An Optimal Solution to a Resource Allocation Problem

to study a well known problem of resource allocation in microeconomics. We formulate the resource allocation problem as a finite-dimensional convex program under appropriate assumptions. Important properties of the constraints and objective function are discussed, which yield the existence and uniqueness of the optimal solution. The optimality conditions and KKT conditions are derived under a constraint qualification result. We then focus on a particular allocation problem for which a closed-form optimal solution is obtained. Finally, an exogenous growth model is discussed. We subsequently derive the relevant economic implications