econ145b-ps1sol-2009

econ145b-ps1sol-2009 - Econ 145B. Advanced Industrial...

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Econ 145B. Advanced Industrial Organization, Spring 2009 Problem Set 1. Solutions 1. The pro f t function is twice di f erentiable. Thus, to check quasi-concavity it is enough to verify that 00 is strictly negative at points that satisfy the f rst order condition 0= 0 ( )= ( )+  0 ( ) 0 ( ( )) 0 ( ) = +  0 0 0 (for the same reason as in the Exercise 1.4 discussed in class). Suppressing the arguments, we can compute 00 =2 0 +  00 00 ( 0 ) 2 0 00 Since 0 6 =0 ,wecanso lvethe f rst order condition for 0 and plug in above to get 00 =2 0 +  00 00 ( 0 ) 2 μ 0 + 00 2 0 0 00 = 1 2( )exp(  ) 1 exp (  ) 1 ( )exp(  ) 1 ( ) 2 exp (  ) = 2exp(  )+exp(  )= exp (  ) 0 where the f
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econ145b-ps1sol-2009 - Econ 145B. Advanced Industrial...

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