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cost function

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  • 1. ` Cost Analysis and Estimation
  • 2. What Makes Cost Analysis Difficult?
    • Link Between Accounting and Economic Valuations
      • Accounting and economic costs often differ.
    • Historical Versus Current Costs
      • Historical cost is the actual cash outlay.
      • Current cost is the present cost of previously acquired items.
    • Replacement Cost
      • Cost of replacing productive capacity using current technology.
  • 3. Opportunity Cost
    • Opportunity Cost Concept
      • Opportunity cost is foregone value.
      • Reflects second-best use.
    • Explicit and Implicit Costs
      • Explicit costs are cash expenses.
      • Implicit costs are noncash expenses.
  • 4. Incremental and Sunk Costs in Decision Analysis
    • Incremental Cost
      • Incremental cost is the change in cost tied to a managerial decision.
      • Incremental cost can involve multiple units of output.
        • Marginal cost involves a single unit of output.
    • Sunk Cost
      • Irreversible expenses incurred previously.
      • Sunk costs are irrelevant to present decisions.
  • 5. Short-run and Long-run Costs
    • How Is the Operating Period Defined?
      • At least one input is fixed in the short run.
      • All inputs are variable in the long run.
    • Fixed and Variable Costs
      • Fixed cost is a short-run concept.
      • All costs are variable in the long run.
  • 6. Short-run Cost Curves
    • Short-run Cost Categories
      • Total Cost = Fixed Cost + Variable Cost
      • For averages, ATC = AFC + AVC
      • Marginal Cost, MC = ∂TC/∂Q
    • Short-run Cost Relations
      • Short-run cost curves show minimum cost in a given production environment.
  • 7. Short Run Cost Graphs AFC Q Q 1. 2. AVC 3. Q AFC AVC ATC MC MC intersects lowest point of AVC and lowest point of ATC. When MC < AVC, AVC declines When MC > AVC, AVC rises
  • 8. Relationships Among Cost & Production Functions
    • AP & AVC are inversely related. (ex: one input)
    • AVC = WL /Q = W/ (Q/L) = W/ AP L
      • As AP L rises, AVC falls
    • MP and MC are inversely related
    • MC = dTC/dQ = W dL/dQ = W / (dQ/dL) = W / MP L
      • As MP L declines, MC rises
    prod. functions cost functions MP L L MC AP AVC Q Q cost
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  • 13. Long-run Cost Curves
    • Economies of Scale
    • Long-run cost curves show minimum cost in an ideal environment.
  • 14. Long Run Cost Functions
    • All inputs are variable (can adjust) in the long run.
    • LAC is long run average cost
      • ENVELOPE of SAC curves
    • LMC is flatter than SMC curves.
    • The optimal plant size for a given output Q 2 is plant size 2. (A SR concept.)
    • However, the optimal plant size occurs at Q 3 , which is the lowest cost point overall. (A LR concept.)
    Q LAC LMC SAC 2 SMC 2 Q 2 Q 3
  • 15. Long Run Cost Function (LAC) Envelope of SAC curves
  • 16. Cost Elasticity and Economies of Scale
    • Cost elasticity is ε C = ∂C/C ÷ ∂Q/Q.
    • ε C < 1 means falling AC, increasing returns.
    • ε C = 1 means constant AC constant returns.
    • ε C > 1 means rising AC, decreasing returns.
  • 17. Long-run Average Costs
  • 18. Economists think that the LAC is U-shaped
    • Downward section due to:
      • Product-level economies which include specialization and learning curve effects.
      • Plant-level economies , such as economies in overhead, required reserves, investment, or interactions among products (economies of scope).
      • Firm-level economies which are economies in distribution and transportation of a geographically dispersed firm, or economies in marketing, sales promotion, or R&D of multi-product firms.
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    • Flat section of the LAC
      • Displays constant returns to scale
      • The minimum efficient scale (MES) is the smallest scale at which minimum per unit costs are attained.
    • Upward rising section of LAC is due to:
      • Diseconomies of scale. These include transportation costs, imperfections in the labor market, and problems of coordination and control by management.
      • The maximum efficient scale (Max ES) is the largest scale before which unit costs begin to rise.
      • Modern business management offers techniques to avoid diseconomies of scale through profit centers, transfer pricing, and tying incentives to performance.
    CRS region MES Max ES DRS LAC
  • 20. Economies of Scope
    • Economies of Scope Concept
      • Scope economies are cost advantages that stem from producing multiple outputs.
      • Big scope economies explain the popularity of multi-product firms.
      • Without scope economies, firms specialize.
    • Exploiting Scope Economies
      • Scope economics often shape competitive strategy for new products.
  • 21. Cost-volume-profit Analysis
    • Cost-volume-profit Charts
      • Cost-volume-profit analysis shows effects of varying scale.
      • Breakeven analysis shows zero profit points of cost coverage.
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