Package Sizes, Tariffs, Quantity Discount and Premium

We analyze nonlinear pricing problem under monopoly using two hidden types of agents with linear demands and fully characterize all possible optimal solutions for both ordered and non-ordered demands. We show that both optimal packages can either contain Pareto-efficient quantities or one package can be undersized or oversized. All these effects are non- degenerate and are expected to hold for nonlinear demands. Surprisingly, the total output under nonlinear price discrimination with self- selection is neither unambigously realted to efficiency nor to the degree of monopoly power (demand elasticity). We also show that under limited range of parameters quantity premia can occur only when demands are ordered.Principal-agent, self-selection, nonlinear pricing, package pricing, Pareto efficiency

Informational Structure and Effciency in Monopoly

The paper focuses on efficiency under monopoly. Contrary to common wisdom, nine examples given in the paper show that a Pareto-efficient output in monopoly is possible under both linear and nonlinear pricing. Pareto efficiency can be achieved when consumers are homogeneous as well as heterogeneous. Since Pareo-efficiency is possible under different demand and cost conditions; different pricing strategies; and different degree of consumer heterogeneity, in general, monopoly per se is not the cause for ineficiency.Monopoly, Pareto Efficiency

All solution graphs in multidimensional screening

We study general discrete-types multidimensional screening without any noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming equality) constraint can be perceived as "envy" arc from one type to another, so the set of active constraints is a digraph. We find that: (1) any solution has an in-rooted acyclic graph ("river"); (2) for any logically feasible river there exists a screening problem resulting in such river. Using these results, any solution is characterized both through its spanning-tree and through its Lagrange multipliers, that can help in finding solutions and their efficiency/distortion properties.incentive compatibility; multidimensional screening; second-degree price discrimination; non-linear pricing; graphs

Equilibrium structures in vertical oligopoly

The central purpose of this paper is to examine vertical integration as an equilibrium phenomenon. We model it as integration between Cournot oligopolists in both the upstream and the downstream stages. We consider the issue of private profitability versus collective profitability and show that under several situations the equilibrium outcomes may result in a Prisoner's dilemma. The analysis is extended to consider equilibrium outcomes in a dynamic setting, where we find no integration to be a relatively common outcome.

An application of Ramsey model in transition economy: a Russian case study

This case study uses the Ramsey model to analyze whether the current electricity prices charged by the natural monopoly Novosibirskenergo in a major industrial region of the Russian Federation are socially optimal. Our estimates of demand elasticities for two major groups of consumers, namely households and industrial users, show that prices are not socially optimal. A decrease in price for industrial users and an increase in price for households would bring the prices closer to socially optimal.Natural monopolies; Transition economy; Ramsey model.

Pay What You Like

We show that when a seller of a di¤erentiated good o¤ers the product allowing consumers an option to pay what they like, then all consumers will never free ride in equilibrium when their valuations of the good are positive, and, under certain conditions, all will consumers would pay. Further, for the seller this pricing could be more pro�table than uniform pricing. If consumers consider the social cost of free riding, or not paying a "fair" price, then our results show that consumers, rather than free riding, may not opt for this option. Instead, they prefer to purchase the good at the market price from a price-setting firm

Pay What You Like

We show that when a seller of a di¤erentiated good o¤ers the product allowing consumers an option to pay what they like, then all consumers will never free ride in equilibrium when their valuations of the good are positive, and, under certain conditions, all will consumers would pay. Further, for the seller this pricing could be more pro�table than uniform pricing. If consumers consider the social cost of free riding, or not paying a "fair" price, then our results show that consumers, rather than free riding, may not opt for this option. Instead, they prefer to purchase the good at the market price from a price-setting firm

All solution graphs in multidimensional screening

We study general discrete-types multidimensional screening without any noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming equality) constraint can be perceived as "envy" arc from one type to another, so the set of active constraints is a digraph. We find that: (1) any solution has an in-rooted acyclic graph ("river"); (2) for any logically feasible river there exists a screening problem resulting in such river. Using these results, any solution is characterized both through its spanning-tree and through its Lagrange multipliers, that can help in finding solutions and their efficiency/distortion properties

All solution graphs in multidimensional screening

We study general discrete-types multidimensional screening without any noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming equality) constraint can be perceived as "envy" arc from one type to another, so the set of active constraints is a digraph. We find that: (1) any solution has an in-rooted acyclic graph ("river"); (2) for any logically feasible river there exists a screening problem resulting in such river. Using these results, any solution is characterized both through its spanning-tree and through its Lagrange multipliers, that can help in finding solutions and their efficiency/distortion properties