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Unformatted text preview: Problem 1 The payoffs are arbitrary but in order to be correct each woman must have the same payoff for going home with either mathematician and both should have a greater value for the economist. In this (and in any correctly set up set of payoffs) the Nash equilibria would be ( M 1 ,E ),( M 2 ,E ),( E,M 1 ), and ( E,M 2 ). Woman 2 M 1 M 2 E Woman 1 M 1 0,0 1,1 1,2 M 2 1,1 0,0 1,2 E 2,1 2,1 0,0 Problem 2 The Nash equilibria are (T,C) and (B,R) Problem 3 Part ai Total utility is: X i U i = nqh * = n (10- nh * ) h * X i U i = 10 nh *- n 2 h * 2 Part aii To maximize take the derivative and set equal to zero 10 n- 2 n 2 h * = 0 h * = 5 n Part aiii Total utility is maximized when 5 hours are used. It is not possible to achieve a higher total utility than the symmetric outcome since all the farmers are symmetric and there are no economies of scale. The only thing that is possible is to shift the allocation around....
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- Spring '08