Pricing Access to a Monopoly Input

What price should downstream entrants pay a vertically integrated incumbent monopoly for use of its assets? Courts, legislators, and regulators have at times mandated that incumbent monopolies lease assets required for the production of a retail service to entrants in efforts to increase the competitiveness of retail markets. This paper compares two rules for pricing such monopoly inputs: marginal cost pricing (MCP) and generalized efficient component pricing rule (GECPR). The GECPR is not a fixed price, but is a rule that determines the input price to be paid by the entrant from the entrant's retail price. Comparing the retail market equilibrium under MCP and GECPR, the GECPR leads to lower equilibrium retail prices. If the incumbent is less efficient than the entrant, the GECPR also leads to lower production costs than does the MCP rule. If the incumbent is more efficient than the entrant, however, conditions may exist in which MCP leads to lower production costs than does the GECPR. The analysis is carried out assuming either Bertrand competition, quantity competition, or monopolistic competition between the incumbent and entrant in the downstream market.     

Pricing traffic in a spanning network

Users need to connect a pair of target nodes in the network. They share the fixed connection costs of the edge. The system manager elicits target pairs from users, builds the cheapest forest meeting all demands, and choose a cost sharing rule satisfying:Routing-proofness: a user cannot lower his cost by reporting as several users along an alternative path connecting his target nodes;Stand Alone core stability: no group of users pay more than the cost of a subnetwork meeting all connection needs of the group.We construct two such rules. When all connecting costs are 0 or 1, one is derived from the random spanning tree weighted by the volume of traffic on each edge; the other is the weighted Shapley value of the Stand Alone cooperative game. Both rules are then extended by the familiar piecewise-linear technique. The former is computable in polynomial time, the latter is not.     

The Costs of Implementing the Majority Principle: The Golden Voting Rule

In a context of constitutional choice of a voting rule, this paper presents an economic analysis of scoring rules that identifies the golden voting rule under the impartial culture assumption. This golden rule depends on the weights β and (1−β) assigned to two types of costs: the cost of majority decisiveness (‘tyranny’) and the cost of the ‘erosion’ in the majority principle. Our first main result establishes that in voting contexts where the number of voters n is typically considerably larger than the number of candidates k, the golden voting rule is the inverse plurality rule for almost any positive β. Irrespective of n and k, the golden voting rule is the inverse plurality rule if β ≥ 1/2 .. This hitherto almost unnoticed rule outperforms any other scoring rule in eliminating majority decisiveness. The golden voting rule is, however, the plurality rule, the most widely used voting rule that does not allow even the slightest ‘erosion’ in the majority principle, when β=0. Our second main result establishes that for sufficiently “small size” voting bodies, the set of potential golden rules consists at most of just three rules: the plurality rule, the Borda rule and the inverse plurality rule. On the one hand, this finding provides a new rationalization to the central role the former two rules play in practice and in the voting theory literature. On the other hand, it provides further support to the inverse plurality rule; not only that it is the golden rule in voting contexts, it also belongs, together with the plurality rule and the Borda method of counts, to the “exclusive” set of potential golden voting rules in small committees. We are indebted to Jim Buchanan, Amichai Glazer, Noa Nitzan, Ken Shepsle, and an anonymous referee for their useful comments.     

Transfer Pricing Rules,OECD Guidelines,and Market Distortions

We study the impact of transfer pricing rules on prices, firms' organizational structure, and consumers' utility in a two‐country monopolistic competition model with source‐based profit taxes. Firms can either be multinationals and serve the foreign market through a fully controlled affiliate, or be exporters and serve the foreign market by contracting with an independent distributor. The use of the OECD's comparable uncontrolled transfer price (CUP) rule distorts firms' output and pricing decisions, because the comparable arm's length transactions between exporters and distributors—which serve as the benchmark—are not efficient. We show that the CUP rule is detrimental to consumers in the low‐tax country, yet benefits consumers in the high‐tax country when compared to the benchmark of unconstrained profit shifting. Using the OECD rule increases tax revenue at the expense of consumer surplus. Those results also hold under the alternative cost‐plus transfer pricing rule.     

Duplicating and Pricing Contingent Claims in Incomplete Markets

The paper studies the problem of pricing contingent claims in the situation where the constraints imposed on an investor's portfolios are important. There are two types of rule of constraint: under a rigid rule, an investor must strictly limit his portfolios inside the constraint; under an elastic rule, an investor pays a penalty when the constraint is violated. The central problem of pricing a contingent claim is to determine the initial investment required to duplicate the contingent claim. The following results are obtained: (i) under elastic rules, the cost to duplicate a contingent claim exists and is unique;(ii) this cost depends nonlinearly and convexly on the contingent claim;(iii) the cost under rigid rules resulting from passing the penalty to infinity is also a nonlinear and convex function of the contingent claim. Owing to this nonlinearity, the cost of duplication may be or may not be the nonarbitrage price of the contingent claim; this depends on how the market organizes the production of contingent claims. The conclusion that the cost of duplication is a convex function of the contingent claim provides an explanation for why the service of providing contingent claims is often a highly profitable business. The main mathematical tool in the analysis is backward stochastic differential equations (BSDEs). In fact the cost to duplicate a contingent claim is the solution of a BSDE in which the contingent claim is the terminal value.     

