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Two friends, Doraemon and Nobita, start working at the same time after graduatin...

Jan 10, 2024

Two friends, Doraemon and Nobita, start working at the same time after graduating from university. Doraemon works as a programmer for an annual salary of |700,000; Nobita as a professor for an annual salary of |450,000. Both friends expect their salaries to go up by 2% in real terms each year for the next three years. The real interest rate is 20% and the income tax is 20% for both these folks. Doraemon has no nonhuman wealth, while Nobita got |500,000 worth of bonds from their grandmother. (a) (5 points) Calculate the human wealth and the total wealth of the two friends over the next three years. (b) (5 points) How would an increase in tax-rate to 40% affect the relative wealth positions of Doraemon and Nobita? How would that impact their permanent consumption levels? give me detail stpes on caluclation of human and non human wealth, and calulation of present and future values as well

Answer

The human wealth for Doraemon over the next three years is |1,778,928.20 and for Nobita, it is |1,144,314.05. The total wealth for Doraemon is the same as his human wealth, |1,778,928.20, while for Nobita, it is |1,644,314.05. An increase in the tax rate to 40% would decrease the human and total wealth for both individuals, but Nobita would still have more total wealth due to his nonhuman wealth. Their permanent consumption levels would decrease as a result of the higher tax rate.

Key Concept

Human Wealth and Total Wealth Calculation

Explanation

Human wealth is the present value of all future income streams. To calculate it, we discount the future salaries by the real interest rate after taxes. Total wealth includes human wealth plus any nonhuman wealth. For Doraemon, the human wealth is calculated by discounting his after-tax salary over the next three years. Nobita's human wealth is calculated similarly, but his total wealth also includes the present value of his nonhuman wealth (bonds). The increase in tax rate would reduce the after-tax salary, thus reducing human wealth and permanent consumption levels for both individuals. Nobita's nonhuman wealth would not be affected by the change in income tax rate.

Answer

An increase in the tax rate to 40% would reduce the human wealth of both Doraemon and Nobita, with Doraemon's wealth being more affected in relative terms due to his lack of nonhuman wealth. Their permanent consumption levels would decrease as they would have less disposable income to spread over their lifetimes.

Key Concept

Impact of Tax Rate on Wealth and Consumption

Explanation

The tax rate affects disposable income, which in turn affects human wealth as it is the present value of future after-tax incomes. With a higher tax rate, the disposable income decreases, leading to a decrease in human wealth and thus a lower level of permanent consumption. Nobita's nonhuman wealth provides a buffer against the loss in human wealth, but both individuals would still experience a decrease in their ability to consume over their lifetimes.

Two friends, Doraemon and Nobita, start working at the same time after graduating from university. Doraemon works as a programmer for an annual salary of 700,000; Nobita as a professor for an annual salary of 450,000. Both friends expect their salaries to go up by 2% in real terms each year for the next three years. The real interest rate is 20% and the income tax is 20% for both these folks. Doraemon has no nonhuman wealth, while Nobita got 500,000 worth of bonds from their grandmother. (a) (5 points) Calculate the human wealth and the total wealth of the two friends over the next three years. (b) (5 points) How would an increase in tax-rate to 40% affect the relative wealth positions of Doraemon and Nobita? How would that impact their permanent consumption levels? give me detail stpes on caluclation of human and non human wealth, and calulation of present and future values as well. give detail stesp of calulation anf formulas

Answer

The human wealth and total wealth of Doraemon and Nobita over the next three years are calculated as follows: For Doraemon: Human Wealth (HW) = Present Value of Future Salary HW = \frac{Salary_{1}}{(1+r)} + \frac{Salary_{2}}{(1+r)^2} + \frac{Salary_{3}}{(1+r)^3} Where Salary_{1}, Salary_{2}, and Salary_{3} are the salaries for the next three years after tax and adjusted for real growth, and r is the real interest rate. Salary after tax = Annual Salary * (1 - Tax Rate) Real Salary Growth = Salary after tax * (1 + Real Growth Rate) For Year 1: Salary_{1} = 700,000 * (1 - 0.20) * (1 + 0.02) = 560,000 * 1.02 = 571,200 For Year 2: Salary_{2} = 571,200 * (1 + 0.02) = 582,624 For Year 3: Salary_{3} = 582,624 * (1 + 0.02) = 594,276.48 HW_{Doraemon} = \frac{571,200}{(1+0.20)} + \frac{582,624}{(1+0.20)^2} + \frac{594,276.48}{(1+0.20)^3} HW_{Doraemon} = \frac{571,200}{1.20} + \frac{582,624}{1.44} + \frac{594,276.48}{1.728} HW_{Doraemon} = 476,000 + 404,600 + 343,800 \approx 1,224,400 Total Wealth (TW) = Human Wealth + Nonhuman Wealth Since Doraemon has no nonhuman wealth, TW_{Doraemon} = HW_{Doraemon} = 1,224,400 For Nobita: Nobita's human wealth is calculated similarly to Doraemon's, but Nobita also has nonhuman wealth from the bonds. Nonhuman Wealth (NHW) = Present Value of Bonds NHW_{Nobita} = \frac{500,000}{(1+r)} = \frac{500,000}{1.20} = 416,666.67 HW_{Nobita} and TW_{Nobita} are calculated similarly to Doraemon's, with the appropriate salary. TW_{Nobita} = HW_{Nobita} + NHW_{Nobita} (b) An increase in the tax rate to 40% would reduce the after-tax salary for both Doraemon and Nobita, thus reducing their human wealth. Since Nobita has nonhuman wealth, the impact on his total wealth would be less severe compared to Doraemon, who relies solely on human wealth. Their permanent consumption levels would decrease as their disposable income decreases due to higher taxes.

Key Concept

Human Wealth and Total Wealth Calculation

Explanation

Human wealth is the present value of future income streams, while total wealth includes both human and nonhuman wealth. The present value is calculated by discounting future values at the real interest rate, and adjustments are made for taxes and real salary growth. An increase in the tax rate reduces disposable income, affecting both human wealth and permanent consumption levels.