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Cost Function

cost function - relates cost to output level for future prediction  

  • VC = bQ
    • linear function, implies constant marginal cost
  • VC = bQ + gQ2
    • quadratic function, implies linear marginal cost
  • VC = bQ + gQ2 + dQ3
    • cubic function, implies quadratic (U-shaped) marginal cost

Cobb-Douglas cost/production function - when production in form Q = AKaLb  

  • C(Q) = wL(Q) + rK(Q)
    • use production function and MRTS to find L and K functions in terms of Q
  • MRTS = w/r = MPL / MPK
    • w/r = (AbKaLb-1) / (AaKa-1Lb) = (bK) / (aL)
    • waL = rbK
    • L = (rb)K / (wa)
    • K = (wa)L / (rb)
    • substitute these back into the production function to find both L and K in terms of Q
    • no need to use lagrangian method
  • substitute L and K functions back into the initial cost function to get final outcome
  • note that in short-run, either K or L will be fixed
    • leaves the production function in terms of just K or L and makes it easy to solve
    • in finding total cost, don't forget to calculate the fixed cost as well
Subject X2: 

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