Market and regulatory forces in the pricing of legal services

New data on individual law firms and attorneys is used to examine the effects of professional licensing restrictions and market forces on prices of legal services. The data allow detailed testing of the hypothesis that licensing restrictions serve to increase the price of professional services as well as the incomes of those providing these services. In general, little support is found for this hypothesis. Instead, the estimates show that market forces are most important in explaining variations in prices and attorney incomes.Dean Lueck is on leave from Louisiana State University. We thank William Boiger, Executive Director of the National Resource Center for Consumers of Legal Services, for providing data on law firms. Andrew Dick, Philip Hersch, Andy Kleit, Bill Kovacic, Fred McChesney, Jeff Moore, and two anonymous referees provided helpful comments on earlier versions. Chris Diener, Jim Larkins, Robert Pace, and Darrin Timothy provided research assistance.     

Responsive pricing

We study the efficiency property of responsive pricing, a scheme that proposes to increase prices as a function of the level of capacity utilization in environments where traditional allocation schemes (e.g. competitive markets, non-linear pricing) cannot be implemented in practice. We show that although responsive pricing implements allocations that are arbitrarily close to full capacity utilization (no wasted capacity and no excess demand), these allocations are not always efficient. We identify conditions under which efficiency occurs and discuss implications for the use of responsive pricing. We would like to thank seminar participants at the LSE, Venezia, Toulouse, and Copenhagen as well as Piero Gottardi, Karel Mertens, Marco Ottaviani, Markus Poschke, Karl Schlag, and Sanne Zwart for useful comments.     

软件产品定价的常见问题及定价策略

本篇文章首先对软件产品定价方式进行阐述,从定价模式问题、价格变动问题、定价针对性问题等多个方面,对软件产品定价的常见问题进行分析,并以此为依据,提出软件产品定价策略。     

Strategic nonlinear pricing

The objective of this paper is to examine the role of nonlinear strategies in a standard oligopoly framework. We demonstrate that nonlinear pricing may indeed emerge as an equilibrium strategy, but only when firms produce differentiated products, when one firm retains market power due to a cost advantage, or as part of an equilibrium in mixed strategies. In addition, we examine the role of nonlinear pricing in a spatial-competition framework. Our main conclusion is that in highly competitive markets, nonlinear pricing strategies are not likely to emerge as an equilibrium.     

Robust monopoly pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.     

Ramsey pricing in a hierarchical structure with an application to network-access pricing

This paper studies a hierarchical structure where an upstream regulated industry sells an intermediate good to a downstream regulated industry. Some sufficient conditions for all Ramsey prices to exceed marginal costs are derived. This hierarchical structure is shown to decrease the profit margin of the intermediate good but preserve its sign. Further, the hierarchical structure also decreases the profit margin of the final good sold by the downstream regulated industry. This is because this final good is a hierarchical complement to the intermediate good sold by the upstream regulated industry. The impacts upon other publicly produced goods, however, could be said to be neutral. Therefore, the hierarchical structure has asymmetric impacts upon publicly produced goods. Accordingly, the equiproportional output-reduction statement of Ramsey rule does not survive. This paper ends with providing an application to the network-access pricing problem.     

Rethinking real-time electricity pricing

Most US consumers are charged a near-constant retail price for electricity, despite substantial hourly variation in the wholesale market price. This paper evaluates the first program to expose residential consumers to hourly real-time pricing (RTP). I find that enrolled households are statistically significantly price elastic and that consumers responded by conserving energy during peak hours, but remarkably did not increase average consumption during off-peak times. The program increased consumer surplus by $10 per household per year. While this is only one to two percent of electricity costs, it illustrates a potential additional benefit from investment in retail Smart Grid applications, including the advanced electricity meters required to observe a household’s hourly consumption.     

Loss-leader pricing and upgrades

A new theory of loss-leader pricing is provided in which firms advertise low (below cost) prices for certain goods to signal that their other unadvertised (substitute) goods are not priced too high. The theory is applied to the pricing of upgrades. The results contrast with most existing loss-leader theories in that firms make a loss on some consumers (who buy the basic version of the good) and a profit on others (who buy the upgrade).     

Vickrey auctions with reserve pricing

Summary. We generalize the Vickrey auction to allow for reserve pricing in a multi-unit auction with interdependent values. In the Vickrey auction with reserve pricing, the seller determines the quantity to be made available as a function of the bidders' reports of private information, and then efficiently allocates this quantity among the bidders. Truthful bidding is a dominant strategy with private values and an ex post equilibrium with interdependent values. If the auction is followed by resale, then truthful bidding remains an equilibrium in the auction-plus-resale game. In settings with perfect resale, the Vickrey auction with reserve pricing maximizes seller revenues.Received: 31 December 2002, Revised: 5 May 2003, JEL Classification Numbers: D44, C78, D82.Correspondence to: Lawrence M. AusubelThe authors gratefully acknowledge the generous support of National Science Foundation Grants SES-97-31025, SES-01-12906 and IIS-02-05489. We appreciate valuable comments from Ilya Segal. Special thanks go to Mordecai Kurz, who served as Larry's dissertation advisor and who introduced both authors to the economics profession back at IMSSS at Stanford. Congratulations and best wishes are extended to Mordecai and his family on the happy occasion of the publication of Assets, Beliefs, and Equilibria in Economic Dynamics: Essays in Honor of Mordecai Kurz, in which this article also appears.     

