Problem 2. (7 points) Consumption and investment under certainty. Suppose an individual has $9,000 today and can invest them in the following projects: Investment outlay per shareholder is the maximum amount each shareholder can invest in a Project Investment Outlay Rate of return per shareholder A $1,000 6% B $3,000 12% C $3,000 4% D $2,000 20% given project. For example, in project A you can invest up to $1,000. d) Jun has utility function U.(Co, C1) = Co*C/ that represents his preferences about consumption today and in the future. He can borrow at the rate of 7% or lend at the rate of 5%. Calculate and show the following points on the graph: his initial wealth Wo; his optimal production point (Po, P/); his optimal consumption point (Co*, C/*); the present value of the final wealth Wo*. Use the method of Lagrange multipliers to calculate the optimal consumption point. Is he a lender or a borrower? How much will he have to borrow/lend and repay/be repaid on the capital market? Show the investment amount, the amount borrowed/lend and the amount repaid on a diagram