Amenability of Groupoids Arising from Partial Semigroup Actions and Topological Higher Rank Graphs

We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if there is countable set $D\subset G$ such that $c(G^{u})D=Q$ for all $u\in G^{(0)}$. We show that our result is applicable to groupoids arising from partial semigroup actions. We explore these actions in detail and show that these groupoids include those arising from directed graphs, higher rank graphs and even topological higher rank graphs. We believe our methods yield a nice alternative groupoid approach to these important constructions.Comment: Revised as suggested by a very helpful referee. In particular, a gap in the proof of Theorem 5.13 has been repaired resulting in a much improved version (with fewer hypotheses

Comparative Advertising: disclosing horizontal match information

Improved consumer information about (symmetric) products can lead to better matching but also higher prices, so consumer surplus can go up or down, while profits rise. With enough firm asymmetry though, the stronger firm's price falls with more information, so both effects benefit consumers. This is when comparative advertising is used, against a large firm by a small one. Comparative advertising, as it imparts more information, therefore helps consumers. While it also improves profitability of the small firm, overall welfare goes down because of the large loss to the attacked firm.comparative advertising, information, product differentiation, quality

Product Characteristics and Price Advertising with Consumer Search

Many advertisements inform the consumer about product characteristics, while others give price information with very little product information, and some provide both types of information. We propose a framework to analyze the incentives for firms to provide various types of information. We consider the case of a single seller. There is no incentive to provide information on product characteristics only, since doing so leads to a holdup problem that the consumers would rationally expect the firm to charge such a high price that no consumer would wish to incur the prior search cost. (A more general argument applies to markets with several firms.) However, price-only and price-and-characteristics advertising can arise depending on the relative strength of product differentiation and consumer search costs. Even when it costs the firm very little to inform consumers the firm may have no incentive to advertise if consumers will sample it anyway. For low search costs the firm has a strict incentive NOT to let consumers know because the firm garners higher profit when consumers have sunk the search cost. Forced disclosure and dissemination of information improves social welfare by eliminating useless search behavior that leads to no purchases (as well as enabling consumers to buy at lower prices). Second, even when the firm must advertise to bring in consumers (i.e., for larger search costs), the firm may prefer to keep consumers in the dark about how much they like the product - this behavior again entails excessive search. Finally, even when the firm finds it optimal to inform consumers of both their match values and the price charged, the level of advertising is too small because the firm only accounts for its private benefit per consumer informed when determining how much to advertise, and not the extra benefit to consumers of making a valuable match.

Pricing, product diversity, and search costs: a Bertrand-Chamberlin-Diamond model

We study price competition in the presence of search costs and product differentiation. The limit cases of the model are the ‘‘Bertrand Paradox,’’ the ‘‘Diamond Paradox,’’ and Chamberlinian monopolistic competition. Market prices rise with search costs and decrease with the number of firms. Prices may initially fall with the degree of product differentiation because more diversity leads to more search and hence more competition. Equilibrium diversity rises with search costs, while the optimum level falls, so entry is excessive. The market failure is most pronounced for low preference for variety and high search costs.

Effciency and surplus bounds in Cournot competition

We derive bounds on the ratios of deadweight loss and consumer surplus to producer surplus under Cournot competition. To do so, we introduce a parameterization of the degree of curvature of market demand using the parallel concepts of ½-concavity and ½-convexity. The ”more concave” is demand, the larger the share of producer surplus in overall surplus, the smaller is consumer surplus relative to producer surplus, and the lower the ratio of deadweight loss to producer surplus. Deadweight loss over total potential surplus is at …rst increasing with demand concavity, then eventually decreasing. The analysis is extended to asymmetric …rm costs.Cournot equilibrium, social surplus analysis, deadweight loss, market performance.

Consumer Information and Firm Pricing: Negative Externalities from Improved Information

We analyze the effect of consumer information on firm pricing in a model where consumers search for prices and matches with products. We consider two types of consumers. Uninformed consumers do not know in advance their match values with firms, whereas informed consumers do. Prices are lower the greater the proportion of uninformed consumers. Hence uninformed consumers exert a positive externality on the others, in contrast to standard results. This leads to socially excessive investment in gathering prior information when aggregate demand is price-sensitive.

Efficiency and surplus bounds in Cournot competition

We derive bounds on the ratios of deadweight loss and consumer surplus to producer surplus under Cournot competition. To do so, we introduce a parameterization of the degree of curvature of market demand using the parallel concepts of ?-concavity and ?-convexity. The ?more concave? is demand, the larger the share of producer surplus in overall surplus, the smaller is consumer surplus relative to producer surplus, and the lower the ratio of deadweight loss to producer surplus. Deadweight loss over total potential surplus is at Þrst increasing with demand concavity, then eventually decreasing. The analysis is extended to asymmetric Þrm costs.Cournot equilibrium, social surplus analysis, deadweight loss, market performance.

comparative Advertising

Consumer information on products affects competition and profits. We analyze firms' decisions to impart product information through advertising: comparative advertising also allows them to impart information about rivals' products. If firms sell products of similar qualities, both want to advertise detailed product information that enables consumers to determine their matches: there is no role for comparative advertising. If qualities are sufficiently dissimilar, the high-quality one will not want to disclose match information. If legal, the low-quality firm rival would like to advertise match information about its rival. Such "comparative" advertising may have a detrimental impact on welfare by leading more consumers to consume the low quality product: this effect can dominate the benefits from improved consumer information and reduce social welfare if qualities are different enough.comparative advertising, information, product differentiation, quality