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An Otherwise Charming Island Is Inhabited by Two Religious Groups

question 7

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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?

Understand the concept of insurable interest and its significance in insurance contracts.
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Comprehend the benefits of bundling types of liabilities in insurance for economic efficiency.

Definitions:

Return On Investment

A measure used to evaluate the efficiency or profitability of an investment compared to its cost.

Operating Assets

Resources owned by a business that are used in its day-to-day operations to generate revenue, such as machinery, buildings, and equipment.

Net Operating Income

The profit a company generates from its operations, before taxes and interest, calculated as gross income minus operating expenses.

Return On Investment

A performance measure used to evaluate the efficiency or profitability of an investment, calculated as net profit divided by the cost of the investment.

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