The marginal pricing rule revisited

The purpose of the paper is to introduce a tighter definition for the marginal (cost) pricing rule. By means of an example, we illustrate the improvements that one gets with the new definition with respect to the former one using Clarke’s normal cone, and we discuss its consequences in terms of the existence of equilibria.      

Comparative statics of monopoly pricing

Summary. When consumers' willingness-to-pay increases by a uniform amount, the change in the resulting monopoly price is generally indeterminate. Our analysis identifies sufficient conditions on the underlying demand curve which predict both the sign and the magnitude of the resulting price change.     

Intertemporal monopolistic pricing of non-durables

This paper provides a tractable analytical framework to study intertemporal equilibria between non-competitive supply and dynamic demand for non-durable goods. The basic hypothesis is that consumers enjoy utility from particular services rather than from commodities. Consumption of the non-durable good follows a dynamic pattern, because it depends on the stock of durables and energy demand provides the prototypical example, e.g., mobility, thermal comfort, etc. are the output of a combination of durable and non-durable goods. Indeed, turmoils in energy markets are to a great deal due to short run inflexibility and this gives this theoretical paper a topical flavour. The outcomes differ substantially across the strategic setups while differences in expectations (myopic versus rational) matter only transiently but not in the long run.      

Natural monopoly and differential pricing

Under uniform pricing a monopolist cannot make a positive profit in equilibrium. I analyze how differential pricing can be exploited by a natural monopolist to deter entry when entry is costless. In a two-stage game with price competition before quantity competition I show that the incumbent firm can deter entry and make a positive profit in equilibrium. The incumbent sets two different prices, the low price to deter entry and the high price to generate profit. Entry is not possible because of scale effects. If dumping is allowed for all firms no positive profits are realizable, but welfare is reduced. I show that for some parameter values the incumbent is forced to engage in a stunt (i.e., set a negative low price) to keep entrants out.     

Asset pricing with adaptive learning

We study the extent to which self-referential adaptive learning can explain stylized asset pricing facts in a general equilibrium framework. In particular, we analyze the effects of recursive least squares and constant gain algorithms in a production economy and a Lucas type endowment economy. We find that (a) recursive least squares learning has almost no effects on asset price behavior, since the algorithm converges relatively fast to rational expectations, (b) constant gain learning may contribute towards explaining the stock price and return volatility as well as the predictability of excess returns in the endowment economy but (c) in the production economy the effects of constant gain learning are mitigated by the persistence induced by capital accumulation. We conclude that in the context of these two commonly used models, standard linear self-referential learning does not resolve the asset pricing puzzles observed in the data.     

Access charges under two-tier pricing

This article analyzes the regulation of access charges in a liberalized postal market where operators use two-tier pricing. It develops a model of vertical product differentiation that allows determination of the demand for First and Second Class mail from an incumbent postal operator and a group of entrants. The optimal access charges for First and Second Class letters are determined as well as the optimal quality for these services.      

The pricing of time-varying beta

We generalize an asset pricing model based on the Arbitrage Pricing Theory (APT) allowing beta to be time-varying. Making beta a random variable adds flexibility to the model because permits a non-linear relation between individual returns and the set of factors, and accounts for the effect of possible omitted variables. We integrate the conditional APT with a general linear stochastic process for beta. We analyze the behavior of the conditional expected return, the conditional variance and conditional covariance of individual asset returns as functions of the conditional moments of beta. On considering time-varying betas we introduce another source of uncertainty (risk) independent of the factors. We need to disentangle if this extra risk is systematic or non-systematic. To this end, we introduce a modified conditional APT model that rationalizes why the time variation of beta may represent extra systematic risk. For a sample of individual stocks, we test the hypothesis of time-varying beta and the feasibility of the modified conditional APT. We present a test for time-varying beta based on the conditional second moments of returns. We find that there is strong evidence against constancy of betas in favor of a random coefficient model, and that the time variation of beta is due to non-systematic behavior of the firms and investors should be able to diversify this risk away.     

Non-parametric and semi-parametric asset pricing

We find that the CAPM fails to explain the small firm effect even if its non-parametric form is used which allows time-varying risk and non-linearity in the pricing function. Furthermore, the linearity of the CAPM can be rejected, thus the widely used risk and performance measures, the beta and the alpha, are biased and inconsistent. We deduce semi-parametric measures which are non-constant under extreme market conditions in a single factor setting; on the other hand, they are not significantly different from the linear estimates of the Fama-French three-factor model. If we extend the single factor model with the Fama-French factors, the simple linear model is able to explain the US stock returns correctly.