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Ex Post vs. Ex Ante Pricing: Optional Calling Plans and Tapered Tariffs
 JOURNAL OF REGULATORY ECONOMICS
, 1992
"... We study optimal nonuniform pricing in a setting where a customer's demand at the start of a billing period contains a random variable whose realization becomes known by the end of the billing period. In this context, an optional calling plan is a tariff which the consumer must select based on ..."
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Cited by 12 (1 self)
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We study optimal nonuniform pricing in a setting where a customer's demand at the start of a billing period contains a random variable whose realization becomes known by the end of the billing period. In this context, an optional calling plan is a tariff which the consumer must select based on his/her expectations about the random variable, whereas, under a tapered tariff, the consumer's choice of usage charge is made after he/she knows the realization of the random variable. We show that for low to moderate levels of uncertainty about the random variable entering the demand function, the optional calling plan approach to nonuniform pricing yields higher expected profit than does the tapered tariff approach, given riskneutral consumers. We illustrate this finding with a case study and argue that it is consistent with the historical evolution of tariffs in the interexchange telecommunications market.
Bayesian Optimal Auctions via Multi to Singleagent Reduction
, 1203
"... We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multidimensional preferences over several possible configurations of the good (furthermore, it allows an agent’s budget and risk preference t ..."
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Cited by 11 (3 self)
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We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multidimensional preferences over several possible configurations of the good (furthermore, it allows an agent’s budget and risk preference to be known only privately to the agent). These are the main challenge areas for auction theory. A singleagent problem is to optimize a given objective subject to a constraint on the maximum probability with which each type is allocated, a.k.a., an allocation rule. Our approach is a reduction from multiagent mechanism design problem to collection of singleagent problems. We focus on maximizing revenue, but our results can be applied to other objectives (e.g., welfare). An optimal multiagent mechanism can be computed by a linear/convex program on interim allocation rules by simultaneously optimizing several singleagent mechanisms subject to joint feasibility of the allocation rules. For singleunit auctions, Border (1991) showed that the space of all jointly feasible interim allocation rules for n agents is a Ddimensional convex polytope which can be specified by 2D linear constraints, where D is the total number of all agents’
2004): “Allunits Discounts in Retail Contracts
 Journal of Economics & Management Strategy
"... Allunits discounts in retail contracts refer to discounts that lower a retailer’s wholesale price on every unit purchased when the retailer’s purchases equal or exceed some quantity threshold. These discounts pose a challenge to economic theory because it is difficult to understand why a manufactur ..."
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Cited by 3 (0 self)
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Allunits discounts in retail contracts refer to discounts that lower a retailer’s wholesale price on every unit purchased when the retailer’s purchases equal or exceed some quantity threshold. These discounts pose a challenge to economic theory because it is difficult to understand why a manufacturer ever would charge less for a larger order if its intentions were benign. In this paper, we show that allunits discounts may profitably arise absent any exclusionary motive. Allunits discounts eliminate double marginalization in a complete information setting, and they extract more profit than would a menu of twopart tariffs in the standard incomplete information setting with two types of buyers. Allunits discounts may improve or may reduce welfare (relative to menus of twopart tariffs) depending on demand parameters. 1.
Adjustment of an Affine Contract with FixedPoint Iteration
 Manuscript. URL: http://www.sal.hut.fi/Publications/pdffiles/mkit07.pdf
, 2003
"... We study a principalagent game where the principal commits to an a#ne contract. We suppose that the principal has incomplete information but he can adjust the contract according to the myopically behaving agent's reactions when the game is played repeatedly. The adjustment process can be c ..."
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Cited by 3 (3 self)
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We study a principalagent game where the principal commits to an a#ne contract. We suppose that the principal has incomplete information but he can adjust the contract according to the myopically behaving agent's reactions when the game is played repeatedly. The adjustment process can be considered as a learning model. We derive convergence conditions for fixedpoint iteration as an adjustment scheme and study a related continuous time process. The analysis is based on parameterizing the problem such that we obtain a degree zero homogeneous system of equations, where the nonlinear mapping satisfies Walras' law.
