Your SlideShare is downloading. ×
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Production and cost
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Production and cost

4,543

Published on

0 Comments
3 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
4,543
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
208
Comments
0
Likes
3
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. 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
  • 2. 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
  • 3. 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
  • 4. Marginal Product of Labor
    • MP L =  Q/  L
    • Measures the output produced by the last worker.
    • Slope of the production function
  • 5. Average Product of Labor
    • AP L = Q/L
    • This is the accounting measure of productivity.
  • 6. Q=F(K,L) Increasing Marginal Returns Diminishing Marginal Returns Negative Marginal Returns Stages of Production Q L MP AP
  • 7. 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
  • 8. Linear Isoquants
    • Capital and labor are perfect substitutes
    Q 3 Q 2 Q 1 Increasing Output L K
  • 9. 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
  • 10. 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
  • 11. 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).
  • 12. Cost Minimization
    • Marginal product per dollar spent should be equal for all inputs:
    • Expressed differently
  • 13. Cost Minimization Q L K Point of Cost Minimization Slope of Isocost = Slope of Isoquant
  • 14. Cost Analysis
    • Types of Costs
      • Fixed costs (FC)
      • Variable costs (VC)
      • Total costs (TC)
      • Sunk costs
  • 15. 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
  • 16. 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)
  • 17. 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
  • 18. 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
  • 19. Variable Cost AVC Variable Cost Q 0 Q 0  AVC = Q 0  [VC(Q 0 )/ Q 0 ] = VC(Q 0 ) $ Q ATC AVC MC
  • 20. ATC Total Cost Q 0 Q 0  ATC = Q 0  [C(Q 0 )/ Q 0 ] = C(Q 0 ) Total Cost $ Q ATC AVC MC
  • 21. Economies of Scale LRAC $ Output Economies of Scale Diseconomies of Scale
  • 22. 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
  • 23. Multi-Product Cost Function
    • C(Q 1 , Q 2 ): Cost of producing two outputs jointly
  • 24. 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.
  • 25. Cost Complementarity
    • The marginal cost of producing good 1 declines as more of good two is produced:
    •  MC 1 /  Q 2 < 0.
  • 26. 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
  • 27. 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?

×