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COSTS

Lecture 10
RETURNS TO SCALE


Chapter 7        2
BIG CITIES
• Metropolis twice the size of one, number of
  gas stations, length of pipelines, infrastructure
  decreases by 15%

• Why?




                         3
Narayan
                Hridalaya
• Provide health care at full price
To patients from well to do background

• These patients subsidize `poor’ patients
• Run at a profit of 7.7%
• Why is Narayan Hridalaya able to do this?


                     4
Narayan
                Hridalaya
• Number of Beds, 2001: 225

• Current No. of Beds across India: 30,000



• How does number of beds play a role in
  profits?

                      5
Returns to Scale
• Rate at which output increases as inputs are
  increased proportionately

  – Increasing returns to scale
  – Constant returns to scale
  – Decreasing returns to scale




                          6
Returns to Scale
• Increasing returns to scale: output more than
  doubles when all inputs are doubled

  – What happens to the isoquants?




                        7
Increasing Returns to Scale
  Capital
(machine                                   The isoquants
  hours)                            A
                                           move closer
                                           together



        4

                               30

        2                 20
                     10
                                        Labor (hours)
            5   10
                 8
Increasing Returns to Scale


      – If input is doubled, output will more than double

      – To double output, input is less than doubled

      – AC decreases at all levels of output




Chapter 7                     9
Increasing Returns to Scale
•       As output increases, firm’s AC of producing is
        likely to decline to a point
      1. On a larger scale, workers can better specialize
      2. Scale can provide flexibility – managers can
         organize production more effectively
      3. Firm may be able to get inputs at lower cost if
         can get quantity discounts. Lower prices might
         lead to different input mix.


Chapter 7                     10
Returns to Scale
• Constant returns to scale: output doubles
  when all inputs are doubled


  –   Isoquants are equidistant apart




                            11
Returns to Scale
  Capital
(machine
                                          A
  hours)
            6
                                                   30

            4                                  Constant Returns:
                                                 Isoquants are
                                      2         equally spaced
                                      0
            2

                            10
                                              Labor (hours)
                  5   10         15
                       12
Constant Returns to Scale

      – If input is doubled, output will double

      – To double output, input has to be doubled

      – AC cost is constant at all levels of output




Chapter 7                      13
Returns to Scale
• Decreasing returns to scale: output less than
  doubles when all inputs are doubled


  –   Isoquants become farther apart




                          14
Decreasing Returns to Scale

      – If input is doubled, output will less than double

      – To double output, input has to more than double

      – AC increases at all levels of output




Chapter 7                     15
Long Run Costs
•       At some point, AC will begin to increase
      1. Factory space and machinery may make it more
         difficult for workers to do their jobs efficiently

      2. Managing a larger firm may become more
         complex and inefficient as the number of tasks
         increase

      3. Bulk discounts can no longer be utilized. Limited
          availability of inputs may cause price to rise.

Chapter 7                      16
Long Run Versus Short Run Cost
                       Curves
• Long-run marginal cost leads long-run average
  cost:
      – If LMC < LAC, LAC will fall
      – If LMC > LAC, LAC will rise
      – Therefore, LMC = LAC at the minimum of LAC

• In special case where LAC is constant, LAC and
  LMC are equal

Chapter 7                   18
Long Run Average and Marginal Cost
              Cost
        ($ per unit
          of output            LMC

                                     LAC




                      A




                                           Output

Chapter 7                 19
Economies and Diseconomies of Scale
• Economies of Scale
      – Increase in output is greater than the increase in
        inputs
• Diseconomies of Scale
      – Increase in output is less than the increase in
        inputs
• U-shaped LAC shows economies of scale for
  relatively low output levels and diseconomies
  of scale for higher levels

Chapter 7                      20
Long Run Costs
• Increasing Returns to Scale
      – Output more than doubles when the quantities of
        all inputs are doubled


• Economies of Scale
      – Doubling of output requires less than a doubling
        of cost



Chapter 7                     21
COST OUTPUT ELASTICITY


Chapter 7        22
Cost-Output Elasticity

• EC is the percentage change in the cost of
  production resulting from a 1-percent increase
  in output



             EC    CC             MC
                             QQ        AC

 Chapter 7              23
• EC is equal to 1, MC = AC
      – Costs increase proportionately with output
      – Neither economies nor diseconomies of scale
• EC < 1 when MC < AC
      – Economies of scale
      – Both MC and AC are declining
• EC > 1 when MC > AC
      – Diseconomies of scale
      – Both MC and AC are rising


Chapter 7                       24
MC AND AC CURVES


Chapter 7       32
Determinants of Short Run Costs – An
             Example
• Assume the wage rate (w) is fixed relative to
  the number of workers hired
• Variable costs is the per unit cost of extra
  labor times the amount of extra labor: wL

                         VC     w L
               MC
                          q      q

Chapter 7               33
Determinants of Short Run Costs – An
             Example
            • Remembering that
                                              Q
                                MPL
                                              L
             And rearranging


