SOS325 Homework #5


SOS 325

Homework #5: Renewable Resources, Common Property and Open

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

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)?
.1 X(1?.gif”>)

Suppose that
harvest occurs according to the following relationship: Yield = Y=qEX, where Eis “effort” pursuing the resource (number of boats for a fishery
or number of hunters for big game hunting) and q = .001.

(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?

(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 “harvest/effort” or “yield/effort”
curve). What level of effort exhausts
the resource? What amount of effort is
consistent with the maximum sustainable harvest of the resource?

(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?

(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 you’ve 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.)

(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)?

(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?

(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



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