eco331-10-ValueOfInformationHandout

eco331-10-ValueOfInformationHandout - Overview A Monopoly...

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Unformatted text preview: Overview A Monopoly Problem Signals Eco331: Value of Information Marciano Siniscalchi November 9, 2009 Overview A Monopoly Problem Signals Overview Dynamic choice: take actions at multiple points in time Value of Information: two choices : Time 1 : Acquire vs. Do not acquire information Time 2 : Make decision, possibly given information Information is good, provided one uses it optimally Foundations: Static vs. Dynamic Choice Models: Information partitions and Signals Overview A Monopoly Problem Signals The Big Picture: No Information ( s 1 , a 1 ) s 1 ( s 2 , a 1 ) s 2 ( s 3 , a 1 ) s 3 ( s 4 , a 1 ) s 4 a 1 ( s 1 , a 2 ) s 1 ( s 2 , a 2 ) s 2 ( s 3 , a 2 ) s 3 ( s 4 , a 2 ) s 4 a 2 No Info Overview A Monopoly Problem Signals The Big Picture: With Info ( s 1 , a 1 )- M s 1 ( s 2 , a 1 )- M s 2 a 1 ( s 1 , a 2 )- M s 1 ( s 2 , a 2 )- M s 2 a 2 I 1 ( s 3 , a 1 )- M s 3 ( s 4 , a 1 )- M s 4 a 1 ( s 3 , a 2 )- M s 3 ( s 4 , a 2 )- M s 4 a 2 I 2 Info Ex-Ante Interim Ex-Post Overview A Monopoly Problem Signals The Basic Model: No Uncertainty Monopolistic firm faces demand Q ( p , s ) = s- p , s R . Marginal cost c = 2. Parameter s [0 , 10] . For now, s is known . Linear utility: u ( x ) = x . Thus, maximize profits . In preparation for future development, let profits be X p ( s ) = ( p- 2) Q ( p , s ) . Then firm solves (disregarding constraints...) max p X p ( s ) = max p ( p- 2) ( s- p ) = max p p ( s + 2)- p 2- 2 s . First-order condition: X p ( s ) p = s +2- 2 p p * ( s ) = 1 2 s +1 , X * ( s ) = 1 2 s- 1 2 . Overview A Monopoly Problem Signals Introducing Uncertainty Now assume firm does not know...
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eco331-10-ValueOfInformationHandout - Overview A Monopoly...

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