Question

Question S. 1 There are essentially two broad categories of forest harvests; those done purely for commercial purposes without regard to future growth and forest development (commercial harvest), and those done to promote a sustainable forest (sustainable harvest) (Sustainable harvest practices take into consideration regeneration and the long-run well-being of the forest). Commercial harvest provides the most revenue in the short run, typically, but its cost is relatively higher when the long-run growth of the forest is accounted for, because any future stand will take relatively longer to grow and will not have the same quality of trees as the previous harvest. However, in the long run, sustainable harvests will produce more income, because higher quality trees will bring more value. Suppose that your town has a forest land in which the volume of the wood of living Yellow Pines is about 10 million cubic feet (length (feet)" width (feet)" height (feet)) at the present time (-0). As an environmental economist working for your town, you have been asked to issue a number of annual permits for harvesting this type of trees in such a way that the volume of this valuable softwood as a common resource remains unchanged after one year. Thus, your main objective is to keep the volume of the wood in the forest land unchanged (sustainable). You know that the annual biological growth rate of the volume of Yellow Pines is 25% (the rate of increase in the wood volume each year as a result of both new saplings and increased volume of the old trees). Furthermore, you know that the natural mortality rate (due to the disease of Needle Cast that eventually causes the tree to die, old age, etc.) of this species is 10%. Furthermore, you know that, typically and on average, there is a loss of size 5% due to wildfire each year. Moreover, you know that there is some harvest mortality rate (called x that refers to harvest rate), which you are asked to determine in an optimal and sustainable way A. Put down the stock variables and flow variables in the standard form of a dynamic optimization problem that we learned in class. (In other words, put down the givens of the problem on the following time line in an organized way that we learned in class.) (10 pts) t 0 B. What is the optimal harvest rate (x) that prevents the tragedy of the commons for this common resource? (6 pts) C. For what volume of Yellow Pine wood do you issue permits annually for this forest land to be harvested as timber in order to prevent the tragedy of the commons for this common resource? (6 pts) Note: Sustainable forest management is very complicated due to the multiple benefits and the large temporal and spatial st be taken into account. This example is only a heavily simplified example that ignores many subtleties of the scales that mu real world (including ages of trees, differential qualities, sizes of trees, etc.) for the sake of simplification.

Answer 1

Answer to question no A :-

vasua blo on tumo linu.: 30 23 20七 is 匕 is 10 5 七
Answer to question no B :-

Step 1 :-

Calculations of growth rate :-

Initial volume = 10 million

Increase in volume =25%=2.5 million

Decrease to due to mortality rate = 10%= 1 million

Decrease due to wildfire :- 0.5% = 0.5 Million

Total stock at t+1 =11 million

Thus growth rate is = 1 million / 10 million *100 = 10%

Step 2= Harvest rate calculations :-

Now we calculate this equation by :-

(Vt +1) -Vt =10Vt ( 1-Vt / 10000000)-hVt

where h is the harvest rate

Now we assume equilibrium volume as Ve setting both Vt and Vt +1 as Ve

Now equation is

Ve -Ve = 10Ve (1-Ve /10000000)- hVe

0= Ve (10 (1-Ve /10000000)-h)

Thus the product will be 0

Equation 2:-

1-Ve /10000000= h /10 = 0.1h

Thus there are two possible equilibrium

Ve =0

Ve = 10000000(1 - 0.1h )

Now the second outcome is negative

Thus taking the first outcome we conclude that the growth rate is 0.1 h=0

H =10%

Answer to question no c :-

To maintain the same volume only 1 million trees should be allowed to cut down