Lyon Econ 7140 April 3, 2008 Third Exam 1. For the utility functions ( ) x x U ln = and ( ) x x V = a. Show they are CRRA utility functions. Explain. b. TFU, At any level of x , U exhibits more risk aversion than does V . Remember that the explanation is the important part. 2. The profit function is ( ) wx x pq − = π where q is a strictly concave production function and x , a scalar, is the only input. The hire-price of x is a stochastic variable with density function ( ) w φ and mean w . Individual A maximizes expected profits and Individual B maximizes expected utility. a. Identify the FONC for Individual A. Show your work and explain everything. b. Now work with Individual B where ( ) u is strictly concave. i. Identify the FONC. Show your work and explain everything. ii. Show that the FONC can be written () () ( ) () ( ) ( ) () ∫ ∫ − ′ = ′ − ′ b a b a dw w w wx x pq u dw w x q p wx x pq φ * * * * * iii.Subtract from both sides () ()
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