Equilibrium price dispersion with heterogeneous searchers

Firms simultaneously set prices in a homogeneous-product market where uninformed consumers search for price information. Some uninformed consumers are “local” searchers who visit only one seller, whereas others search sequentially with an optimal reservation price. Equilibrium prices may follow a mixture distribution, with clusters of high and low prices separated by a zero-density gap. When the (exogenous) reservation price of local searchers depart from that of the optimizing sequential searchers by a relatively small amount, the presence of local searchers either has no effect on market outcomes or benefits all consumers. A reduction in search cost sometimes leads to higher equilibrium prices.     

Search, Bargaining and Optimal Asking Prices

This paper analyzes a search-and-bargaining model in which the asking price influences the rate at which potential customers arrive to inspect the seller's house, and the buyer's valuation of the asset is not learned until after the seller makes his initial offer (the asking price). The optimal asking and reservation prices are characterized, and the existence of a subgame-perfect equilibrium asking-price—reservation-price strategy is established. Comparative-statics analysis illustrates how seller and buyer discount rates and the buyer's outside opportunity affect the optimal reservation and asking prices.     

Ordered search in differentiated markets

This paper presents an ordered search model in which consumers search both for price and product fitness. I construct an equilibrium in which there is price dispersion and prices rise in the order of search. The top firms in consumer search process, though charge lower prices, earn higher profits due to their larger market shares. Compared to random search, ordered search can induce all firms to charge higher prices and harm market efficiency.     

Capacity reservation under spot market price uncertainty

Capacity reservation contracts and spot markets are two alternative purchasing practices. We focus on the cost-effective management of the combined use of these two procurement sources. Due to the variability of the spot market prices and demand uncertainty, the flexibility of combined sourcing can be advantageous. Spot market purchasing is a benefit in case of low spot market prices or insufficient reserved capacity, and the capacity reservation contract is an operational risk hedging for high spot market price incidents. The structure of the optimal combined purchasing policy is complex. In this paper we consider a simple and easy-to-implement capacity reservation—base stock policy and compare it to single sourcing options. We examine the joint effect of demand and spot market price uncertainty. Our analysis shows that in the case of large spot market price variability the combined sourcing is superior over spot market sourcing even in the case of low average spot price. The combined sourcing is also superior over long-term sourcing even in the case of high average spot price if there is large spot market price variability. Analytical and simulation results are presented to show the effect of the different price, cost, and uncertainty parameters on the optimal capacity reservation—base stock policy and on the expected percentage gain over single sourcing.     

Nonsequential search equilibrium with search cost heterogeneity

We generalize the model of Burdett and Judd (1983) to the case where an arbitrary finite number of firms sells a homogeneous good to buyers who have heterogeneous search costs. We show that a price dispersed symmetric Nash equilibrium always exists. Numerical results show that the behavior of prices and consumer surplus with respect to the number of firms hinges upon the nature of search cost dispersion: when search costs are relatively concentrated, entry of firms leads to lower average prices and greater consumer surplus; however, for relatively dispersed search costs, the mean price goes up and consumer surplus may decrease with the number of firms.     

Price Strategies for Idiosyncratic Goods—The Case of Housing

We determine the mechanism that a rational, profit-maximizing seller would use to revise his reservation price for a heterogeneous or infrequently exchanged good. For instance, while one dimension of a home's quality may be easily determined in competitive markets (e.g., the valuation of floor size, location, etc.), other dimensions of quality may be idiosyncratic (unit specific) and unobservable by the seller (e.g., aesthetics of the home). Here, a seller of a new or infrequently exchanged housing unit may use sales success information to revise his expectation of the unit's market-determined value and hence revise his reservation price. The rational seller will, upon arrival of the first buyer inspecting the unit, determine a sequence of reservation prices for this and expected subsequent buyers. This price sequence falls for subsequent buyers and starts from a lower initial price if the first buyer arrives later than expected. Through this mechanism, we offer an explanation for price dispersion and vacancy durations in housing markets. While we explicitly model the real estate market here, this price revision mechanism is also applicable to rental markets, labor markets, used car markets, and other markets characterized by heterogeneity and infrequent sales.     

WHEN DO CONSUMERS SEARCH?*

This paper provides empirical evidence relating search to price movements. We measure consumer search directly from traffic statistics for web sites that report gasoline prices. We show empirically that consumers search more as prices rise than they do when prices fall. Asymmetric search patterns have consequences for price behavior. Our findings indicate that retail margins are squeezed by increased search. In addition, we show that there is more price dispersion when prices are falling than when prices are either stable or rising. Our results provide a search‐based explanation for the ‘rockets and feathers’ phenomenon of asymmetric price adjustment.     

