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101A_lec17 - Economics 101A(Lecture 17 Stefano DellaVigna...

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Economics 101A (Lecture 17) Stefano DellaVigna March 19, 2009
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Outline 1. Cost Curves 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 Case 2. Non-convex technology. Plot production function, total cost, average and marginal. Supply 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. Yes! Supply function is upward sloping.
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2 One-step Pro fi t Maximization Nicholson, Ch. 11, pp. 374-380 (Ch. 9, pp. 265— 270, 9th) One-step procedure: maximize pro fi ts Perfect competition. Price p is given Firms are small relative to market Firms do not a ff ect market price p M Will fi rm produce at p > p M ? Will fi rm produce at p < p M ? = p = p M
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Revenue: py = pf ( L, K ) Cost: wL + rK Pro fi t pf ( L, K ) wL rK
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Agent optimization: max L,K pf ( L, K ) wL rK First order conditions: pf 0 L ( L, K ) w = 0 and pf 0 K ( L, K ) r = 0 Second order conditions? pf 00 L,L ( L, K ) < 0 and | H
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