An Otherwise Charming Island Is Inhabited by Two Religious Groups

question 7

Essay

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?

---

Definitions:

Elimination Half-life

The time it takes for the concentration of a substance in the body to reduce by half through natural processes.

Beta Half-life

Refers to the time it takes for a substance to reduce to half its initial amount in the body, often related to the metabolic clearance of drugs; similar to therapeutic half-life but specific to pharmacokinetics.

12-Step Philosophy

A set of guiding principles for recovery from addiction, compulsion, or other behavioral problems, originally developed by Alcoholics Anonymous (AA).

Brickman's Model

A psychological framework that categorizes people based on their views of personal control and responsibility towards achieving or not achieving success.