Lecture on Return to Scale, Time Scale, and Return to Scope

Introduction

• Topics discussed:
  • Return to Scale
  • Time Scale
  • Return to Scope

Return to Scale

• Production Technology
  • Represented by an isoquant or a production function
  • Examined what happens if inputs are scaled by a factor of Lambda (λ)
• Key Concepts:
  • Constant Return to Scale (CRS): Output increases exactly by factor of λ
  • Increasing Return to Scale (IRS): Output increases by more than factor of λ
  • Decreasing Return to Scale (DRS): Output increases by less than factor of λ
• Four Possible Cases
  • CRS for all input combinations
  • IRS for all input combinations
  • DRS for all input combinations
  • Combination: CRS in some ranges, IRS in others, and DRS in the rest

Logic Behind Return to Scale

• CRS
  • Replication Argument: Replicating the process exactly, e.g., 2 units of input giving 2 units of output
  • Assumptions: Additivity and divisibility
• IRS
  • Example: Making a box with steel. Doubling input increases output by a cube factor
  • Access to better production technology at larger scale
  • Probabilistic Efficiency: Larger scale reduces errors and stabilizes customer behavior
• DRS
  • Existence of unaccounted factors (e.g., limited classroom size impacting teaching output)
  • Example: Managerial inefficiencies at larger scales

Return to Scale Graphs

• Graphical Representation of Average Cost
  • CRS: Constant average cost
  • IRS: Decreasing average cost
  • DRS: Increasing average cost
• Graphical Representation of Total Cost
  • CRS: Linear increase
  • DRS: Increasing rate
  • IRS: Decreasing rate

Time Scale

• Short Run vs. Long Run
  • Short Run: At least one factor of production cannot be varied (e.g., capital)
  • Long Run: All factors can be varied
  • Cost: Sum of wage (W) and rental (R), with capital cost being fixed in short run
• Graphical Understanding
  • Short run shows higher costs due to inflexibility
  • Long run minimizes cost by varying all production factors

Return to Scope

• Definition: Efficiencies gained when producing multiple types of outputs
• Comparison with Return to Scale: More items/different products vs. more output of a single item
• Example: Boeing producing both civil and defense airplanes
• Counterexample: Pet food supplier facing increased costs with more varieties

Conclusion

• Return to Scale, Time Scale, and Return to Scope evaluated
• Practical examples and theoretical explanations provided

Note: Always consider the context when evaluating returns to scale or scope.