ANOTHER LOOK AT PRICE PROMOTION*

Weekly sales at retail stores exhibit several patterns that the literature on price promotion does not fully capture. In this paper we develop a simple symmetric model where duopoly manufacturers distribute through a monopoly retailer to serve consumers with heterogeneous reservation prices. We show that the heterogeneity in consumers' reservation prices coupled with the retailer's market power is sufficient to resolve the deficiency in the literature. We then show that, while pricing patterns under this model differ significantly from those under a model where the retailer has no market power, the manufacturers' expected profits are the same in both cases.     

Discount Brokerage in Residential Real Estate Markets

Transaction costs are thought to affect asset prices and market liquidity, but the direction and magnitude of these effects continue to be the subject of debate. In the single‐family residential market, discount brokers offer to list a house for a lower price and thus reduce the transaction costs associated with obtaining a match. In this article we obtain empirical estimates of the price and liquidity impact of a seller selecting a discount broker to market a single‐family residential property. The unique data set allows for the identification of residential properties that were listed by a discount brokerage firm. The empirical results confirm the predictions of our theoretical model. Using a sample of 318,221 listings and 243,625 sales, we find that houses listed by discount brokers sell at prices similar to non‐discount brokerage listings, but are less likely to sell, and when they do sell, take approximately three days longer to sell. The results indicate that lower transaction costs do not impact housing prices in this market, but that they are related to asset liquidity.     

Missing Price Information and Its Impact on Equilibrium Price Dispersion: Evidence From Gasoline Signboards*

This article seeks to quantify the importance of price information in reducing consumer search costs and equilibrium price dispersion in a competitive setting. It exploits a natural experiment in the retail gasoline industry in which stations post the prices of only certain grades of gasoline on large street-side signboards, and not others, except where required by law. Differential-by-grade signboard information predicts a specific curvature in price dispersion across grades, and differentiates itself from other noninformational factors such as income and cost. The impact of readily-available price information on search and price dispersion is found to be exceptionally large.     

The impact of price adjustment costs on price dispersion in e-commerce

We analyze price dispersion using panel data from a large price comparison site. We use past pricing behavior to instrument for potential endogeneity of firms to select into certain product markets. Our main result is that greater price adjustment costs result in greater price dispersion even in e-commerce markets where price adjustment cost are thought to be negligible. Although the impact of price adjustment costs on price dispersion became weaker over time, the causal effect of price adjustment costs on price dispersion is still present at the end of our observation period. Our results are robust to many alternative empirical specifications. We also control for a range of alternative explanations of price dispersion, such as search cost, service differentiation, obfuscation, vertical restraints, and market structure.     

Who Loses when Prices are Negotiated? An Analysis of the New Car Market

We establish that there are large and persistent differences in final transaction prices for identical new cars, and that demographic characteristics explain at least 20% of the observed variation. Older consumers perform progressively worse in negotiations, and the age premium is greater for women than for men. Our results suggest that the complex nature of vehicle transactions leads to price dispersion in this market, and that the worst performing groups—older women—have the lowest rates of market participation. We conjecture that the results are driven by the sharp increases in women's education and labor force participation in recent decades.     

Commercial Real Estate Valuation, Development and Occupancy Under Leasing Uncertainty

A model of commercial property valuation is developed where individual property owners are price takers and tenants randomly arrive and depart. Spot lease and tenant reservation prices are stochastic and correlated and can divert from but eventually revert back to market equilibrium. Within this framework we examine built property values and vacancy rates for varying parameter sets representing differing markets and economic conditions. We also examine how potential and existing vacancies, spot lease prices and tenant reservation prices feed back into development decisions. We demonstrate how preleasing acts as a hedge to the developer against the risk of leasing uncertainty.     

COSTLY BUYER SEARCH IN LABORATORY MARKETS WITH SELLER ADVERTISING*

In this experiment, sellers simultaneously choose prices and advertising strategies. Buyers either purchase at an advertised price or search sequentially for other prices. In the unique symmetric equilibrium, sellers charge a high unadvertised price or advertise a price chosen from a lower interval. Increases in search or advertising costs raise equilibrium prices and affect equilibrium advertising intensity. Empirical results are consistent with most comparative static predictions. Sellers, however, price much lower and advertise more intensely than predicted. Consequently, market outcomes more closely resemble a perfect information, Bertrand‐like equilibrium than the imperfect information, mixed strategy equilibrium with significant seller market power.     