Optimal pricing and capacity choice for a public service under risk of interruption

We develop rules for pricing and capacity choice for an interruptible service that recognize the interdependence between consumers’ perceptions of system reliability and their market behavior. Consumers post ex ante demands, based on their expectations on aggregate demand. Posted demands are met if ex post supply capacity is sufficient. However, if supply is inadequate all ex ante demands are proportionally interrupted. Consumers’ expectations of aggregate demand are assumed to be rational. Under reasonable values for the consumer’s degrees of relative risk aversion and prudence, demand is decreasing in supply reliability. We derive operational expressions for the optimal pricing rule and the capacity expansion rule. We show that the optimal price under uncertainty consists of the optimal price under certainty plus a markup that positively depends on the degrees of relative risk aversion, relative prudence and system reliability. We also show that any reliability enhancing investment—though lowering the operating surplus of the public utility—is socially desirable as long as it covers the cost of investment.     

Pricing rules and Arrow–Debreu ambiguous valuation

This paper considers pricing rules of single-period securities markets with finitely many states. Our main result characterizes those pricing rules C that are super-replication prices of a frictionless and arbitrage-free incomplete asset structure with a bond. This characterization relies on the equivalence between the sets of frictionless securities and securities priced by C. The former captures securities without bid-ask spreads, while the second captures the class of securities where, if some of its delivers is replaced by a higher payoff, then the resulting security is characterized by a higher value priced by C. We also analyze the special case of pricing rules associated with securities markets admitting a structure of basic assets paying one in some event and nothing otherwise. In this case, we show that the pricing rule can be characterized in terms of capacities. This Arrow–Debreu ambiguous state price can be viewed as a generalization for incomplete markets of Arrow–Debreu state price valuation. Also, some interesting cases are given by pricing rules determined by an integral w.r.t. a risk-neutral capacity. For instance, incomplete markets of Arrow securities and a bond are revealed by a Choquet integral w.r.t. a special risk-neutral capacity.     

Optimal card payment systems

This paper presents a model of a card payment system to address the pricing and rules that govern such systems. It evaluates the social optimality of privately set interchange fees and the adoption of a rule by payment systems to prevent merchants surcharging for card transactions using two extremes of merchant pricing—monopolistic pricing and perfect competition. Both types of merchant pricing constrain the ability of card schemes to use interchange fees and the no-surcharge rule in anticompetitive ways, although for quite different reasons. The positive role of the no-surcharge rule in preventing excessive merchant surcharging is also highlighted.     

Cost Sharing under Increasing Returns: A Comparison of Simple Mechanisms

A technology with decreasing marginal costs is used by agents with equal rights. Each agent demands a quantity of output and costs are divided by means of a fixed formula. Several such mechanisms are compared for the existence of Nash equilibrium demand profiles and for the equity properties of these equilibria. Among three mechanisms, average cost pricing, the Shapley–Shubik cost sharing, and serial cost-sharing, only the latter two possess at least one Nash equilibrium on a reasonable domain of individual preferences. Only the serial cost sharing equilibria pass the equity tests of No Envy and Stand Alone cost.Journal of Economic LiteratureClassification Numbers: C72, D63.     

Why equity cannot be separated from efficiency: the welfare economics of progressive social pricing

Applied neoclassical microeconomists maintain that when profits are constrained, and average costs are higher than marginal costs, Ramsey “inverse elasticity” pricing optimizes static consumer welfare. However, when weighted, instead of unweighted, consumer surplus aggregation is used, the Ramsey pricing rule becomes a “progressive social pricing rule,” which suggests that under plausible conditions “direct-elasticity” rather than “inverse-elasticity” pricing is consumer welfare optimal.     

Price cap regulation of a dominant firm facing competition

Price cap regulation is typically applied to natural monopolies operating with subadditive costs. Price caps are known to provide superior incentives for the regulated monopoly to pursue cost reduction and, in a multiservice/product context, undertake welfare enhancing price discrimination. It is well known that capping a Laspeyres index of the firm’s prices induces the monopoly to charge socially optimal “Ramsey” prices in the long run. This paper examines the suitability of the Laspeyres form of regulation when the regulated firm faces competition in the market for one of its services (outputs). We present the appropriately modified Ramsey pricing rule for the regulated dominant firm and demonstrate that capping a Laspeyres index of the dominant firm’s prices leads to prices that satisfy this pricing rule in the long run.     

Behavioral rules and sequences of macroequilibria

This paper compares the dynamic consequences of several diferent behavioral rules involving price or quantity adjustments in a temporary equilibrium, macroeconomic framework. The central rule studied is the widely practiced, cost mark-up, administered pricing rule. A competitive, quantity adjustment rule based on a target rate of return is also examined. These are contrasted with monopolistic, profit maximizing price and quantity adjusting rules. Although the analysis represents but an initial foray into the territory where the interests of behavioral and macroeconomic theories overlap, the results, which trace stagflation to instabilities in ‘permanent’, full-employment equilibrium, suggest that further work in this direction may improve our understanding of present inflationary phenomena.     

