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Managerial Economics

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  • 1. Managerial Economics & Business Strategy Chapter 5 The Production Process and Costs
  • 2. Overview
    • I. Production Analysis
      • Total Product, Marginal Product, Average Product
      • Isoquants
      • Isocosts
      • Cost Minimization
    • II. Cost Analysis
      • Total Cost, Variable Cost, Fixed Costs
      • Cubic Cost Function
      • Cost Relations
    • III. Multi-Product Cost Functions
  • 3. Production Analysis
    • Production Function
      • Q = F(K,L)
      • The maximum amount of output that can be produced with K units of capital and L units of labor.
    • Short-Run vs. Long-Run Decisions
    • Fixed vs. Variable Inputs
  • 4. Total Product
    • Cobb-Douglas Production Function
    • Example: Q = F(K,L) = K .5 L .5
      • K is fixed at 16 units.
      • Short run production function:
      • Q = (16) .5 L .5 = 4 L .5
      • Production when 100 units of labor are used?
    • Q = 4 (100) .5 = 4(10) = 40 units
  • 5. Marginal Product of Labor
    • MP L =  Q/  L
    • Measures the output produced by the last worker.
    • Slope of the production function
  • 6. Average Product of Labor
    • AP L = Q/L
    • Measures the output of an “average” worker.
  • 7. Q=F(K,L) Increasing Marginal Returns Diminishing Marginal Returns Negative Marginal Returns Stages of Production Q L MP AP
  • 8. Isoquant
    • The combinations of inputs (K, L) that yield the producer the same level of output.
    • The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output.
    L
  • 9. Linear Isoquants
    • Capital and labor are perfect substitutes
    Q 3 Q 2 Q 1 Increasing Output L K
  • 10. Leontief Isoquants
    • Capital and labor are perfect complements
    • Capital and labor are used in fixed-proportions
    Q 3 Q 2 Q 1 K Increasing Output
  • 11. Cobb-Douglas Isoquants
    • Inputs are not perfectly substitutable
    • Diminishing marginal rate of technical substitution
    • Most production processes have isoquants of this shape
    Q 1 Q 2 Q 3 K L Increasing Output
  • 12. Isocost
    • The combinations of inputs that cost the producer the same amount of money
    • For given input prices, isocosts farther from the origin are associated with higher costs.
    • Changes in input prices change the slope of the isocost line
    K L C 1 C 0 L K New Isocost Line for a decrease in the wage (price of labor).
  • 13. Cost Minimization
    • Marginal product per dollar spent should be equal for all inputs:
    • Expressed differently
  • 14. Cost Minimization Q L K Point of Cost Minimization Slope of Isocost = Slope of Isoquant
  • 15. Cost Analysis
    • Types of Costs
      • Fixed costs (FC)
      • Variable costs (VC)
      • Total costs (TC)
      • Sunk costs
  • 16. Total and Variable Costs
    • C(Q): Minimum total cost of producing alternative levels of output:
      • C(Q) = VC + FC
    • VC(Q): Costs that vary with output
    • FC: Costs that do not vary with output
    $ Q C(Q) = VC + FC VC(Q) FC
  • 17. Fixed and Sunk Costs FC: Costs that do not change as output changes Sunk Cost: A cost that is forever lost after it has been paid $ Q FC C(Q) = VC + FC VC(Q)
  • 18. Some Definitions
    • Average Total Cost
      • ATC = AVC + AFC
      • ATC = C(Q)/Q
    • Average Variable Cost
      • AVC = VC(Q)/Q
    • Average Fixed Cost
      • AFC = FC/Q
    • Marginal Cost
      • MC =  C/  Q
    ATC AVC AFC $ Q MC
  • 19. Fixed Cost ATC AVC Q 0 AFC Fixed Cost Q 0  (ATC-AVC) = Q 0  AFC = Q 0  (FC/ Q 0 ) = FC $ Q ATC AVC MC
  • 20. Variable Cost AVC Variable Cost Q 0 Q 0  AVC = Q 0  [VC(Q 0 )/ Q 0 ] = VC(Q 0 ) $ Q ATC AVC MC
  • 21. ATC Total Cost Q 0 Q 0  ATC = Q 0  [C(Q 0 )/ Q 0 ] = C(Q 0 ) Total Cost $ Q ATC AVC MC
  • 22. Economies of Scale LRAC $ Output Economies of Scale Diseconomies of Scale
  • 23. Cubic Cost Function
    • C(Q) = f + a Q + b Q 2 + cQ 3
    • Marginal Cost?
      • Memorize:
    • MC(Q) = a + 2bQ + 3cQ 2
      • Calculus:
    • dC/dQ = a + 2bQ + 3cQ 2
  • 24. An Example
      • Total Cost: C(Q) = 10 + Q + Q 2
      • Variable cost function:
    • VC(Q) = Q + Q 2
      • Variable cost of producing 2 units:
    • VC(2) = 2 + (2) 2 = 6
      • Fixed costs:
    • FC = 10
      • Marginal cost function:
    • MC(Q) = 1 + 2Q
      • Marginal cost of producing 2 units:
    • MC(2) = 1 + 2(2) = 5
  • 25. Multi-Product Cost Function
    • C(Q 1 , Q 2 ): Cost of producing two outputs jointly
  • 26. Economies of Scope
    • C(Q 1 , Q 2 ) < C(Q 1 , 0) + C(0, Q 2 )
    • It is cheaper to produce the two outputs jointly instead of separately.
    • Examples?
  • 27. Cost Complementarity
    • The marginal cost of producing good 1 declines as more of good two is produced:
    •  MC 1 /  Q 2 < 0.
    • Examples?
  • 28. Quadratic Multi-Product Cost Function
    • C(Q 1 , Q 2 ) = f + aQ 1 Q 2 + (Q 1 ) 2 + (Q 2 ) 2
    • MC 1 (Q 1 , Q 2 ) = aQ 2 + 2Q 1
    • MC 2 (Q 1 , Q 2 ) = aQ 1 + 2Q 2
    • Cost complementarity: a < 0
    • Economies of scope: f > aQ 1 Q 2
    • C(Q 1 ,0) + C(0, Q 2 ) = f + (Q 1 ) 2 + f + (Q 2 ) 2
    • C(Q 1 , Q 2 ) = f + aQ 1 Q 2 + (Q 1 ) 2 + (Q 2 ) 2
    • f > aQ 1 Q 2 : Joint production is cheaper
  • 29. A Numerical Example:
    • C(Q 1 , Q 2 ) = 90 - 2Q 1 Q 2 + (Q 1 ) 2 + (Q 2 ) 2
    • Cost Complementarity?
    • Yes, since a = -2 < 0
    • MC 1 (Q 1 , Q 2 ) = -2Q 2 + 2Q 1
    • Economies of Scope?
    • Yes, since 90 > -2Q 1 Q 2
    • Implications for Merger?