Lecture 15 - Economics 101A (Lecture 15) Stefano DellaVigna...

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Economics 101A (Lecture 15) Stefano DellaVigna October 20, 2009
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Outline 1. Two-step Cost Minimization II 2. Cost Minimization: Example 3. Cost Curves and Supply Function
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1 Two-step Cost minimization II First Step. Minimize input costs for given production Firm objective function: min L,K wL + rK s.t.f ( L, K ) y Derived demand for inputs: L = L ( w, r, y ) K = K ( w, r, y ) Value function at optimum is cost function: c ( w, r, y )= ( r, w, y )+ ( )
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Second step. Given cost function, choose optimal quantity of y as well Price of output is p. Firm’s objective: max py c ( w, r, y ) First order condition: p c 0 y ( w, r, y )=0 Price equals marginal cost — very important!
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Second order condition: c 00 y,y ( w, r, y ) < 0 For maximum, need increasing marginal cost curve.
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2 Cost Minimization: Example Continue example above: y = f ( L, K )= AK α L β Cost minimization: min wL + rK s.t.AK α L β = y What is the return to scale for this example? Increase of all inputs: f ( t z ) with t scalar, t> 1 How much does input increase?
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Lecture 15 - Economics 101A (Lecture 15) Stefano DellaVigna...

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