Solving Numerical Allocation Problems Using Excel's Solver

Abstract

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” resource-allocation problems. By a numerical problem , I mean a problem where functional forms have been specified, and all relevant parameters and initial conditions have been estimated or assigned values. For example, in Section 1.4, the general net-benefit function took the form π t = π( X t , Y t ). A specific functional form , used in Exercises E1.1 through E1.3, was, where p > 0 was a parameter denoting the per-unit price for fish on the dock, Y t was the level of harvest in period t, c > 0 was a cost parameter, and X t was the fish stock in period t . In a numerical problem, we would need values for p > 0 and c > 0, which might be estimated econometrically or simply assigned values based on a knowledge of current market prices and the cost of operating a fishing vessel. Numerical analysis might involve solving an implicit equation for the steady-state value of a resource stock, the deterministic or stochastic simulation of a harvest or extraction policy, or the selection of escapement, harvest, or extraction rates to maximize some measure of present value.