An otherwise charming island is inhabited by two religious groups who hate each other. The island is presided over by a benevolent monarch who is extremely concerned about envy between groups. He chooses the distribution of income on the island so as to maximize the social welfare function, W(x, y) = min{2x - y,2y - x}, where x is the utility of the average member of group X and y is the utility of the average member of group Y.
a. If the monarch can accomplish any distribution of utility such that x + 3y = 24, diagram the utility possibilities frontier and the monarchs isowelfare lines.
b. What income distribution maximizes W?
c. Show that an equal increase in both groups income will always please the monarch.
d. If the initial incomes are equal, when do increases in both groups utility reduce W?

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The Answer of An otherwise charming island is inhabited by two religious groups who hate each other. The island is presided over by a benevolent monarch who is extremely concerned about envy between groups. He chooses the distribution of income on the island so as to maximize the social welfare function, W(x, y) = min{2x - y,2y - x}, where x is the utility of the average member of group X and y is the utility of the average member of group Y.
a. If the monarch can accomplish any distribution of utility such that x + 3y = 24, diagram the utility possibilities frontier and the monarchs isowelfare lines.
b. What income distribution maximizes W?
c. Show that an equal increase in both groups income will always please the monarch.
d. If the initial incomes are equal, when do increases in both groups utility reduce W?

An Otherwise Charming Island Is Inhabited by Two Religious Groups