Introduction and Overview

Numerical allocation problems can serve at least two functions. First, they can make theory and methods less abstract and more meaningful. Second, they can serve as a useful bridge from theory and general models to the actual analysis of “real-world” allocation problems.

By a numerical problem we mean a problem in which functional forms have been specified and all relevant parameters and initial conditions have been estimated or calibrated. Recall in Section 1.2 that the general net benefit function took the form πt = π(Xt, Yt). The specific functional form adopted in E1.2 was πt = pYt − cYt/Xt, where p > 0 was a parameter denoting the per unit price for fish at the dock, Yt was the level of harvest in period t, c > 0 was a cost parameter reflecting the cost of effort for a particular fishing technology, and Xt was the fishable stock in period t. In a numerical problem we would need values for p and c which might be econometrically estimated from cross-sectional or time-series data, or calibrated on the basis of knowledge of a particular vessel or fleet of vessels.

Numerical analysis might involve both the simulation and the optimization of a dynamic system. By simulation we will usually mean the forward iteration of one or more difference equations. For example, in E1.1, you were told that a fish stock evolved according to the equation Xt+1 − Xt = rXt(1 − Xt/K) − Yt, or in iterative form Xt+1 = Xt + rXt(1 − Xt/K) − Yt.