                                              L   1
                    L for a 1 unit        Q
                                              Q   MPL


Chapter 7                            34
Determinants of Short Run Costs – An
             Example
            • We can conclude:
                                   w
                       MC
                                  MPL

             …and a low marginal product (MPL) leads
              to a high marginal cost (MC) and vice
              versa

Chapter 7                    35
LONG RUN COSTS


Chapter 7       36
Costs2
Costs2

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Costs2

  • 3. BIG CITIES • Metropolis twice the size of one, number of gas stations, length of pipelines, infrastructure decreases by 15% • Why? 3
  • 4. Narayan Hridalaya • Provide health care at full price To patients from well to do background • These patients subsidize `poor’ patients • Run at a profit of 7.7% • Why is Narayan Hridalaya able to do this? 4
  • 5. Narayan Hridalaya • Number of Beds, 2001: 225 • Current No. of Beds across India: 30,000 • How does number of beds play a role in profits? 5
  • 6. Returns to Scale • Rate at which output increases as inputs are increased proportionately – Increasing returns to scale – Constant returns to scale – Decreasing returns to scale 6
  • 7. Returns to Scale • Increasing returns to scale: output more than doubles when all inputs are doubled – What happens to the isoquants? 7
  • 8. Increasing Returns to Scale Capital (machine The isoquants hours) A move closer together 4 30 2 20 10 Labor (hours) 5 10 8
  • 9. Increasing Returns to Scale – If input is doubled, output will more than double – To double output, input is less than doubled – AC decreases at all levels of output Chapter 7 9
  • 10. Increasing Returns to Scale • As output increases, firm’s AC of producing is likely to decline to a point 1. On a larger scale, workers can better specialize 2. Scale can provide flexibility – managers can organize production more effectively 3. Firm may be able to get inputs at lower cost if can get quantity discounts. Lower prices might lead to different input mix. Chapter 7 10
  • 11. Returns to Scale • Constant returns to scale: output doubles when all inputs are doubled – Isoquants are equidistant apart 11
  • 12. Returns to Scale Capital (machine A hours) 6 30 4 Constant Returns: Isoquants are 2 equally spaced 0 2 10 Labor (hours) 5 10 15 12
  • 13. Constant Returns to Scale – If input is doubled, output will double – To double output, input has to be doubled – AC cost is constant at all levels of output Chapter 7 13
  • 14. Returns to Scale • Decreasing returns to scale: output less than doubles when all inputs are doubled – Isoquants become farther apart 14
  • 15. Decreasing Returns to Scale – If input is doubled, output will less than double – To double output, input has to more than double – AC increases at all levels of output Chapter 7 15
  • 16. Long Run Costs • At some point, AC will begin to increase 1. Factory space and machinery may make it more difficult for workers to do their jobs efficiently 2. Managing a larger firm may become more complex and inefficient as the number of tasks increase 3. Bulk discounts can no longer be utilized. Limited availability of inputs may cause price to rise. Chapter 7 16
  • 17.
  • 18. Long Run Versus Short Run Cost Curves • Long-run marginal cost leads long-run average cost: – If LMC < LAC, LAC will fall – If LMC > LAC, LAC will rise – Therefore, LMC = LAC at the minimum of LAC • In special case where LAC is constant, LAC and LMC are equal Chapter 7 18
  • 19. Long Run Average and Marginal Cost Cost ($ per unit of output LMC LAC A Output Chapter 7 19
  • 20. Economies and Diseconomies of Scale • Economies of Scale – Increase in output is greater than the increase in inputs • Diseconomies of Scale – Increase in output is less than the increase in inputs • U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels Chapter 7 20
  • 21. Long Run Costs • Increasing Returns to Scale – Output more than doubles when the quantities of all inputs are doubled • Economies of Scale – Doubling of output requires less than a doubling of cost Chapter 7 21
  • 23. Cost-Output Elasticity • EC is the percentage change in the cost of production resulting from a 1-percent increase in output EC CC MC QQ AC Chapter 7 23
  • 24. • EC is equal to 1, MC = AC – Costs increase proportionately with output – Neither economies nor diseconomies of scale • EC < 1 when MC < AC – Economies of scale – Both MC and AC are declining • EC > 1 when MC > AC – Diseconomies of scale – Both MC and AC are rising Chapter 7 24
  • 25. MC AND AC CURVES Chapter 7 32
  • 26. Determinants of Short Run Costs – An Example • Assume the wage rate (w) is fixed relative to the number of workers hired • Variable costs is the per unit cost of extra labor times the amount of extra labor: wL VC w L MC q q Chapter 7 33
  • 27. Determinants of Short Run Costs – An Example • Remembering that Q MPL L  And rearranging L 1 L for a 1 unit Q Q MPL Chapter 7 34
  • 28. Determinants of Short Run Costs – An Example • We can conclude: w MC MPL  …and a low marginal product (MPL) leads to a high marginal cost (MC) and vice versa Chapter 7 35

Editor's Notes

  1. What can you say about average cost?