2. LC} 3 Tom lives on an island and has 2t] coconut trees in the current period, which currently produce 18G coconuts. Tom detests coconuts, but he can trade them with people on neighbouring islands for things that he wants. Further, Tom can borrow and lend coconuts with neighbouring islands. In the coconut credit market, a loan of 1 coconut in the current period is repaid with 2 coconuts in the future period. In each period, Tom's trees produce, and then HHS of them die. If Tom plants a coconut 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 an},F rernaining coconut trees for 1 coconut each. When Torn plants coconuts in the current period, he plants them in successively less fertile ground, and the less fertile the ground, the less productive the coconut tree. For convenience, we will assume here that fractions of coconuts can be produced by trees. Output in the future period, for given numbers of trees in production in the future period, is given in the following table: \fa. Plot the level of output against the quantity of capital for the future period. b. Plot the marginal product of capital against the quantity of capital for the future period. c. Calculate Tom's present value of profits given each quantity of future trees. d. Calculate the net marginal product of capital for each quantity of future trees. e. Determine Tom's optimal quantity of investment, and explain your results