Paula, a small-scale farmer, has an apple orchard, which has 12 trees in the current periodthat is, K = 12. For simplicity, suppose that the quantity of labour required to operate the orchard does not depend on the number of trees Paula has, at least for the number of trees that Paula can plant on her land. In the current period, the 12 trees produce 100 kilograms of apples; that is, Y = 100. Paula can invest in more trees by taking some of the apples, extracting the seeds (which we assume makes the apples useless), and planting them. Very few of the seeds grow, and it takes 1 kilogram of apples to yield 1 tree that will be productive in the future period. The first extra tree that Paula grows will be on her best land, and therefore it will have a high marginal product, bearing a relatively large amount of fruit. The second tree will be planted on slightly worse land, and so will have a smaller marginal product, and so on. Every period, some trees die. In fact, at the end of each period, Paula loses 25% of her trees. At the end of the future period, Paula can liquidate her trees and exchanges 1 tree for 1 kilogram of apples on the open market. The real interest rate is 5%. Output in the future period, for given number of trees in production in the future period, is given in the table above When future output is 100, the net marginal product of future capital is

Trees in Production in the Future Future Output 8 000 95 98 9 10 100 101 11 12 13 101.5 14 101.65 101.75 101.77 15