1. (20%)Tom lives on an island and has 20 coconut trees in the current period, which currently produce 180 coconuts. Tom can borrow and lend coconuts with neighboring islands. In the coconut credit market, a loan of 1 coconut in the current period is repaid with 2 coconuts in the future period. Each period, Tom's trees produce, and then 10% of them die. If Tom plants a coconut in the ground in the current period, it will grow into a productive coconut tree in the future period. At the end of the future period, Tom can sell any remaining coconut trees for 1 coconut each. Output in the future period, for given numbers of trees in production in the future, is given in the following table: Trees in Production Future Output MP, - d I in the Future of Coconuts 18 173 19 177 20 180 21 182 22 183.8 23 184.8 24 185.2 25 185.4 (1) In terms of the notations of the class, K (current capital) = ? Y (current output) = ? d (depreciation rate) = ? r (real net interest rate) = ? (4%) (2) Fill in the two columns of the above table. (5%) (3) When trees in production in the future equal 20, calculate Tom's present value of profits. (5%) (4) Determine Tom's optimal quantity of investment, and explain your results. (6%)