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as372s06t1

as372s06t1 - Actsc 372 Test#1 SPRING 2006 Marks Name I.D...

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Actsc 372 Test #1 - SPRING 2006 Name: Marks: /40 I.D.#: June 5, 2006, 1:30-3:00pm (90 minutes) 5 Questions, 5 Pages Aids: Calculator 1. [8 marks] (a) State the Independence Axiom and the Monotonicity Axiom. (b) Show that the von Neumann-Morgenstern utility function is uniquely determined up to a positive linear transformation.

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2 2. [8 marks] An individual has the following power utility function: u ( x ) = x γ (a) State the condition(s) under which the above utility can be used to describe a risk-averse individual. (b) Determine the Arrow-Pratt absolute risk aversion coefficient (ARA) of the above utility function. Will a risk averse individual be willing to invest more, less, or the same, with increasing wealth?
3 3. [8 marks] Consider two projects that you can invest in: Project A pays \$100 with certainty, while project B pays \$200 with probability 0.1, \$80 with probability 0.6, and \$50 with probability 0.3. Your utility is of the type u ( x ) = αx - x 2 . You know that you are indifferent between the choice of receiving \$1000 for sure, or \$2000 and \$400 with a fifty-fifty chance. Which project (A or B) would you choose? Justify your choice.

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