Shin-Kun Peng

Production Externalities and Urban Configuration

Jacobs (1969) argues that uncompensated knowledge spillovers have played a crucial role in population agglomeration and thus in the generation of cities. We explore this idea formally by extending the Romer (1986) model of (inter-firm) externalities in production to an explicit spatial context. We postulate that knowledge spillovers between firms decrease with the distance between the firms. A general equilibrium model with households and firms residing in a linear or long, narrow city is constructed. The allocation of goods and factors, the locational choice of firm sites and household residences, as well as factor prices and land rents are all endogenously determined. The equilibrium urban configuration may be concentrated (with monocentric firm locations), dispersed (with completely mixed firm and household locations) or a combination (with incompletely mixed firm and household location), depending on the population of firms as the transportation and firm-interaction parameters. Due to the distance-dependent production externalities, firms will be clustered together in any equilibrium. As a consequence, the duo-centric or any multi-centric urban configuration is never an equilibrium configuration. Moreover, except for a set of parameters of measure zero, the equilibrium urban configuration is unique.

Cooperation vs. competition in a spatial model

Abstract This paper discusses the element of cooperation between firms in the form of information exchange through communication into the Hotelling spatial competition model. It is shown that subgame perfect equilibrium in a two-stage game can be achieved in a wide range from minimum differentiation to maximum differentiation, depending upon the relative strength of the cooperation effect over the competition effect. This result is exemplified in the economics of the Silicon Valley.

Economic Integration and Agglomeration in a Middle Product Economy

The paper examines the interactions between economic integration and population agglomeration in a middle product economy displaying neoclassical growth. There are two vertically integrated economies. Each consists of a large number of final good competitive firms operating plants in both regions, and a large number of intermediate goods monopolistically competitive firms operating each in only one region. While immobile workers are employed with intermediate goods to produce the final good, mobile workers are used to design the line of differentiated intermediategood inputs. Capital is immobile, the final good is non-traded, whereas the intermediate goods are traded. We find that employment agglomeration and output growth need not be positively related. Furthermore, trade is not necessarily beneficial to regional growth, whereas trade between the two regions need not be associated with a widened skilled-unskilled wage gap.

Multiproduct Duopoly with Vertical Differentiation

This paper investigates a two-stage competition in a vertically differentiated industry, where each firm produces an arbitrary number of similar qualities and sells them to heterogeneous consumers. The number of products, qualities, prices, and the extent of the market coverage are endogenously determined. We show that when unit costs of quality improvement are increasing and quadratic, each firm has an incentive to provide a disconnected set of similar qualities approximating a continuum. The finding contrasts sharply with the single-quality outcome when the market coverage is exogenously determined. We also show that allowing for multiple qualities intensifies the level of competition, lowers the profit of each firm, and raises the consumer surplus and the social welfare in comparison to the single-quality duopoly.

Sorting by foot: ‘travel‐for’ local public goods and equilibrium stratification

We re-examine Tiebouts hypothesis of endogenous sorting in a competitive spatial equilibrium framework, by considering both income and preference heterogeneity and by allowing agents to decide endogenously the number of visits to a `travel-for local public good. The equilibrium configuration may be completely segregated, incompletely segregated, or completely integrated, depending on relative market rents and income-preference-local tax parameters. A segregated equilibrium may feature endogenous sorting purely by income or by both income and preferences. While the rich need not be closer to the local public facility site, multiple equilibria may arise when the equilibrium configuration is incompletely segregated.

Quality and Quantity Competition in a Multiproduct Duopoly

This article proposes a Cournot model of two-stage competition to examine the patterns of vertical product differentiation in a multiproduct duopoly. Firms simultaneously choose the number of products and their qualities at the first stage and compete in quantities at the second stage. We show that when the fixed setup cost of a product is high enough to result in a monopoly outcome, the monopolist always sells a single product. Moreover, in any equilibrium of a multiproduct duopoly, quality differentiation between them will develop into a nonsegmented pattern because each firm desires to avoid a strong effect of cannibalization. The set of equilibria reveals the properties of quality differentiation between multiproduct firms. In a multiproduct duopoly, the profit from a high-quality product can be lower than that from a low-quality product. This finding sharply contrasts with the literature on single-product firms, which finds the high-quality advantage.

Spatial Monopoly with Product Differentiation

Most theoretical work on the behavior of spatial monopoly focuses on the single-product case, while, in reality, a firm usually produces (or sells) many differentiated products. In this paper, I introduce a new model of spatial monopoly with a multiple-product firm where the firm chooses both the measure of product varieties and the price of each variety to maximize its profit. I also examine the monopolist’s optimal decision and its economic effects on the spatial economy with a fixed and variable market fringe, respectively. For a class of preferences to product differentiation, I find that both the quantities produced and the consumer surpluses vary across three different spatial pricing policies. This finding is in contrast to the literature on a single-product spatial monopoly where those results are invariant across different pricing policies.

The location of governmental facilities and equilibrium urban configuration

Most existing models of spatial agglomeration economics do not include the effects of the governmental sector in an urban configuration, although the governmental sector plays an important role in economic activity. We discuss how an exogenous distribution of locations of governmental facilities and the level of service provided affect the equilibrium urban configuration under the assumption that governmental service is necessary component for production of goods by a firm. The model yields multiple equilibrium urban configurations endogenously, depending on the set of parameters, and that the governmental sector is responsible for the movement of equilibrium market land rents stemming from its determination of location.

The effect of government taxation policies on spatial monopoly

Abstract This paper reexamines and generalizes the analysis of monopolistic pricing in a spatial context with a government tax (or subsidy). The analysis begins with a model containing most of the assumptions adopted by prior studies, and we obtain the more general results that the existence of a sales tax (or subsidy) has a strong effect on both the monopolists decision and the structure of social benefits. Previous findings are shown to be special cases of these results.

Public Good Inputs, Housing Quality, and Locational Stratification

Our paper contributes to the literature on economic segregation by showing that heterogeneity in preferences for housing quality as a result of the location-specific provision of public goods can generate locational stratification. We develop a general equilibrium framework of endogenous sorting in which agents are allowed to differ in their incomes, opportunity costs of commuting, and preferences for housing quality. Housing quality is endogenously determined by location-specific public infrastructure that is financed by property taxes. We characterize the configuration of the competitive spatial equilibrium. We find that complete integration arises only under a set of parameters of measure zero such that the ratio of the opportunity costs of commuting facing different types of agents is in a specific homothetic relation to the ratio of the marginal valuations of housing quality. By contrast, locational stratification is generic. When the difference between agents commuting costs is sufficiently large (resp. small) compared to the difference in their respective preferences for housing quality, the equilibrium is segregated with all rich residing in the central city (resp. suburb) as observed in Asia and Europe (resp. U.S. metropolitan areas).