Optimal pricing when rational consumers anticipate monitoring cost

This article considers a monopolistic firm’s optimal pricing decision over two periods among dynamic pricing, preannounced pricing and single pricing. In the models, consumers rationally determine whether to exhibit strategic waiting by weighing their costs against prospectively lower price. Our analysis yields three main results. First, single pricing that completely eliminates strategic waiting surely would be dominated by intertemporal pricing when facing rational consumers. Second, preannounced pricing may actually yield lower revenue than dynamic pricing when considering its effect on the reduction of consumer monitoring cost. Only when monitoring costs under dynamic pricing and under preannounced pricing are equal, is firm revenue weakly greater under preannounced pricing than under dynamic pricing. Third, in dynamic pricing equilibrium, increasing monitoring cost may increase firm revenue, consumer surplus and social welfare simultaneously.     

Endogenous fluctuations under evolutionary pressure in Cournot competition

An evolutionary game theoretic model of Cournot competition is investigated. Individuals choose from a finite set of different behavioral rules. Each rule specifies the quantity to be produced in the current period as a function of past quantities. Using more sophisticated rules may require extra information costs. Based upon realized payoffs, the fractions of the population choosing a certain behavioral rule are updated according to the replicator equation with noise. The long-run behavior of the evolutionary system consisting of the population dynamics coupled with the quantity dynamics of the Cournot game may be complicated and endogenous fluctuations may arise. We consider a typical example where firms can choose between two rules: the Nash rule and the best-reply rule. We show that a homoclinic tangency between the stable and unstable manifold of the equilibrium occurs as evolutionary pressure increases, implying bifurcation routes to complicated dynamics and strange attractors.     

On the optimality of the full-cost pricing

This article is aimed at defining the full-cost pricing as a leader-follower game in two-tier organizations: (i) the upstream unit fixes the production capacity and uses it as a cost driver to compute the average cost; (ii) the downstream unit operates on the market and chooses the output level on the basis of the average cost. In the Cournot oligopoly case, the full-cost pricing is compared with other pricing rules. There exists a wide range of values of the fixed cost, for which the full-cost pricing dominates any other pricing rules, in terms of gross profit.     

A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems

In this paper we present an axiomatic characterization of the weighted Shapley value of the optimistic TU game associated with a minimum cost spanning tree problem. This characterization is based on two monotonicity properties, population monotonicity (if a new agent joint the society nobody is worse off) and the strong cost monotonicity (if the connection cost between any pair of agents increases nobody is better off), and weighted share of extra costs (the extra costs should be divided proportionally to the weights of the agents).      

Fair waste pricing: an axiomatic analysis to the NIMBY problem

A waste disposal facility has to be sited in one of several districts producing different amounts of waste. The construction cost of the facility depends on where it is sited. When a district accepts the facility, it bears a disutility. The problem here is to choose a siting district and to share the construction cost while considering fair compensation for the siting district. We provide an axiomatic framework to analyze this problem and seek normatively desirable and practical decision rules. A fair pricing rule is one that selects a district so as to minimize the social loss, applies a negative price to waste according to the social loss involved, and provides full compensation to the siting district. We show that this rule is a unique rule that satisfies certain requirements of efficiency, fairness, and robustness regarding the strategic transfers of waste. We then establish the nearly robustness of this rule to the misrepresentation of disutility information.     

An expected utility analysis of k-majority rules

Buchanan and Tullok (The calculus of consent: logical foundations of constitutional democracy. University of Michigan Press, Ann Arbor, 1962) argued that the optimal k-majority rule should minimize the sum of external costs and decision costs. Dougherty et al. (Public Choice, 163(1–2):31–52, 2015) formalized their approach using various groups of voters. In this study, we analyze the optimal k-majority rule in terms of expected utility and compare our results to Dougherty et al. (2015), which focuses on costs alone. Specifically, we replace Buchanan and Tullock’s external cost function with an external utility function that accounts for both the benefits and costs of enacting proposals. We find that analyzing k-majority rules in terms of utility, rather than costs, affects the optima. Furthermore, in terms of utility, the optimal k-majority rule can vary depending on the group one expects to be in during a vote. With some interesting exceptions, individuals from groups that favor the proposal often find small k-majority rules optimal. Individuals from groups that oppose the proposal often find large k-majority rules optimal.     

Discrete clock auctions: an experimental study

We analyze the implications of different pricing rules in discrete clock auctions. The two most common pricing rules are highest-rejected bid (HRB) and lowest-accepted bid (LAB). Under HRB, the winners pay the lowest price that clears the market; under LAB, the winners pay the highest price that clears the market. In theory, both the HRB and LAB auctions maximize revenues and are fully efficient in our setting. Our experimental results indicate that the LAB auction achieves higher revenues. This revenue result may explain the frequent use of LAB pricing. On the other hand, HRB is successful in eliciting true values of the bidders both theoretically and experimentally.