## SOS325 Homework #5

Name:

________________________________

SOS 325

Homework #5: Renewable Resources, Common Property and Open

Access

Answer all questions

on this sheet of paper and turn it in in-class or submit it electronically via

Blackboard by 4:30 pm December 3rd (the last day of class). Do NOT email it to me or the TA. Make your answers clear, legible and to the

point.

1.(100 pts.) Consider a resource whose net

growth in biomass (X) each year F(X)is given by a logistic growth

function where r=.1and K=10.

(You can think of the units of the biomass as being millions of animals

so that the carrying capacity of the environment is ten million animals.)

X

F

( X)?

rX(1

?

X/

K)?

.1 X(1?.gif”>)

10

Suppose that

harvest occurs according to the following relationship: Yield = Y=qEX, where Eis âeffortâ pursuing the resource (number of boats for a fishery

or number of hunters for big game hunting) and q = .001.

a.

(10 pts.) Graph the growth function of the

biomass F(X), being clear to label

maximum sustainable yield (MSY) harvest, biomass levels at MSY and carrying

capacity on your graph. What is the

maximum amount of harvest that can be sustainably achieved in this system? What level of biomass generates this amount

of harvest?

b.

(15 pts.) Now, using the equation derived in

class and in Keohane and Olmstead, graph the curve showing the sustainable

harvest for any given amount of effort (the âharvest/effortâ or âyield/effortâ

curve). What level of effort exhausts

the resource? What amount of effort is

consistent with the maximum sustainable harvest of the resource?

c.

(15 pts.) Suppose ecologists discover that r=.05rather than .1 so that the growth

rate for any level of biomass is now much lower than thought. Graph the new yield/effort curve. How does this change your answers to the

previous question? If managers set

effort to the level that would maximize sustainable yields in question b), what

would happen to the biomass over time?

d.

(20 pts.) Sticking to the parameter values given

in a) and b), suppose that the price of a single unit of harvest is 1000 (so

that the sustainable revenue/effort curve is 1000 times the harvest/effort

curve youâve already found in question b) and the cost of a unit of effort is

constant and =1. Find the level of

effort that maximizes sustainable profits.

(NOTE: It is ok to find this number graphically or by trial and error

substitution into the equation.)

e.

(20 pts.) Find the level of effort that you

would expect to occur under open access conditions. How does this compare to the level found in

question d)? Can you tell if the stock

will be biologically overexploited (i.e. at a level of biomass below the level

consistent with the production of maximum sustainable yield)?

f.

(10 pts.) Suppose that the resource stock is

privatized to a single individual or corporation. How much effort would you expect them to

utilize assuming that they have as their goal the maximization of sustainable

profits? Would they have an incentive to

defend the resource against encroachment by other users? Why?

g.

(10 pts.)

Resource managers, faced with the open access conditions described in

e), subsidize fuel costs and supply low-interest loans to harvesters, lowering

the marginal cost of a unit of effort.

The objective of this program is to improve the livelihoods of

resource-dependent communities.

Graphically demonstrate how this affects the amount of long-run effort

in the industry. What happens to

sustainable profits? Resource

stocks?