Charles, Gilberto, and Lorenzo are roommates who are trying to decide how much money to spend on heat in their apartment each month.
Gilberto would ideally contribute $20, but he would prefer contributing $50 to $0 because he does not want to be freezing. His utility, therefore, increases from $0 up until they are each contributing $20, at which point his utility from additional spending on heat begins to decline. Gilberto’s preferences for spending on heat (are / are not) single peaked.
Lorenzo does not care about heat and is on a tight budget; therefore, he prefers to contribute no money to heat, and his utility is constantly declining as they increase the amount of money they spend. Lorenzo’s preferences (are / are not) single peaked.
Charles hates being cold; therefore, he would ideally like each to contribute $50 to heat. If they decide to contribute less than $30 each, he will end up spending most nights sleeping at his parents’ house. Thus, he prefers contributing no money to heat to contributing any amount between $0 and $30 (because in going from $0 to $30, the amount he pays increases, but he doesn’t spend time at the apartment and thus gets no benefit from the heat). Charles’s preferences (are / are not) single peaked.
Suppose the three roommates vote on purchasing either $0, $20, or $50 on heat. Among these proposals there (is/ is not) a Condorcet winner.
Please note that the multiple choices are in bold. Choose one answer.
Please provide explanation to your answers. Thanks.