Marcus Berliant

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.

On the fair division of a heterogeneous commodity

Abstract Consider a heterogeneous but divisible commodity, bundles of which are represented by the (measurable) subsets of the good. One such commodity might be land. The mathematics literature has considered agents with utilities that are nonatomic measures over the commodity (and hence are additive). The existence of ‘α-fair’ allocations, in which each agent receives a utility proportional to his utility of the endowment of the entire economy, was demonstrated there. Here we extend these existence results to α-fair efficient allocations, envy-free allocations, envy-free efficient allocations, group envy-free and nicely shaped allocations of these types. We examine utilities that are not additive and relate the mathematics literature to the economics literature. We find sufficient conditions for the existence of egalitarian-equivalent efficient allocations. Finally, we consider the problem of allocating a time interval (uses of a facility). Existence of an envy-free allocation had been demonstrated in earlier literature. We show that any envy-free allocation is efficient as well as group envy-free. We extend this last result to a more general setting.

Knowledge Creation As A Square Dance On The Hilbert Cube

This paper presents a micro-model of knowledge creation and transfer in a small group of people. Our model incorporates two key aspects of the cooperative process of knowledge creation: (i) heterogeneity of people in their state of knowledge is essential for successful cooperation in the joint creation of new ideas, while (ii) the very process of cooperative knowledge creation aects the heterogeneity of people through the accumulation of knowledge in common. The model features myopic agents in a pure externality model of interaction. Surprisingly, in the general case for a large set of initial conditions we …nd that the equilibrium process of knowledge creation may converge to the most productive state, where the population splits into smaller groups of optimal size; close interaction takes place within each group only. This optimal size is larger as the heterogeneity of knowledge is more important in the knowledge production process. Equilibrium paths are found analytically, and they are a discontinuous function of initial heterogeneity. JEL Classi…cation Numbers: D83, O31, R11

The Endogenous Formation of a City: Population Agglomeration and Marketplaces in a Location-Specific Production Economy

Much of the literature on the endogenous generation of a city employs increasing returns to scale in order to obtain agglomeration. In contrast, the model considered here focuses on the role of marketplaces or trading centers in the agglomeration of population as cities. Gains to trade in combination with transportation and marketplace setup costs suffice to endogenously generate a city or cities with one or multiple marketplaces. It is assumed that consumers are fully mobile while production functions are location-specific. The exchange of commodities takes place in competitive markets at the marketplaces, while the number and locations of the marketplaces are determined endogenously using a core concept. Unlike the standard literature of urban economics, our model can deal with differences in geography by letting the setup costs of marketplaces and the transportation system depend on location. After showing that an equilibrium exists and that equilibrium allocations are the same as core allocations, we investigate the equilibrium number and locations of marketplaces, the population distribution, and land prices. In contrast with earlier literature, the results are general in the sense that specific functional forms are not needed to obtain existence of equilibrium, equilibria are first best, and equilibria are locally unique (in our examples).

Equal sacrifice and incentive compatible income taxation

Abstract The concepts of equal sacrifice and incentive compatibility in income taxation have been of interest to economists for some time. Here we attempt to integrate the two literatures in a model that offers a labor-leisure choice to consumers while imposing an equal relative or absolute sacrifice tax system. The main result is that equal sacrifice incentive compatible income tax systems generally exist and are locally unique. Examples are presented where this tax system is easy to compute. Comparative statics are calculated. Finally, some remarks about the welfare properties of these tax systems are made.

The Dynamics of Knowledge Diversity and Economic Growth

How is long run economic growth related to the endogenous diversity of knowledge? We formulate and study a microeconomic model of knowledge creation, through the interactions among a group of heterogeneous research and development (R&D) workers, embedded in a growth model to address this question. The composition of the research work force in terms of knowledge heterogeneity, in addition to its size, matters in determining the production of new knowledge. Moreover, the heterogeneity of the work force is endogenous. Income to these workers accrues as patent income, whereas transmission of newly created knowledge to all such workers occurs due to public transmission of patent information. Whether or not the system reaches the most productive state depends on the strength of the public knowledge transmission technology. Long run economic growth is positively related to both the effectiveness of pairwise R&D worker interaction and to the effectiveness of public knowledge transmission.

Endogenous formation of a city without agglomerative externalities or market imperfections: Marketplaces in a regional economy

Abstract This paper develops a general equilibrium model to endogenously generate a linear city. Rather than assuming agglomerative externalities or increasing returns in production/transportation technology, interregional transactions costs are considered. To rectify a deficiency associated with the standard continuum framework, we modify the concept of social optimum. A modified social optimum exists under appropriate assumptions and exhibits a concentrated market structure when there are high market set-up costs, thus yielding a unitary central business district. In an economy without trust, a standard monocentric city may emerge. The social optimum generating a monocentric city has competitive price support under proper assumptions.

Equilibrium models with land: A criticism and an alternative☆

Models of economies either of urban areas or with local public goods often involve the use of a continuum of consumers along with the use of a commodity called land; each consumer generally owns a parcel of land of positive area. The purpose of the present study is to show that such models are internally inconsistent (independent of the other assumptions employed) in that only countably many consumers can own parcels of land of non-zero area if land lies in a Euclidean space. This result applies, in particular, to monocentric city models. Moreover, it is shown that the standard justification for the use of economies with an infinity of agents, that they approximate large economies with a finite number of consumers, does not necessarily apply in the case of economies with land and a continuum of consumers. A model where land is represented by subsets of R2 is presented as an alternative.

A foundation of location theory: existence of equilibrium, the welfare theorems, and core

Abstract An exchange economy with land and a finite number of traders is examined. Land is modeled as a sigma algebra of subsets of a Euclidean space. Since this commodity space has no natural convex or linear structure, standard existence results cannot be applied. The contribution of this paper is the introduction of continuity, convexity, and “nonwasteful partition” assumptions (the latter joint on the land supply and consumer preferences) for such a situation. Examples are provided where no equilibrium exists when each of these assumptions is violated. Under these assumptions, equilibrium is shown to exist, the core is shown to be nonempty, and the welfare theorems are proved. Examples satisfying all the assumptions are provided.

An equilibrium existence result for an economy with land

Abstract This research uses a different set of assumptions for land than those used in the standard general equilibrium framework. In particular, land is modelled explicitly as a subset of the plane with anything immobile, from flowers and trees to houses, embedded in it. There is a finite number of consumers with preference orderings over land parcels satisfying certain axioms along with endowments of land that partition this subset of the plane. Allowing for recombinations of parcels, the main result demonstrates the existence of prices in L 1 and a partition of land among consumers so that the land market clears.