Social preferences? Google Answers!

We analyse pricing, effort and tipping decisions at the online service ‘Google Answers’. Users set a price for the answer to their question ex ante, and they can additionally tip the researcher who provided the answer ex post.A positive wage-effort relationship is frequently found in laboratory gift-exchange games, yet field evidence for reciprocity in two-stage settings (wage, effort) is mixed. Our field data confirms lab findings for the three-stage design (wage, effort, bonus). Tipping is motivated by reciprocity, but also by reputation concerns among frequent users. Moreover, researchers seem to adjust their effort based on the user's previous tipping behaviour. An efficient sorting takes place when sufficient tip history is available.In addition, we analyse how tipping is adopted when the behavioural default is not to tip and suggest estimates for reciprocal and selfish (strategic and myopic) user types.     

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.     

When redistribution makes personalized pricing of externalities useless

We consider a standard optimal taxation framework in which consumers' preferences are separable in consumption and labor and identical over consumption, but are affected by consumption externalities. For every nonlinear, income-dependent pricing of goods there is a linear pricing scheme, combined with an adjusted income tax schedule, that leaves all consumers equally well-off and weakly increases the government's budget. The result depends on whether a linear pricing scheme exists that keeps the aggregate amount of consumption at its initial level observed under nonlinear pricing. We provide sufficient conditions for the assumption to hold. If adjusting the income tax rate is not available, personalized prices for an externality can enhance social welfare if they are redistributive, that is, favor consumers with a larger marginal social value of income.     

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.     

DIRECTED SEARCH AND THE BERTRAND PARADOX

I study a directed search model of oligopolistic competition, extended to incorporate general capacity constraints, congestion effects, and pricing based on ex post demand. In the presence of any one of these ingredients, the Bertrand paradox fails to hold. Hence, despite the emphasis that has been placed by the literature on sellers' capacity constraints as a resolution to the paradox, the existence of such constraints is only a subcase of a general class of environments where the paradox fails. Specifically, Bertrand's paradox will not arise whenever the buyers' expected utility from visiting a seller is decreasing in that seller's realized demand.     

INFLATION,OUTPUT, AND WELFARE*

We study the effects of anticipated inflation on aggregate output and welfare within a search‐theoretic framework. We consider two pricing mechanisms: ex post bargaining and a notion of competitive pricing. Under bargaining, the equilibrium is generically inefficient and an increase in inflation reduces buyers' search intensities, output, and welfare. If prices are posted and buyers can direct their search, search intensities are increasing with inflation for low inflation rates and decreasing for high inflation rates. The Friedman rule achieves the efficient allocation, and inflation always reduces welfare, although it can have a positive effect on output for low inflation rates.     

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.     

Separation of Regulatory Powers When Contracts Are Incomplete

The investment of a regulated firm affects the service/good provided on many dimensions. Should an integrated regulator take care of them all? Or is it better to have separate regulators responsible for them? We analyze the effect of the separation of regulatory powers on the regulated firm's ex ante incentive to invest in a “cooperative” innovation. The effects of the innovation are not verifiable and the cost of investing is sunk, hence, there is a problem of hold‐up. We find that when the innovation produces opposite effects the ex ante firm's incentive to invest is larger in the case of separation than in the case of integrated regulation. We also stress the risk of over‐investment that the separation of regulatory powers may induce. We maintain that along with classical incentive regulation—which mainly provides incentives for the firm to be efficient—the separation of regulatory powers may play a role in providing an incentive for cooperative innovations.     

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.     

Optimal Liquidity Provision Through a Demand Deposit Scheme: The Jacklin Critique Revisited

We derive conditions such that optimal liquidity provisions through a demand deposit scheme can be sustainably implemented in a subgame perfect Nash equilibrium under the assumption that renegade investors have free access to ex post asset markets. As our qualitative main finding we demonstrate that such sustainability is more likely for ‘poor’ than for ‘rich’ scheme participants in terms of future income. By establishing sustainability for low future income populations, our formal analysis therefore offers an important qualification of Jacklin's (1987) influential claim that an optimal demand deposit scheme is not sustainable whenever there exists the possibility of an ex post asset market.     

Feasibility of predatory pricing in a capacity-constrained duopoly

Predatory pricing is feasible only if the minimax profit of the prey is strictly smaller than the expected profit in the corresponding Bertrand-Nash equilibrium. We completely characterize the conditions for feasibility of predatory pricing in Kreps and Scheinkman's model of capacity-constrained duopoly. The predator must have a capacity larger than that of the prey, and also larger than the Cournot capacity. Surprisingly, predatory pricing may be infeasible not only if the prey is too large but also if it is too small.     

