Hotelling’s webshop

We extend Hotelling’s model of spatial competition by adding an outside good, provided by a webshop. Unlike the commonly used reservation price, the price of the webshop is endogenous. We establish that a Nash equilibrium exists if the outside good is not too different from the goods sold by the bricks-and-mortar shops. Equilibrium prices positively depend on transport costs, which would not be the case for an exogenous reservation price. If the webshop serves an alternative market as well, the price of that market is partly imported into the local market. The bricks-and-mortar shops compete only with the the webshop. The lower the webshop’s delivery costs are relative to the transport cost parameter, the wider the feasible range for locations of the bricks-and-mortar shops.     

The impact of bargaining on markets with price takers: Too many bargainers spoil the broth

In this paper we study how bargainers impact on markets in which firms set a list price to sell to those consumers who take prices as given. The list price acts as an outside option for the bargainers, so the higher the list price, the more the firms can extract from bargainers. We find that an increase in the proportion of consumers seeking to bargain can lower consumer surplus overall, even though new bargainers receive a lower price. The reason is that the list price for those who do not bargain and the bargained prices for those who were already bargaining rise: sellers have a greater incentive to make the bargainers’ outside option less attractive, reducing the incentive to compete for price takers. Competition Authority exhortations to bargain can therefore be misplaced. We also consider the implications for optimal seller bargaining.     

Hotelling's competition with general customer distributions

Hotelling and his critics assumed uniformly distributed demand. In this note the solution is characterized for any distribution F and some propositions follow. For any F an equilibrium does not exist if the duopolists are located too closely together, but another distribution can be always found for which an equilibrium does exist. When we observe duopolies in equilibrium with closer and closer proximity we can expect the density in the area of contention to go up and prices and profits to go down. Hotelling's known suggestion that any duopolist has an advantage to move his location towards the other, and thus creating a tendency for the differentiation to diminish, holds whenever an equilibrium exists.     

Are input prices irrelevant for make-or-buy decisions?

The 1996 Telecommunications Act requires incumbent providers to lease network inputs to rivals at cost-based prices in order to jump-start competition. Sappington (Sappington, D. (2005). American Economic Review, 95(5), 1631–1638) uses the Hotelling model to show that input prices are irrelevant for an entrant’s decision to make or buy an input required for downstream production. We show that this result depends upon the particular model of competition employed. Specifically, input prices are not necessarily irrelevant in the Bertrand vertical differentiation model and are not irrelevant in the Cournot model. It follows that departures from cost-based input prices may distort entrants’ make-or-buy decisions in settings of practical interest.      

The benefits of storage and non‐renewable resource price dynamics

Abstract Both the Theory of Storage and the Hotelling model play a prominent role in the study of non‐renewable resource prices. This paper combines these approaches by modifying the Hotelling model to allow firms to hold inventory in addition to in‐ground reserves, contributing three new results. First, inventory is more likely to be held if future demand and/or the marginal cost of extraction are uncertain. Second, the market price of the commodity is based on the Theory of Storage when inventory is held. Third, the optimal extraction of the resource is based on the Hotelling model.     

Inside and outside fiat money, gains to trade, and IS-LM

Summary. We build a one-period general equilibrium model with money. Equilibrium exists, and fiat money has positive value, as long as the ratio of outside money to inside money is less than the gains to trade available at autarky. We show that the nominal effects of government fiscal and monetary policy can be completely described by a diagram identical in form to the IS-LM curves introduced by Hicks to describe Keynes' general theory. IS-LM analysis is thus not incompatible with full market clearing, multiple commodities, and heterogeneous households. We show that as the government deficit approaches a finite threshold, hyperinflation sets in (prices converge to infinity and real trade collapses). At the other extreme, if the government surplus is too large, the economy enters a liquidity trap in which nominal GNP sinks and monetary policy is ineffectual. Received: January 2, 2002; revised version: April 8, 2002 Correspondence to: P. Dubey     

Multilateral Bargaining Problems

In many situations in economics and political science there are gains from forming coalitions but conflict over which coalition to form and how to distribute the gains. This paper presents an approach to suchmultilateral bargaining problems. Asolutionto a multilateral bargaining problem specifies an agreement for each coalition that is consistent with the bargaining process in every coalition. We establish the existence of such solutions, show that they are determined by reservation prices, and characterize these reservation prices as the payoffs ofsubgame perfect equilibrium outcomesof a non-cooperative bargaining model.Journal of Economic LiteratureClassification Numbers: C71, C72, C78.     

