Question

В стране есть три группы жителей: бедные, средний класс и богатые. Они составляют 30, 50 и 20 % от всего населения соответственно. Доходы распределены между группами в соотношении 10, 60 и 30 % соответственно, а внутри групп – равномерно. Правительство решило ввести прогрессивную налоговую шкалу и все полученные от налогов деньги перераспределить равномерно между бедными гражданами. В результате такой политики в стране установилось равенство доходов. Какую из этих шкал они ввели (шкалы округлены до целого значения процентных пунктов)? 1.Налог для бедных – 5 %, для среднего класса – 8 %, а для богатых – 51 % 2. Налог для бедных – 0 %, для среднего класса – 34 %, а для богатых –23 %. 3.Налог для бедных – 10 %, для среднего класса – 30 %, а для богатых – 50 %. 4.Налог для бедных – 2 %, для среднего класса – 40 %, а для богатых – 27 %. 5.Налог для бедных – 0 %, для среднего класса – 17 %, а для богатых – 33 %.

Answer 1

Второй вариант ответа.

Answer 2

Progressive Taxation and Income Redistribution

In this scenario, the government has decided to introduce a progressive tax system and redistribute all the tax revenue equally among the poor citizens, resulting in income equality across the country. We are given the distribution of the population and the income distribution among the groups.

The three groups of residents in the country are: - Poor: 30% of the population, receiving 10% of the income. - Middle Class: 50% of the population, receiving 60% of the income. - Rich: 20% of the population, receiving 30% of the income.

Calculating the Tax Rates

To determine the tax rates for each group, we can calculate the average income for each group and then use the given income distribution to find the tax rates that would result in equal income after redistribution.

1. Poor Group: - Average Income: 10% / 30% = 0.33% of the total income per person. - Tax Rate: Let's denote the tax rate for the poor as x. - After tax income: (1 - x) * 0.33% of the total income per person.

2. Middle Class: - Average Income: 60% / 50% = 1.2% of the total income per person. - Tax Rate: Let's denote the tax rate for the middle class as y. - After tax income: (1 - y) * 1.2% of the total income per person.

3. Rich Group: - Average Income: 30% / 20% = 1.5% of the total income per person. - Tax Rate: Let's denote the tax rate for the rich as z. - After tax income: (1 - z) * 1.5% of the total income per person.

Equating the After Tax Incomes

Since the government redistributes all the tax revenue equally among the poor citizens, the after-tax income for each group should be equal after redistribution.

We can set up the following equation: (1 - x) * 0.33% = (1 - y) * 1.2% = (1 - z) * 1.5%

Solving this equation will give us the tax rates for each group.

Conclusion

Using the given information and the equation for equal after-tax income, we can calculate the tax rates for each group. After solving the equation, we can determine which of the provided tax rate options align with the calculated rates.