Figure 6 below shows the factor substitution
  effect of a fall in the wage.

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Chapter 9, Figure 6Effect of a Fall in the Wage
Rate on the Cost Minimum
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The Firms Long Run Expansion Path

• Now consider cost minimization at different
  outputs as in Figure 7 below.
• The result of repeated cost minimization is a
  one-to-one relationship between cost and outputa
  cost function.
• The total cost function is shown in Figure 8.

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Chapter 9, Figure 7The Expansion Path and The
Long-Run Cost Curve (a)
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Chapter 9, Figure 8The Expansion Path and The
Long-Run Cost Curve (b)
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The Firms Long Run Expansion Path

• In deriving this total cost function three
  assumptions are being made
• 1) there are no fixed costs in the long run
• 2) output rises in the same proportion as labor
  and capital inputs (constant returns).
• 3) factor prices stay the same.
• The third assumption makes sense few firms are
  big enough to change wages.

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The Firms Long Run Expansion Path

• But the first assumption can be called into
  question. Can a company avoid start-up costs?
• The second assumption is debatable too what if
  important inputs are held constant?
• But if the assumptions hold you will get linear
  total cost as shown in Figure 8.

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A More General Analysis of Long Run Cost

• Figure 9 shows a more general situation, though
  setup costs are still neglected in this figure.
• As shown in the top panel total cost C at first
  rises at a decreasing rate (some inputs are
  underutilized at first), and then at a decreasing
  rate (eventually, some inputs are strained to
  capacity).

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Chapter 9, Figure 9 Long-Run Cost Curves
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A More General Analysis of Long Run Cost

• This means that average cost (AC) falls at first
  and then increases.
• In the lower panel of Figure 9 notice that
• When AC is falling, MC is below AC
• When AC is rising, MC is above AC
• When AC is at a minimum, MCAC
• Most efficient size occurs at q since AC equals
  resource cost per unit produced.

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A More General Analysis of Long Run Cost

• Each segment of the average cost curve in Figure
  9 reflects a particular returns to scale.
• Falling AC implies increasing returns to scale
• Rising AC implies decreasing returns to scale
• At the AC minimum constant returns to scale
  applies

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L-Shaped Average Cost

• In some industries fixed start-up costs generate
  falling average cost or increasing returns to
  scale.
• This seems to be the case in the cement industry
  see Figure 10.
• Of course the data may stop just before AC turns
  up, yielding part of the curve, which is then
  L-shaped.

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Chapter 9, Figure 10Average Cost of Cement Firms
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Long Run and Short Run AC

• In the long run a firm chooses the plant size
  (capital, K) that minimizes the total and average
  cost of every output.
• But K is fixed in the short run.
• The firm increases output in the short run by
  moving along the flat expansion path in figure 11
  using labor alone.
• This is not cost-efficient in the long run.

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Chapter 9, Figure 11Long-Run and
Short-Run Expansion Paths
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Long Run and Short Run AC

• In the long run the firm can increase both
  capital and labor, where the returns to scale are
  more favorable.
• Thus long run AC (LRAC) is less than or equal to
  short run AC (SRAC) in figure 12.
• LRAC is often called an envelope curve.

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Chapter 9, Figure 12Long Run AC, the Envelope of
Short Run AC Curves
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Examples of LRAC Curves

• The next two figures show examples of the long
  run average cost curve.
• The Norwegian printing firm has a flat or
  constant returns LRAC in Figure 13.
• The US oil pipeline example in Figure 14 shows
  declining LRAC or increasing returns. Note how
  the pipeline diameter increases with the
  through-put of oil.

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Chapter 9, Figure 13Long Run Cost Curves In A
Norwegian Printing Firm
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Chapter 9, Figure 14Long-Run Cost Curves For US
Oil Pipelines
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Learning by Doing

• One reason why costs are less in the long run is
  learning by doing.
• Definition
• Learning by doing refers to a decline in current
  cost caused by an increase in past production.
• Figure 15 illustrates this situation.

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Chapter 9, Figure 15--Learning by Doing
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Economies of Scope and Multiple Product Firms

• Sometimes its cheaper to produce goods together
  than separately.
• Definition
• An economy of scope (SC) occurs when
• Cockburn and Henderson (1996) found economies of
  scope in drug research.