The political economy of marine reserves: Understanding the role of opportunity costs

Authors: M. Smith, J. Lynham, J. Sanchirico, and J. Wilson, 2009.

This paper takes as its point of departure an elementary model for the costs and benefits of working in a fishery. The meat of the work consists of a qualitative analysis of how changes in certain model parameters yield changes in incentives for fishermen. The basic "willingness to pay" model (WTP) is

$\displaystyle{ E(WTP) = \ln \left[ e^{\alpha} + \sum_{j=1}^J \exp \left( p_t q_j X_{jt} - c - \phi z_j\right) \right] - \ln \left[ e^{\alpha} + \sum_{j=1}^{J-1} \exp \left( p_t q_j X_{jt} - c - \phi z_j\right) \right] .}$

By adjusting these parameters, the authors generate Table 1 and Figure 1 in the paper. Figure 2 considers the "long term", i.e. analyzes how these preferences change over time. The data are produced by a meta-population growth model of the form

$\displaystyle{ X_{jt+1} - X_jt = f(X_{jt}) X_{jt} - d(X_{1t}, X_{2t}, X_{3t}) - \sum_i^N q_j E_{ijt} X_{jt} }$

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Matlab code is here.

Comments/Questions:

1. This is a toy model, and it doesn't involve data. I find it interesting that this was of sufficiently wide-spread interest that it found its way into PNAS.

2. In the long-term model, are there only three patches (i.e. "choices" for the fisherman), or are there subpatches within the meta-patches?