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Costs

Costs. Conditional Demand. Conditional Factor Demand The choice of inputs that will yield minimal costs for the firm will in general depend on the input prices (w, r) and the level of output the firm wants to produce, i.e., L=L(w,r, y ) K=K(w, r, y) (y represents a given level of output).

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Costs

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  1. Costs

  2. Conditional Demand • Conditional Factor Demand The choice of inputs that will yield minimal costs for the firm will in general depend on the input prices (w, r) and the level of output the firm wants to produce, i.e., L=L(w,r, y) K=K(w, r, y) (y represents a given level of output)

  3. Short Run Costs Total Costs = VC + FC VC is variable costs and FC is fixed costs. We usually think of Labour as being the variable factor and Capital as being the fixed factor.

  4. Short Run Costs Average costs ATC = VC/Y +FC/Y ATC = AVC + AFC Marginal costs MC=TC/Y = VC/Y = MVC (MFC = 0)

  5. Short Run Costs MC AC € AVC Recall the relationship between MC and AC AFC Y

  6. Short Run Costs: Example • Trying to get TC = C = F(Y) • Trying to get AC = TC/Y = C/Y = F(Y) • Trying to get MC = F(Y)

  7. Short Run Costs: Example Capital (K) is fixed in the short run. Let

  8. Short Run Costs: Example Square the production function equation in order to simplify Rearrange to find

  9. Short Run Costs: Example We know that TC=wL+rk We also know that w=r=1 (e.g. €1) and that K=10 We also know L in terms of Y and K. Substitute all this information into TC=wL+rK Since w=r=1 and K=10 then

  10. Short Run Costs: Example Now find average cost and marginal cost

  11. Short Run Costs: Example • You can now graph this example, i.e. AC, AVC and MC. (Homework)

  12. Long Run Costs TC Constant Returns to Scale Y € AC = MC Y

  13. Long Run Costs TC Increasing Returns to Scale Y € AC MC Y

  14. Long Run Costs TC Decreasing Returns to Scale Y MC € AC Y

  15. Linking Short Run and Long Run Costs • The basic idea is that the long run costs of producing Y* are less than or equal to the short run cost of producing Y*. (Otherwise, there would be a contradiction.)

  16. Linking Short Run and Long Run Costs € SRAC(K2) SRAC(Kn) SRAC(K1) LRAC Y

  17. Derivation of Short Run and Long Run Cost Curves: Review K is fixed in the short run f e a K* Y=300 Y=200 Y=100 L1 L2 L3

  18. Derivation of Short Run and Long Run Cost Curves: Review K is variable in the long run (a to b to c) K3 c K2 b Y=300 a K1 Y=200 Y=100 L1 L2 L3

  19. Short Run Short run a to e to f SRMC AP MP € APL SRAC MPL L Y

  20. Long Run Long run a to b to c (assuming CRS) AP MP € APL = MPL LRAC L Y

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