A note on the Hotelling principle of minimum differentiation: Imitation and crowd

This paper investigates price competition in the Hotelling location model with linear transportation costs when consumer preferences are affected by the number of consumers shopping at the same store. A consumption externality permits us to consider the imitation and the congestion effects which are opposite forces at work. The coexistence of the two effects confers new validity to the principle of minimum differentiation as it was in the original Hotelling model. I show that firms do not need to set apart in order to earn higher profits. The results show firms endogenously choosing to locate in the center of the interval sharing the market with positive prices.     

Paying the expected externality for a price quote achieves bargaining efficiency

A seller and buyer have reservation prices x and y. Each has a subjective distribution on the other's reservation price. Paying an offer or the expected benefit the other participant receives from his offer induces honest price quotations, hence efficiency: sale iff y> x.     

On the Non-Existence of Redundant Options

In a seminal paper, Ross (Q J Econ 90:75–89, 1976) shows that if security markets are resolving, then there exist (non-redundant) options that generate complete security markets. Complementing his work, Aliprantis and Tourky (2002) show that if security markets are strongly resolving and the number of primitive securities is less than half the number of states, then every option is non-redundant. Our paper extends Aliprantis and Tourky’s result to the case when their condition on the number of primitive securities is not imposed. Specifically, we show that if there exists no binary payoff vector in the asset span, then for each portfolio there exists a set of exercise prices of full measure such that any option on the portfolio with an exercise price in this set is non-redundant. Since the condition that there exists no binary payoff vector in the asset span holds generically, redundant options are thus rare. I am grateful to an anonymous referee for very helpful comments. Research support from the School of Business at The George Washington University is gratefully acknowledged     

Fixed versus variable supply in the public provision of goods

Using discriminatory price auctions with variable supply, we explore a situation in which a corruptible public employee is in charge of producing and allocating a finite number of goods among consumers with uniformly distributed valuations. The negative effects of corruption are lower when the employee‘s task is to “provide at least q₀ goods” than when the employee is required to “provide exactly q₀ goods”.     

Geographical separation of oligopolists can be very competitive

A given number of single, differentiated product oligopolists locate in one of two separate market-places, which consumers access at a cost. Firms set prices and the CES consumers choose purchases at one or both market-places. Firm agglomeration in one market-place produces positive profits because of product differentiation. But if consumer access costs are homogeneous and products are sufficiently good substitutes, geographical separation of firms produces prices analogous to homogeneous product Bertrand, and is “very competitive”, the reverse of textbook Hotelling. Hence a novel explanation emerges for the geographical agglomeration of firms producing very similar products.     

A structural model of competing sellers: Auctions and posted prices

In an original data set of goods listed for sale online, I observe that both auctions and posted prices are popular with buyers and sellers in the compact-disc market. To explain why these two mechanisms coexist, I estimate a structural model of competing sellers who differ in the value of their outside options. Buyers are allowed to value auctioned and posted-price goods differently but the estimated value distributions suggest that differences across buyers do not explain the mechanism coexistence that I observe. In contrast, differences across sellers' outside options are important: the value of the outside option segments the market with high outside-option sellers choosing to post a fixed price. There are two key forces at work that drive this empirical result. First, competition between sellers favors coexistence over an auction-only or a posted-price-only marketplace because sellers prefer to be in a market with fewer rivals. Second, sellers with more valuable outside options prefer the posted-price mechanism because posted-price goods sell less often than auctioned goods but at a higher price. As a result, a larger outside option reduces the loss from not selling and favors the posted-price mechanism.     

Consumer search markets with costly revisits

This paper characterizes equilibrium outcomes in consumer search markets taking the cost of going back to stores already searched explicitly into account. We show that the optimal sequential search rule under costly revisits is very different from the traditional reservation price rule in that it is non-stationary and not independent of previously sampled prices. We explore the implications of costly revisits on market equilibrium in two celebrated search models. In the Wolinsky model, some consumers search beyond the first firm. In this class of models, costly revisits do make a substantive difference and their impact can be of the same order of magnitude as the initial search cost. In the Stahl oligopoly search model where consumers do not search beyond the first firm, there remains a unique symmetric equilibrium that has firms use pricing strategies that are identical to the perfect recall case.     

