An Optimal Solution to a Resource Allocation Problem under COVID-19 Financial Constraints

Abstract

Public health implications of COVID-19 resulted in widespread business closures and job losses. Disruptions in the service and transportation sectors, acute reductions in income, and an uptick in unemployment were the outcome of pandemic mitigating procedures adopted by many governments. While these measures succeeded in curving death rates, they failed to protect the economy and resulted in many parts of the world in economic covidmageddon. In this paper, we use optimization tools to study a well known problem of resource allocation in microeconomics and adapt it to the financial constraints created by COVID-19. 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 under the constraints created by COVID-19. The optimality conditions and KKT conditions are derived under a constraint qualification result. We then focus on the COVID-19 allocation problem for which a closed-form optimal solution is obtained. The corresponding exogenous growth model is discussed. The Solow model is derived using raw dynamic programming. We subsequently obtain and present the relevant economic implications for the protection of economic prosperity during pandemics such as COVID-19.