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?

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Definitions:

Fiscal Year

A one-year period used by governments and businesses for accounting and budget purposes, which may not align with the calendar year.

Welfare Spending

Government expenditure on social protection programs intended to support the well-being of citizens, such as health care, unemployment benefits, and social security.

Federal Outlays

Expenditures by the U.S. federal government, including spending on defense, education, social security, and health care.

Federal Budget Process

The procedure by which the federal government creates and approves a budget, detailing the allocation of funds to different departments and programs.