Question 9 12 pts Suppose that you own both a lake and a fishing boat as an inve

Question

Question 9 12 pts Suppose that you own both a lake and a fishing boat as an investment package. You plan to proht 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 70% 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 sea be the same as at the beginning of the current seasorn. The initial fish population is 5 tons. Your profit is $1 per ton. The interest rate is constant at 16%. 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.)

Explanation / Answer

Assumption - Discounted rate and interest rate nullify each other.

Case 1 - Fishing in all 3 seasons

First season output is 70% of initial population = 3.5 ton

Similarly for second and third season the population is 3.5 ton each season

Therefore, total profit is 3.5 + 3.5 + 3.5 = 10.5$

Case 2 - Fishing done directly in third season

The fish will double after first season. So at the start of sevond season the population will be 10 ton and at the start of third season the popultion will be 20 ton

So total profit at end of third season will be 70% of 20 ton = 14 $.

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