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Lecture 16 - Economics 101A(Lecture 16 Stefano DellaVigna...

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Economics 101A (Lecture 16) Stefano DellaVigna October 22, 2009
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Outline 1. Cost Curves and Supply Function II 2. One-step Pro fi t Maximization 3. Second-Order Conditions 4. Introduction to Market Equilibrium 5. Aggregation 6. Market Equilibrium in the Short-Run
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1 Cost Curves II Assume only 1 input (expenditure minimization is trivial) Case 1. Production function. y = L α Cost function? (cost of input is w ): c ( w, y ) = wL ( w, y ) = wy 1 Marginal cost? ∂c ( w, y ) ∂y = 1 α wy (1 α ) Average cost c ( w, y ) /y ? c ( w, y ) y = wy 1 y = wy (1 α )
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Case 1a. α > 1 . Plot production function, total cost, average and marginal. Supply function? Case 1b. α = 1 . Plot production function, total cost, average and marginal. Supply function? Case 1c. α < 1 . Plot production function, total cost, average and marginal. Supply function?
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Case 2. Non-convex technology. Plot production function, total cost, average and marginal. Supply function? Case 3. Technology with setup cost. Plot produc- tion function, total cost, average and marginal. Sup- ply function?
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1.1 Supply Function Supply function: y = y ( w, r, p ) What happens to y as p increases? Is the supply function upward sloping? Remember f.o.c: p c 0 y ( w, r, y ) = 0 Implicit function: ∂y ∂p = 1 c 00 y,y ( w, r, y ) > 0 as long as s.o.c. is satis fi ed.
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