Question

1) Capital stocks and resource maintenance

A fishery contains 5,000 tons of fish, and has a 3% annual replenishment rate (that is, 3% is its population growth rate). Assume that 200 tons of fish are harvested at the end of each year.

a) How many tons of fish will the fishery contain at the end of the first year? Show how you calculated this.
b) Draw a stock-flow diagram illustrating the change in the fishery stock from the start to the end of Year 1.

c) How many tons of fish will there be at the end of two years? (Calculate the 3% replenishment from the beginning of the year).
d) How many tons of fish will there be at the end of three years? Set up a table showing fishing activity through ten years, accounting both for natural growth and the annual harvest. How many tons remain after 10 years? [Hint: You might want to do this on an Excel spreadsheet].

e) How many years will it take to fully deplete the fishery? Clearly show how you calculated this.
f) Now assume that the annual harvest is only 100 tons. How many tons will be in the fishery after 10 years? Compare to 10 years of harvesting 200/year and discuss.
g) For the fish harvest to be sustainable, what is the largest number of tons of fish that can be harvested each year (starting with the first year)? Explain why this amount does not change.

Answer 1

(a) Initial Stock:- 5000 tons of fish

Inflow:- 3% of 5000(Replenishment Rate) = 3x5000/100=150 tons

Outflow:- 200 tons

Final Stock at the end of 1st year:- Initial Stock+Inflow-Outflow

5000+150-200= 4950 Tons

(b):-

(c) Initial Stock:- 4950 tons of fish

Inflow:- 3% of 4950(Replenishment Rate) = 3x4950/100=148.5 tons

Outflow:- 200 tons

Final Stock at the end of 2nd year:- Initial Stock+Inflow-Outflow

4950+148.5-200= 4898.5 Tons

(d):-

Tons of Fish at the end of 3 years:- 4845.46

Tons of Fish at the end of 10 years:- 4426.81