David owns a firm. His von Neumann-Morgenstern utility-of-money function is given by U(m) = 4m. David...

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David owns a firm. His von Neumann-Morgenstern utility-of-money function is given by U(m) = 4m. David is considering hiring Carol to run the firm for him. Carol's von Neumann- Morgenstern utility-of-money function is given by V(m) = √m. If Carol runs the firm the possible outcomes are: profits probability $98 $242 $392 1 1 1 6 3 2 If David runs the firm himself the possible outcomes are: profits probability $50 $150 1 1 2 2 Carol offers to run the firm in exchange for 50% of the profits. (a) Is David better off running the firm himself or accepting Carol's offer? (b) Carol's suggested contract, call it contract A, is not Pareto efficient. Why? [Although in class I only talked about the case with only two outcomes, the general principle for Pareto efficiency applies also when there are more than two outcomes.] (c) David and Carol are about to sign contract A. Suggest an alternative contract, call it B, that David finds just as good as contract A, but Carol prefers to contract A. [Don't worry about negative numbers: David is very rich!] (d) Suggest an alternative contract to contract A, call it C, that David prefers to contract A, while Carol finds just as good as contract A. David owns a firm. His von Neumann-Morgenstern utility-of-money function is given by U(m) = 4m. David is considering hiring Carol to run the firm for him. Carol's von Neumann- Morgenstern utility-of-money function is given by V(m) = √m. If Carol runs the firm the possible outcomes are: profits probability $98 $242 $392 1 1 1 6 3 2 If David runs the firm himself the possible outcomes are: profits probability $50 $150 1 1 2 2 Carol offers to run the firm in exchange for 50% of the profits. (a) Is David better off running the firm himself or accepting Carol's offer? (b) Carol's suggested contract, call it contract A, is not Pareto efficient. Why? [Although in class I only talked about the case with only two outcomes, the general principle for Pareto efficiency applies also when there are more than two outcomes.] (c) David and Carol are about to sign contract A. Suggest an alternative contract, call it B, that David finds just as good as contract A, but Carol prefers to contract A. [Don't worry about negative numbers: David is very rich!] (d) Suggest an alternative contract to contract A, call it C, that David prefers to contract A, while Carol finds just as good as contract A.

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a To determine whether David is better off running the firm himself or accepting Carols offer we need to compare their expected utilities in each scenario If David runs the firm himself Expected utili... View the full answer