[Exercise 6.4.4.1 in McAfee*] Consider a baby-sitting cooperative, where parents rotate supervision of the children of...

 

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[Exercise 6.4.4.1 in McAfee*] Consider a baby-sitting cooperative, where parents rotate supervision of the children of several families. Suppose that, if the sitting service is available with frequency Y, the value placed by person i is v; Y and the costs of contribution y is ½ ny², where Y is the sum of the individual contributions and n is the number of families. Rank v₁ ≥ V2 ≥...> Vn. a) What is the size of the service under voluntary contributions? [Hint: Let y; be the contribution of family i. Identify the payoff of family j as vjyj + ΣizjYi)- ½/2n(yj)². What value of y, maximizes this expression?] i=1 b) What contributions maximize the total social value (Σ=1 vj) (Σ-1 y₁) − n)}=₁3²? [Hint: Are the values of y; different for different i?] [Exercise 6.4.4.1 in McAfee*] Consider a baby-sitting cooperative, where parents rotate supervision of the children of several families. Suppose that, if the sitting service is available with frequency Y, the value placed by person i is v; Y and the costs of contribution y is ½ ny², where Y is the sum of the individual contributions and n is the number of families. Rank v₁ ≥ V2 ≥...> Vn. a) What is the size of the service under voluntary contributions? [Hint: Let y; be the contribution of family i. Identify the payoff of family j as vjyj + ΣizjYi)- ½/2n(yj)². What value of y, maximizes this expression?] i=1 b) What contributions maximize the total social value (Σ=1 vj) (Σ-1 y₁) − n)}=₁3²? [Hint: Are the values of y; different for different i?]

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a b Differentiate the expression in the hint with respect to ... View the full answer