Ajaz_204_2009_lectur - University of Toronto Department of Economics ECO 204 2009 2010 Sayed Ajaz Hussain Lecture 2 Ajaz Hussain Department of

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University of Toronto Department of Economics ECO 204 2009 2010 Sayed Ajaz Hussain Lecture 2 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George)
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Today ± Quick review of unconstrained and equality constrained optimization from last time ± The envelope theorem ² What is it and when to use it? ² An application to unconstrained optimization ² An application to equality constrained optimization ² Lagrange multiplier λ interpreted Ajaz Hussain. Department of Economics. University of Toronto (St. George) 2
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(Static) Optimization Ajaz Hussain. Department of Economics. University of Toronto (St. George) 3 Optimization “Maximization” or “Minimization” Problems Unconstrained Optimization Equality Constrained Optimization Inequality Constrained Optimization ECO 204 Chapter 1.1 ECO 204 Chapter 1.2
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Last Time: T.O. Airport Parking Garage You’re the parking manager at T.O. airport You’ve identified two segments of customers Ajaz Hussain. Department of Economics. University of Toronto (St. George) 4 Short Term Parkers Demand Curve: P S = 3 Q S /200 Long Term Parkers Demand Curve: P L = 2 Q L /200 Q P 3 2 D S D L
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Road Plan Ahead Ajaz Hussain. Department of Economics. University of Toronto (St. George) 5 Review Unconstrained Revenue Optimization Solution Review Equality Constrained Revenue Optimization Solution Envelope Theorem Application: Envelope Theorem on Unconstrained Problem Application: Envelope Theorem on Equality Constrained Problem
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Last Time: Short Term Parking Unconstrained Optimization For now, focus on short term parking problem only Max R S = P S Q S Max R S = 3Q S Q S 2 /200 dR/dQ S = 0 3 Q S /100 = 0 Q S = 300 P S = $1.5 Ajaz Hussain. Department of Economics. University of Toronto (St. George) 6 R S R S Q S
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Last Time: Short Term Parking Equality Constrained Optimization For now, focus on short term parking problem only Max R S s.t. Q S = 200 Max R S s.t. Q S 200 = 0 MaxL= R S ‐λ [Q S 200] Max L = 3Q S Q S 2 /200 ‐ λ [Q S 200] dL/dQ S = 0 3 Q S /100 ‐ λ = 0 dL/d λ = 0 Q S 200 = 0 Q S = 200 Q S = 200 P S = $2 R S = $400 Ajaz Hussain. Department of Economics. University of Toronto (St. George) 7 FOC with respect to λ always gives the equality constraint
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Ajaz Hussain. Department of Economics. University of Toronto (St. George)
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto- Toronto.

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Ajaz_204_2009_lectur - University of Toronto Department of Economics ECO 204 2009 2010 Sayed Ajaz Hussain Lecture 2 Ajaz Hussain Department of

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