ASYMMETRIC INFORMATION AND EXCHANGE OF INFORMATION ABOUT PRODUCT DIFFERENTIATION

We introduce asymmetric information about consumers’ transportation costs (i.e., the degree of product differentiation) in the model of Hotelling. When transportation costs are high, both firms have lower profits with asymmetric information than with perfect information. Contrarily, if transportation costs are low, both firms may prefer the asymmetric information scenario (the informed firm always prefers the informational advantage, while the uninformed firm may or may not prefer to remain uninformed). Information exchange is ex‐ante advantageous for both firms, but ex‐post damaging if transportation costs turn out to be low. If the information is unverifiable, the informed firm does not represent a reliable source of information, since it always prefers to announce that transportation costs are high and there is no contract that induces truthful revelation.     

Some evidence in the trading and pricing of equity LEAPS

This paper documents some evidence in the trading and pricing of equity Long-term Equity AnticiPation Securities (LEAPS). The main findings on trading are that LEAPS open interest, trading volume, and put/call ratio are seasonal on a yearly basis possibly due to the impact of the “melding” process that is unique to equity LEAPS. This paper also finds that the Black–Scholes Option Pricing Model, in general, overprices or underprices out-of-the-money (OTM) or in-the-money (ITM) equity LEAPS calls, respectively, and the model tends to overprice when the options are very deep in-the-money (VDITM). Furthermore, the evidence indicates that the deviations of the Black–Scholes prices from the observed option market prices are more pronounced in equity LEAPS than in standard options, suggesting that the Black–Scholes Option Pricing Model is less well suited to the pricing of equity LEAPS than to the pricing of standard options.     

Testing the Assumptions and Predictions of the Hotelling Model

In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. We consider nonlinear functional forms for the extraction cost and resource demand to develop an empirical Hotelling model with technological progress and stock dependent extraction costs. Using panel data on fourteen nonrenewable natural resources to estimate this empirical Hotelling model, we get qualitatively different results as compared to the related literature. We find evidence of stock-dependent extraction costs for most resources. There is no evidence against the linearity of the optimal extraction rate in the resource stock for almost all resources studied. Furthermore, the Hotelling model may sustain a zero long-run growth rate in resource prices. These results depend on whether firms use different extractive technologies or whether the structural break observed on resource prices is taken into account.     

AN ANALYSIS OF INTERNATIONAL PRICE DIFFERENTIALS ON EBAY

Online auction sites like eBay provide ways to measure what consumers buy and how much they pay. Does this imply that consumers pay similar prices, irrespective of their location? Comparing prices for homogeneous, tradable goods in the euro area and the United Kingdom, we find that prices differ significantly. The differential is not related to countries' having different currencies. However, price dispersion—the variance of prices—does seem to be smaller if two countries share a common currency. Our results confirm the importance of national borders in explaining price differences and their magnitude is related to (not) sharing a common currency. (JEL E30, E31, E50, F40)     

Voting with abstention

Most voting models in the literature neglect abstention, but is such a simplification justified? I investigate this question in a model with outside pressure on voters. For sequential voting (e.g., roll call votes), with and without an abstention option, there is a unique subgame perfect equilibrium, which implies that true majorities always succeed. Abstention can be an equilibrium strategy for some voters, in particular under complex decision rules (e.g., weighted voting, double majorities). Simultaneous voting often has a unique pure strategy equilibrium but also a plethora of mixed and pure/mixed strategy equilibria. Therefore, only with equilibrium selection, can we evaluate the consequences of neglecting abstention. For equal weight voting, equilibria selected by the procedure of Harsanyi and Selten change completely with an abstention option, even if abstention itself is not or rarely used. With small enough outside pressure, however, the selected equilibrium honors true majorities in both cases.     

A Mixed Duopoly With Switching Costs

We examine the effects of switching costs in a two‐period Hotelling‐type model where a profit‐maximising private firm competes with a welfare‐maximising public firm. We show that, in contrast with the case in which both firms are private, where switching costs raise prices in both periods, in the mixed duopoly they raise prices in the second period but reduce them in the first period. Moreover, the first‐period price reduction is of such magnitude that switching costs reduce firms’ profits and raise consumer welfare. We also find that switching costs affect the consequences of privatisation in favour of firms and against consumers.