要旨：The purpose of this paper is to analyze Nash tax competition among governments that differ in geographical aspects such as their sizes and positions. Each government lying on a linear market maximizes its revenue with respect to its own commodity tax rate, taking into account the cross-border shoppings induced by the difference in tax rates. In particular, we examine how the size of the countries and their spatial arrangement affect tax rates and government revenues at a Nash equilibrium. We show that a small country chooses a lower tax rate than a big country, and obtains more than its size-proportional share of total revenue at the Nash equilibrium. We also prove that when the size of all countries are identical, the tax rates levied by the governments go down from either market boundary toward the market center, and the adjoining countries of peripheral countries can obtain the larges government revenue.

要旨：When incidence rates are mapped at the basis of areal units, the modifiable areal unit problem (MAUP) becomes apparent. Although small units with high spatial accuracy can present unreliable rates, large spatial units may remove relevant geographical variation. This study proposes a new methodology for solving the mentioned trade-off problem and the search for informative geographical aggregation in map construction. This approach essentially involves regarding as a kind of statistical modeling.

要旨：It has long been recognized that the pleasure of consuming a good may be affected by the consumption choice of other consumers. At least two types of motivations may explain such a behavior. In some cases social pressures may lead to conformity; while in some other cases individuals may feel the need of exclusiveness under the form of vanity. Such externalities have proven to be important in several markets where the decision to buy a product is positively or negatively affected by the number of consumers purchasing the same product. However, the market and welfare implication of these effects are still unclear. To investigate them, we propose to graft the consumption externality model onto the spatial duopoly model. When conformity is present but not too strong, both firms remain in business but price competition is fiercer and results in lower prices. The market share of the large firm increases with the population size; as the population keeps rising, the large firm serves the entire market and sets a price which has the nature of a limit price. When conformity is strong enough, different equilibria may exist. These equilibria are such that only one firm has a positive market share or both firms split the market. At the other extreme, when vanity is at work, price competition is relaxed.