Positive And Negative Externality Effects On Product Pricing And Capacity Planning
, 1996
"... Physically constrained subscriptionbased telephone network services can experience opposing market forces which affect new product adoption. In such networks, a positive externality due to increases in subscribership encourages more consumers to sign up. As a result, the addition of users to the sy ..."
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Cited by 2 (0 self)
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Physically constrained subscriptionbased telephone network services can experience opposing market forces which affect new product adoption. In such networks, a positive externality due to increases in subscribership encourages more consumers to sign up. As a result, the addition of users to the system then leads to an increase in network load (measured in call minutes for the entire system). At some point, call demand exceeds network capacity and subscribers are forced to wait for call completion. This translates to a negative externality in the form of congestion and not only reduces the consumption by current customers but also discourages subscriber set expansion. These concurrent positive and negative externalities ultimately determine demand dynamics, given subscriber attitudes and pricing changes. A typical example of these subscriptionbased services can be found in the mobile communications industry. In the past few years, metropolitan cellular telephone has been plagued by m...
Constrained Monopoly Pricing with Endogenous Participation
, 2005
"... We present a flexible model of monopoly nonlinear pricing with endogenous participation decisions of heterogeneous consumers. Wemake use of themoments that define the few selfselecting tariff options that are commonly used to implement the optimal nonlinear tariff to estimate how demand and cost va ..."
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We present a flexible model of monopoly nonlinear pricing with endogenous participation decisions of heterogeneous consumers. Wemake use of themoments that define the few selfselecting tariff options that are commonly used to implement the optimal nonlinear tariff to estimate how demand and cost variables affect the pricing strategies offered by incumbent monopolists in several early U.S. local cellular telephone markets through the different elements of the theoretical model: marginal costs, average price sensitivity of demand, indexing parameters governing the distribution of the twodimensional type components, support of the distribution of types, and costs associated to the commercialization of tariff options. Intuitively, the sources of identification are the position and shape of each tariff offered by monopolists, the actual number and features of the tariff options used to implement them, as well as a measure of market penetration in each cellular market during the first and last quarter of monopoly regime. We use our model and the structural estimates to provide a performance comparison (profit+welfare) of nonlinear tariffs relative to linear (uniform), optimal twopart, Coasian marginal costplus fixed fee, and flat tariffs. We
J Optim Theory Appl (2008) 137: 641–673 DOI 10.1007/s1095700793391 Monotone Comparative Statics: Geometric Approach
, 2007
"... Abstract We consider the comparative statics of solutions to parameterized optimization problems. A geometric method is developed for finding a vector field that, at each point in the parameter space, indicates a direction in which monotone comparative statics obtains. Given such a vector field, we ..."
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Abstract We consider the comparative statics of solutions to parameterized optimization problems. A geometric method is developed for finding a vector field that, at each point in the parameter space, indicates a direction in which monotone comparative statics obtains. Given such a vector field, we provide sufficient conditions under which the problem can be reparameterized on the parameter space (or a subset thereof) in a way that guarantees monotone comparative statics. A key feature of our method is that it does not require the feasible set to be a lattice and works in the absence of the standard quasisupermodularity and singlecrossing assumptions on the objective function. We illustrate our approach with a variety of applications.
Handbook of Computational Economics, Volume 1, Elsevier Science Publishers, 1995. Chapter I.E. Nonlinear Pricing and Mechanism Design
, 1994
"... In applications of theories of incentives, the information known privately by an economic agent is represented by a point in a Euclidean space. Other agents know the probability distribution of this point, but not its realization, which is called the agent's type. For models of this sort, des ..."
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In applications of theories of incentives, the information known privately by an economic agent is represented by a point in a Euclidean space. Other agents know the probability distribution of this point, but not its realization, which is called the agent's type. For models of this sort, designs of optimal incentive schemes present few difficulties when agents ' types are onedimensional. The computational difficulties are severe, however, when the types are multidimensional. When the types are mdimensional, the main task is to solve a family of partial differential equations to obtain a map p: R in —> that provides the Lagrange multipliers for each type ' incentivecompatibility constraints. This chapter describes methods for solving simple versions that arise in nonlinear pricing and mechanism design. 1. Mirrlees ' Formulation To illustrate the origin of the central computational problem, we present the formulation