Essays on Nonlinear Pricing and Welfare

University dissertation from Department of Economics, Lund University, P.O. Box 7082, S-220 07, LUND, Sweden

Abstract: The price of a good is said to be nonlinear if the unit price not is constant but depends on some aspect of the quantity (or quality) purchased. This form of pricing is commonly used in many industries, e.g. the electricity and water industries, and has many desirable properties. For example, nonlinear pricing is often necessary for (Pareto) efficiency and nonlinear pricing can be used as an instrument to redistribute income among consumers. This thesis consists of three theoretical essays on nonlinear pricing and welfare. Our main objective is to characterize “optimal” nonlinear pricing schedules and investigate their welfare properties. The economy under consideration consists of a finite set of differing consumer types and one publicly owned monopoly. The preferences of the consumers are assumed to be linear in money and the demand curves are assumed not to cross. The monopoly is restricted by a balanced-budget requirement. In the first essay, we consider an economy that is based on the above premises with the additional assumption that net utility from consumption is so high that that every consumer in the economy receives a non-negative utility by consuming the publicly provided good. The chapter contributes to the existing literature in two senses. Firstly, we completely characterize the set that consists of all envy-free (i.e. incentive compatible), budget-balanced and Pareto efficient nonlinear pricing schedules. Secondly, we introduce a new procedure to investigate and analyze nonlinear pricing schedules. In the second essay, we investigate nonlinear pricing schedules that are based on a cooperative surplus sharing game with transferable utility. The chapter contributes to the existing literature in three senses. Firstly, we characterize the envy-free core of the cooperative pricing game and provide necessary and sufficient conditions for the envy-free core to be non-empty. Secondly, we implement nonlinear outlay schedules that are based on a cooperative surplus pricing game with transferable utility in a nonlinear pricing environment with asymmetric information. Lastly, we investigate and analyze nonlinear pricing schedules that are based on some well known solution concepts for the cooperative game (the Shapley value, the Lorentz criterion and the equal share rule). In the third essay, we implement the equality of opportunity (EOp, henceforth) criterion in a nonlinear pricing environment that is based on the same premises as in the first essay, and investigate the welfare properties of the optimal nonlinear EOp outlay schedule. In our analysis, the maximin and the utilitarian nonlinear schedules serve as benchmarks. We demonstrate that the optimal EOp policy is a reasonable compromise between the optimal maximin and the optimal utilitarian policy in that the EOp policy is more (less) efficient, from a first-best perspective, than the maximin (utilitarian) policy and, at the same time, more (less) egalitarian than the utilitarian (maximin) policy. The main contribution to the literature is that we present a framework under which the EOp criterion can be applied in order to derive optimal EOp nonlinear pricing schedules.

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