Suppose local councils spend money only on roads and clean water. The share of the expenditures for clean water is α ∈[0,1]. Voter preferences are Ui = −|α−pi|, where pi is the bliss point of voter i. Suppose for men pi ∼ U[0; 0.75] (uniform distribution), whereas for women pi ∼U[0.25; 1]. There are equal shares of men and women in the population.
(a) Are these preferences single-peaked?
(b) What is the policy outcome if only men can vote?
(c) What is the policy outcome if everyone can vote?
(d) Which outcome does better represent what women want?

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a To determine whether the preferences are singlepeaked we need to check if the utility function is maximized at a single point In this case the utili... View the full answer