On the efficiency of ex ante and ex post pricing institutions

Summary This paper compares the performance of three pricing institutions in a decentralized matching model in which random matching occurs. In the first, sellers make public ex ante commitments to trade at pre-specified prices before matching occurs. In the second, the buyer and seller engage in an alternating offer bargaining game once a match has occurred. In the final pricing institution, one party is chosen at random to make a take it or leave it price offer. The steady state equilibrium with ex ante pricing pareto dominates the steady state equilibrium with ex post take it or leave it offers, which in turn pareto dominates the steady state equilibrium with alternating offers. As the discount factor goes to one, the equilibrium with ex ante pricing generates participation rates that tend toward the pareto efficient level. The ex post pricing institutions generate participation rates that are bounded away from efficient levels. The surplus loss associated with switching from ex ante pricing to take it or leave it offers is small when the discount factor is close to one. Contrary to many models of decentralized trade, ex post pricing institutions encourage too much search by buyers.The financial support of the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. The research for this paper was completed while the author was visiting the University of California at San Diego. The author thanks Douglas Gale for comments.     

Alternative Perspectives on Post-Keynesian Price Theory

We present an overview of recent developments in methodological and epistemological discussion in post-Keynesian work. We use these developments as a basis for judging various contributions to the post-Keynesian literature on pricing, in particular the arguments presented by Lee in recent issues of this journal, whilst acknowledging the positive contribution of Lee's work, we argue that his critique of post-Keynesian pricing theory is flawed and that his 'empirical pricing model' is consequently ill-founded.     

Efficient performance in two agent bargaining

This paper concerns ex ante incentive efficient performance in the bargaining of one buyer and one seller over a single item. For any element in a specified class of distributions of the buyer's and the seller's valuations of the item, all of the (interim) individually rational and efficient allocation rules are characterized. It is also shown that the “buyer's bid” and the “seller's price” double auctions are efficient for all distributions in the specified class. These results are obtained by studying efficiency as a linear programming problem.     

Cable Service and Its Implicit Marginal Valuation

The objective is to estimate the implicit marginal value of channel offerings by cable systems in the USA. Hedonic analysis is a convenient framework in which to explore the relationship between the price of cable service and the channels offered by a cable system. Two separate hedonic equations are estimated-- one for the price of analog cable service and one for the price of digital cable service. With regard to the price of analog cable service, the implicit marginal valuation is statistically significant and positive for just 15 of 106 channel offerings and negative for seven channels. For the price of digital cable service, the implicit marginal valuation is statistically significant and positive for just eleven of 105 channel offerings and negative for five channels. The results suggest that a subscriber's utility would be enhanced by a pricing structure different from the typical approach used by cable systems today of offering a bundled package consisting of several channels. One alternative is to allow consumers to subscribe to just those programming services for which they have a positive implicit marginal value (i.e. an a la carte pricing structure).     

Quality Uncertainty as Resolution of the Bertrand Paradox

It is well‐known that product differentiation eliminates the Bertrand paradox (i.e. marginal cost pricing under duopoly). While differentiation is often justified with reference to the consumer's ‘preference for variety’, the conditions under which such a preference is likely to arise are rarely considered. We investigate this question in a setting in which uncertainty about product quality can endogenously generate either convex or non‐convex preferences. We show that even when two goods are ex ante homogeneous, quality uncertainty can eliminate the Bertrand paradox.     

Monopoly Price Dispersion Under Demand Uncertainty

When a monopolist sets its price before its demand is known, then it may set more than one price and limit the availability of its output at lower prices. This article adds demand uncertainty and price rigidities to the standard model of monopoly pricing. When there are two states of demand and the ex post monopoly price is greater when demand is high then the monopolist's optimal ex ante pricing strategy is to set two prices and limit purchases at the lower price.     

Strategyproof sharing of submodular costs:budget balance versus efficiency

Summary. A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served, and then share the cost among them. If such a mechanism is budget balanced (covers cost exactly), it cannot be efficient (serve the surplus maximizing set of users) and vice-versa. We characterize the rich family of budget balanced and group strategyproof mechanisms and find that the mechanism associated with the Shapley value cost sharing formula is characterized by the property that its worst welfare loss is minimal. When we require efficiency rather than budget balance – the more common route in the literature – we find that there is a single Clarke-Groves mechanism that satisfies certain reasonable conditions: we call this the marginal cost pricing mechanism. We compare the size of the marginal cost pricing mechanism's worst budget surplus with the worst welfare loss of the Shapley value mechanism. Received: October 26, 1998; revised version: December 3, 1999     

Optimality versus practicality in market design: A comparison of two double auctions

We consider a market for indivisible items with m buyers and m sellers. Traders privately know their values/costs, which are statistically dependent. Two mechanisms are considered. The buyer's bid double auction collects bids and asks from traders and determines the allocation by selecting a market-clearing price. It fails to achieve all possible gains from trade because of strategic bidding. The designed mechanism is a revelation mechanism in which honest reporting of values/costs is incentive compatible and all gains from trade are achieved. This optimality, however, comes at the expense of plausibility: (i) the monetary transfers among the traders are defined in terms of the traders' beliefs about each other's value/cost; (ii) a trader may suffer a loss ex post; (iii) the mechanism may run a surplus/deficit ex post. We compare the virtues of the simple yet mildly inefficient buyer's bid double auction to the flawed yet perfectly efficient designed mechanism.