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Problem 4 (25 points) Jim has $200 for investment purposes and two projects to invest in Both projects are risk-free and will bring money 1

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Problem 4 (25 points) Jim has $200 for investment purposes and two projects to invest in Both projects are risk-free and will bring money 1 year after investment according to the data in the table below. Initial investment Revenue in 1 year Project A 100 150 Project B 100 100 Also, Jim can put any amount of money to the bank deposit with an annual interest rate of 10% (r = 0.1). He can borrow any amount of money at th same annual rate, (a) Calculate the rate of return for each project (b) In (O. C.) axes, depict the bundles available to Jim through investment into projects Label these points X(no investment). Y investment in one preferable project), and Z (investment in both projects), (c) Which bundle will Jim choose for investment if he can also lend or borrow money in the same graph, depict the set of bundles he can achieve by the combination of investing and lending/borrowing, (d) Jim's utility function is U = In(c)+c2. Find his optimal bundle. Illustrate your answer in the same graph. (In(x) is the logarithm of x to the base of e Hence, In'(x) = 1/x.) Problem 4 (25 points) Jim has $200 for investment purposes and two projects to invest in Both projects are risk-free and will bring money 1 year after investment according to the data in the table below. Initial investment Revenue in 1 year Project A 100 150 Project B 100 100 Also, Jim can put any amount of money to the bank deposit with an annual interest rate of 10% (r = 0.1). He can borrow any amount of money at th same annual rate, (a) Calculate the rate of return for each project (b) In (O. C.) axes, depict the bundles available to Jim through investment into projects Label these points X(no investment). Y investment in one preferable project), and Z (investment in both projects), (c) Which bundle will Jim choose for investment if he can also lend or borrow money in the same graph, depict the set of bundles he can achieve by the combination of investing and lending/borrowing, (d) Jim's utility function is U = In(c)+c2. Find his optimal bundle. Illustrate your answer in the same graph. (In(x) is the logarithm of x to the base of e Hence, In'(x) = 1/x.)

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