An Optimal Tax Incentive Scheme for a Decentralized Multi-Product Firm

Consider a multi-product firm facing an uncertain demand. It will be shown that the firm may benefit from decentralizing the decisions of how much to produce. To obtain these benefits, the firm should use the suggested internal tax incentive scheme. The quantities determined under the suggested scheme are equal to the sum of the quantities determined under centralization and a random vector with zero mean. This result is attributed to the dynamics by which a decentralized solution is obtained. It follows that the central planner may improve his decisions by behaving according to similar dynamics. A tax incentive scheme which guarantees improvement by decentralization may be unfair to some decentralized units. Sufficient conditions will be given for the existence of a fair scheme which improves on the centralized solution. It will be shown that if the uncertainty in the demand is large such a scheme will usually exist.