In the coconut credit market, a loan of 1 coconut in the current period is repaid with 2 coconuts in the future period. Further, Tom can borrow and lend coconuts with neighboring islands. Tom detests coconuts, but he can trade them with people on other neighboring islands for things that he wants. Output in the future period, for given numbers of trees in production in the future period, is given in Table 1 (a) 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 result:s Table 1: Relationship between the number of trees and output of coconuts Trees in Production in the Future Future Output of Coconuts 15 16 155 162 168 173 18 19 20 21 180 182 183.8 184.8 185.2 185.Tom lives on an island and has 20 coconut trees in the current period, which currently produce 180 coconuts. For convenience, we assume here that fractions of coconuts can be produced by trees. When Tom plants coconuts in the current period, he plants them in successively less fertile ground, and the less fertile the ground, the less productive is the coconut tree. At the end of the future period, Tom can sell any remaining coconut trees for 1 coconut each. If Tom plants a coconut in the ground in the current period, it will grow into a productive coconut tree in the future period. Each period, Tom's trees produce, and then 10% of them die.
Transcribed image text: Problem 8: An example of the real intertemporal model with investment 1.8 Tom lives on an island and has 20 coconut trees in the current period, which currently produce 180 coconuts. Show transcribed image text Expert Answer (e) Determine Tom’s optimal quantity of investment, and explain (d) Calculate the net marginal product of capital for each quantity (c) Calculate Tom’s present value of profits given each quantity of (b) Plot the marginal product of capital against the quantity of (a) Plot the level of output against the quantity of capital for Of trees in production in the future period, is given in Table Output in the future period, for given numbers When Tom plants coconuts in theĬurrent period, he plants them in successively less fertile ground,Īnd the less fertile the ground, the less productive is the coconutĬonvenience, we assume here that fractions of coconuts can be At the end of the future period, Tom can sell any remainingĬoconut trees for 1 coconut each. Period, it will grow into a productive coconut tree in the future
If Tom plants a coconut in the ground in the current Each period, Tom’s trees produce, and then 10% of In the coconut credit market, a loan of 1Ĭoconut in the current period is repaid with 2 coconuts in theįuture period. Further, Tom can borrow and lend coconuts Tom detests coconuts,īut he can trade them with people on other neighboring islands for Period, which currently produce 180 coconuts. Tom lives on an island and has 20 coconut trees in the current
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