Triple benefits from spatial resource management

Authors: M. Neubert and G. Herrera, 2008.

Considers the same model as Neubert (2003), i.e.

$ u_t(t,x) = ru(t,x)(1-u(t,x)/k) + d\frac{\partial^2 u(t,x)}{\partial x^2} - qE(t,x)u(t,x) $

but instead of approaching the problem from the perspective of a single owner, i.e. maximizing yield

$\int_0^L h(x)u(x)dx$,

this paper maximizes rents, which happen to be modeled as

$ \int_0^L [pqu(x) - (w_0 + w_1E(x))]E(x) dx $.

(Note the odd cost structure. Idea: quadratic captures the fact that high effort density means more fishermen are tripping over one another's lines.)

Solutions are numeric and graphical, but show several things:

1. Effort concentrated near boundaries, where population levels are low.

2. At rent-maximizing equilibrium, stock levels and effort levels are often both higher than at open access equilibrium.

3. Conditions that support this phenomenon basically boil down to having heterogeneity and misaligned incentives (i.e. harvestors want one thing, regulators another.)


Questions/TODO

1. Are these numerics any stabler than the one for Neubert (2003)? I'll want to try to reproduce the graphics.

2. Can some of the corresponding patch or age-structured models be easily worked out? Worth taking a look.