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200a_f08_ps_8_ak

200a_f08_ps_8_ak - University of California Davis ARE/ECN...

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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 pro¡ts p ¡ y ; When the price is p 1 ; the ¡rm reaches pro¡ts p 1 ¡ y 1 : Thus, the expected pro¡ts is (1 & & ) p ¡ y + &p 1 ¡ y 1 : Second environment: The ¡rm will have certain pro¡ts of p & ¡ y & : You recommend the ¡rst enviroment, which is (weakly) better for the risk-neutral ¡rm because of the convexity of the pro¡t 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 pro¡ts of the ¡rst environment are higher than the pro¡ts of the second environment....
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200a_f08_ps_8_ak - University of California Davis ARE/ECN...

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