Price dispersion and seller heterogeneity in retail food markets

Price dispersion, i.e. a homogeneous product being sold at different prices by different sellers, is among the most replicated findings in empirical economics. The paper assesses the extent and determinants of spatial price dispersion for 14 perfectly homogeneous food products in more than 400 retailers in a market characterized by the persistence of a large number of relatively small traditional food stores, alongside large supermarkets. The extent of observed price dispersion is quite high. When prices in an urban area (where the spatial concentration of sellers is higher) are compared with those in smaller towns and rural areas, differences in search costs and the potentially higher degree of competition do not yield lower prices. Other counteracting factors, including differences in seller costs and consumer incomes, make prices, on average, higher in the urban area for 11 of the 14 products considered. For many, but not all, the products supermarkets proved to be less expensive than traditional retailers, although average savings from food shopping at supermarkets were extremely low. Finally, the results of the study provide evidence that retailers have different pricing strategies and these differences also emerge for supermarkets belonging to the same chain. The results presented in the paper suggest that a variety of factors play a role in explaining price dispersion. In addition to differences in seller costs, the contemporaneous heterogeneity of retailers (in terms of services provided) and consumers (in terms of search costs and preferences) makes the emergence of monopolistic competition possible as well as allowing small traditional food retailers to remain in business.     

An Arbitrage-Free Estimate of Prepayment Option Prices in Fixed-Rate GNMA Mortgage-Backed Securities

In an efficient market, the no-arbitrage condition implies that the price difference between any two assets must be the market value of all differences in their cash flows. We use this logic to deduce the price of the prepayment option embedded in fixed-rate Government National Mortgage Association (GNMA) mortgage-backed securities. The option price equals the difference between an observed GNMA price and the cost of a synthetic, nonprepayable GNMA constructed from the least expensive portfolio of Treasury securities that exactly replicates the promised GNMA cash flow stream, assuming prepayment is precluded. We regress the option prices on variables found significant in previous prepayment studies, finding that five key regressors explain more than 90% of the prepayment option value in pooled time-series cross-sectional analysis. We also show that the time value of the prepayment option calculated by our method displays a pattern similar to that produced by the Black-Scholes (1973) option pricing model. An additional empirical result is the existence of negative option prices and negative time value of the option prices. We attribute these to the fact that homeowners sometimes exercise their prepayment options when they are out-of-the-money, and to refinancing transaction costs. Our method is independent of assumptions regarding interest rate processes and the homeowner's prepayment behavior, and it provides a benchmark for testing theoretical prepayment models.     

Optimal Selling Mechanism,Auction Discounts and Time on Market

This article examines the optimal selling mechanism problem in real estate market using mean‐variance analysis and downside risk analysis. When sellers can choose between accepting the first offer above a reservation price or auctions (waiting an optimal and fixed time), sellers having higher risk aversion choose auctions and wait a fixed time while sellers having lower risk aversion choose an optimal reservation price and wait a random time. Positive auction discounts are compensated by reduced risks, and there exists a connection between liquidity risk and conditional auction discount. More (Fewer) sellers will choose to sell their houses through auctions in a hot (cold) market or when holding cost increases (decreases). When sellers choose auctions, sellers having higher risk aversion who have lower holding cost wait longer and obtain higher sale price. Loss‐averse sellers unanimously choose the mechanism of setting an optimal reservation price.     

Price Dispersion in Mortgage Markets

Using transaction‐level data on Canadian mortgage contracts, we document an increase in the average discount negotiated off the posted price and in rate dispersion. Our aim is to identify the beneficiaries of discounting and to test whether dispersion is caused by price discrimination. The standard explanation for dispersion in credit markets is risk‐based pricing. Our contracts are guaranteed by government‐backed insurance, so risk cannot be the main factor. We find that lenders set prices that reflect consumer bargaining leverage, not just costs. The presence of dispersion implies a lack of competition, but our results show this to be consumer specific.     

Internet Search Behavior,Liquidity and Prices in the Housing Market

We employ detailed internet search data to examine price and liquidity dynamics of the Dutch housing market. We show that the number of clicks on properties listed online proxies demand and the number of listed properties proxies supply. From this internet search behavior, we create a market tightness indicator and we find that this indicator Granger causes changes in both house prices and housing market liquidity. The results of a panel VAR suggest that a demand shock results in a temporary increase in liquidity and a permanent increase in prices in urban areas. This is in accordance with search and matching models.     

Search and price dispersion in online grocery markets

Consumers often purchase multiple products at a time from retailers, creating multi-product incentives for search. In this paper we consider how product variety affects consumer search intensity and the dispersion of prices in multi-product retail markets. We employ online grocery pricing data from four large retailers in the UK to estimate search costs and equilibrium price dispersion for food products under circumstances where: (i) consumers search for single products; and (ii) consumers search for multiple products at once. We compare estimates in each case between a model in which utility increases with product variety and a model in which utility is not a function of variety. Relative to our preferred specification with variety effects in utility, we find estimates of both search cost and search frequency to be biased upwards in single product settings when variety effects are ignored; however, we find estimates of search costs are biased upwards while search frequency is biased downwards in multi-product settings when variety effects in utility are ignored.