Economic Theory and Experiments - David Delacretaz (University of Manchester)

Title: Public Good Provision: The Lindahl-VCG Relationship

Abstract: We consider a public good environment in which the agents consuming the public good have quasilinear utility. We show that if the public good must be provided as a single, indivisible unit, then the VCG transfer paid by each agent is equal to the smallest Lindahl expenditure of this agent, while the largest Lindahl revenue of the firm is equal to the VCG transfer received by the firm. If the public good can be provided in multiple units, then the smallest Lindhal price of an agent is an upper bound on the agent’s marginal VCG transfer for each unit on which the agent is pivotal, and the largest Lindahl revenue of the firm is a lower bound on the firm’s VCG transfer. Consequently, the difference between the largest Lindahl revenue of the firm and the sum of the smallest Lindahl expenditures of each agent is equal to the VCG deficit with a single unit and a lower bound on the VCG deficit with multiple units. Our results extend to the provision of public bads such as data usage by platforms that harms consumers.