Cost-Minimizing Input Choices

1
Cost-Minimizing Input Choices
Mathematically, we seek to minimize total costs
given q f(K,L) q0. Setting up the
Lagrangian L wL rK ?q0 - f(K,L) First
order conditions are ?L/?L w - ?(?f/?L)
0 ?L/?K r - ?(?f/?K) 0 ?L/?? q0 - f(K,L) 0
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Cost-Minimizing Input Choices

• Dividing the first two conditions we get

• The cost-minimizing firm should equate the MRTS
  for the two inputs to the ratio of their prices