Suppose that you own both a lake and a fishing boat as an investment package. You plan to profit by taking fish from the lake. Each season you decide either to fish or not to fish. If you do not fish, the fish population in the lake will double by the start of the next season. If you do fish, you will extract 77% of the fish that were in the lake at the beginning of the season. The fish that were not caught (and some before they are caught) will reproduce, and the fish population at the beginning of the next season will be the same as at the beginning of the current season.
The initial fish population is 11 tons. Your profit is $1 per ton. The interest rate is constant at 15%. Here assume that you obtain the cash at the end of the season , if you do fish, (so you have to discount your profit).
Now, you have only three seasons to fish.
(a) Draw a suitable binomial lattice for this optimal management problem.
(b) Assign the value of 0 to each of the final nodes. Then, calculate the optimal running present values for each of the other nodes in the lattice given in (a).
(c) Determine in which of those seasons you should fish.
Key in the optimal running present value for the initial node (Keep your answer to 2 decimal places, e.g. xx.12.)