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Unformatted text preview: University of California, Davis ARE/ECN 200A Fall 2008 Joaquim Silvestre & Shaofeng Xu PROBLEM SET 8 ANSWER KEY 1. Certain vs. Uncertain Prices Let y j solve PROFITMAX [ p j ] ;j = 0 ; 1 and y & solve PROFITMAX & p & ; where p & = (1 & & ) p + &p 1 : First environment: When the price is p ; the rm reaches prots p y ; When the price is p 1 ; the rm reaches prots p 1 y 1 : Thus, the expected prots is (1 & & ) p y + &p 1 y 1 : Second environment: The rm will have certain prots of p & y & : You recommend the rst enviroment, which is (weakly) better for the risk-neutral rm because of the convexity of the prot function. In detail, p y p y & (because y solves PROFITMAX [ p ] ) and p 1 y 1 p 1 y & (because y 1 solves PROFITMAX [ p 1 ] ). Thus, (1 & & ) p y + &p 1 y 1 [(1 & & ) p + &p 1 ] y & = p & y & ; i.e., the expected prots of the rst environment are higher than the prots of the second environment....
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