untitled

as a function of abundance is dictated by the Ricker logistic equation (f(N)) and pro-

portionate harvest (H(N)) by the fixed effort equation (see Fig. 19.5):

R(N) =f(N) −N

H(N) =qEN

At equilibrium, H(N) =R(N) and N=H(N)/qE. By substitution and doing some alge-

braic rearrangement (we encourage you to try this yourself ), we can obtain the fol-

lowing solution for the harvest at equilibrium as a function of effort Heq(E):

This implies that there is an equilibrium harvest level for each effort that might be

exerted by resource users. We are now going to use this information to calculate the

most profitable level of effort to invest. We assume that the revenue scales with the

equilibrium harvest (with price per unit catch p=0.75) and that harvesting costs

(C) escalate linearly with effort (with cost per unit effort c=0.40) (Fig. 19.13):

costs(E) =cE

revenue(E) =pHeq(E)

Presumably resource users want to maximize profit (which we will denote Π), which

is the difference between revenue and costs:

Π(E) =pHeq(E) −cE

When economists discuss the cost of a particular activity, they are usually referring

to the opportunity cost. This is the difference between a given economic activity and

H E qEK

qE

r

e

eq()^

log ( )

=−

⎡ +

⎣⎢

⎤

⎦⎥

1

1

348 Chapter 19

40

30

20

10

0

0 20 40 60 80 100

Effort

Revenue or cost

Revenue

Cost

Stable equilibrium

Fig. 19.13Revenue and
costs under constant
environmental
conditions as a function
of effort. The
intersection of the
revenue curve and the
cost line identifies the
economic equilibrium,
at which cost equals the
potential gain.