Group Problem Set 1 Due: 11 pm, October 26, 2023 instruction: Submit a complete solution in pdf format. with paper size ofA4, and written in black or blue pen in your group homepage in canvas. Problem 1. (25 pts) Find the area bounded by the graphs of F(:1:) : 9:3 6:32 l 91 and C(1) = 1:. Compute your answer to 3 decimal places. Problem 2. (25 pts) An economist showed that the Lorenz curve forthe current income distribution in the country is p(a;) = 0.1x + 0.9:c2. She projected that the income distribution in 10 years will be yo) = x\" 2,1 Compute the Gini index of income concentration (to two decimal places) for the current and projected Lorenz curves 2.2 What can you say about the distribution of income 10 years from now? Is it more equitable or less? Problem 3. (15 pts) In the rst 5 years of business operation, the continuous income stream of a businessman has a rate of ow of t) : 8, 00060053 Find the total income produced in the rst 5 years Problem 4. (35 pts) An investor has 10,000 USD to invest in either a bond that matures in 5 years or a business that will produce a continuous stream of income over the next 5 years with rate of ow of f(t) : 2, 250' if both the bond and the continuous income stream earn 3.75% compounded continuously, which is the better investment