TWO-DIMENSIONAL BERTRAND COMPETITION: BLOCK METRIC,EUCLIDEAN METRIC,AND WAVES OF ENTRY*

This paper examines two-dimensional spatial competition, with Bertrand price determination. With a block metric, equilibrium prices are significantly lower when market areas are squares than when they are diamonds (rotated squares) of the same size. If demand density grows, waves of entry occur, and the shapes of market areas change from squares to diamonds and back to squares again. The former change leaves prim unchanged, whereas the latter cuts prices in half. Results are also derived for a Euclidean metric, with square and hexagonal market areas. Optimal waves of entry are examined with the block metric. With either metric, the socially optimal market shape becomes suboptimal if market areas are constrained to be of the zero-profit size.     

THE SCOPE FOR PURE PROFITS IN A STANDARD LOCATION MODEL*

ABSTRACT. This paper examines the possibility of sustaining a collusive equilibrium in a standard location model. Drawing on recent developments in game theory, it is suggested that collusion is only feasible if market areas lie within a certain range. When market areas are large the threat of entry is likely to undermine any collusive agreement. In contrast when market areas are small, defection from the cartel is shown to be profitable. Thus collusion is shown to be feasible only when market areas and demand lie within certain bounds. More generally, this result appears to be consistent with the somewhat ambiguous empirical evidence which suggests that competitive pricing behavior is likely to prevail in periods of excessively high demand and during recessions.     

GENERAL EQUILIBRIUM OF SPATIAL PRODUCT AND LABOR MARKETS*

ABSTRACT A simple general equilibrium model relates spatial product markets and spatial labor markets. The firm is treated as being a spatial monopolist or as a Löschian competitor in the output market and as a spatial monopsonist in the labor market. Derived free spatial demand and free regional labor supply are defined, and their properties examined. The model provides the framework for analyzing the impact of a technological improvement in labor productivity on the structure of the spatial markets. The impact of entry on spatial labor supply is an important determinant of whether or not entry lowers wages and raises output prices. Unlike the spaceless competitive paradigm, zero-profit long-run equilibrium can occur in a space economy under conditions of increasing returns to scale.     

SPATIAL ENTRY DETERRENCE UNDER OLIGOPOLY*

ABSTRACT. This paper examines colluding, oligopolistic firms in a linear market. By assuming that rivals do not compete for consumers at their market boundaries, it is shown that an equilibrium exists without adopting a convex transportation cost function. Two price profiles are derived. The first describes firm prices in the absence of threatened entry. The second details profit-maximizing prices which forestall entrants. Given infinite relocation costs, threatened entry leads to price adjustments by the incumbent firms.     

AMENITIES VERSUS LABOR MARKET OPPORTUNITIES: CHOOSING THE OPTIMAL DISTANCE TO MOVE*

ABSTRACT. A recent debate in the regional economics literature has focused attention on the motivation behind an individual's decision to migrate. Human-capital migration models emphasize labor market disequilibria whereas alternative (hedonic) migration models stress households’altered demand for nontraded goods. In this paper, we test the relative importance of these two possible motivations for moving between metropolitan areas. We use an intercity hedonic model to decompose wages into equilibrium and disequilibrium components. We then compare the separate influences of amenities and the disequilibrium component of wages on the distance moved between two metropolitan areas. Our findings indicate that both economic factors and amenity differentials are significant factors in explaining regional migration.     

Geographies of temporary markets: an anatomy of the Canton Fair

While recent research on temporary clusters and temporary markets has emphasized the knowledge generation processes associated with trade fairs, little is known about the knowledge exchanges that are embedded in market relations at these events. This paper uses the case of the Canton Fair in Guangzhou, the largest trade fair in China, to illustrate that such events do not operate as a single market, but that they generate multiple dynamic market configurations, which entail different flows of knowledge, goods and people. In a typical case study, four types of market configurations are identified that simultaneously develop at this event. The findings contribute to a more comprehensive understanding of the dynamics of market relations, knowledge and transactions in temporary spatial settings.     

Is X-ray diffraction able to distinguish between animal and human bones?

The possibility of determining the human or animal origin of bones from the lattice parameters of their inorganic bioapatite phase, when subjected to a high temperature treatment using the powder X-ray diffraction (XRD) technique, has been explored on a wide number of specimens. Forty-two animal bones were treated in a furnace at 1100 °C for 36 min and compared to 53 cremated human bones from a range of ancient necropolises. The X-ray diffraction patterns of bioapatite were simulated using both monoclinic P21/b and hexagonal P63/m structures to verify any occurrence of phase transformation and any difference in the lattice parameters due to the model. It was determined that the differences between the a-axis and c-axis of the monoclinic and hexagonal lattice were unimportant. Some outlying values were revealed to be caused by the presence of chlorine ions diffused into the apatite structure increasing its average unit cell values. Nevertheless, our results clearly show that in terms of lattice parameters the variability of human specimens are completely overlapped by the non-human variability making the use of XRD in order to distinguish animal from human bones questionable.     

The Regular Component in Settlement Patterns as Shown on a Map

The author uses the concept of entropy from information theory to test the application of Christaller's hexagonal trade-area concept to actual settlement patterns. The entropy measure is used to separate the settlement pattern into its hexagonal and random components, just as incoming radio signals would be separated into the original outgoing signals and noise interference. Medvedkov derives formulas for two methods, one using the density of points within cells of a lattice, the other using the nearest-neighbor technique. The entropy approach is tested in seven actual situations, including three control situations, and shows the regular, or hexagonal, pattern to be the predominant component in five out of seven cases.     

Determining Market Areas Captured by Competitive Facilities: A Continuous Equilibrium Modeling Approach

Many existing models concerning locations and market areas of competitive facilities assume that customers patronize a facility based on distance to that facility, or perhaps on a function of distances between the customer and the different facilities available. Customers are generally assumed to be located at certain discrete demand points in a two-dimensional space, or continuously distributed over a one-dimensional line segment. In this paper these assumptions are relaxed by employment of a continuum optimization model to characterize the equilibrium choice behavior of customers for a given set of competitive facilities over a heterogeneous two-dimensional space. Customers are assumed to be scattered continuously over the space and each customer is assumed to choose a facility based on both congested travel time to the facility and on the attributes of the facility. The model is formulated as a calculus of variations problem and its optimality conditions are shown to be equivalent to the spatial customer-choice equilibrium conditions. An efficient numerical method using finite element technique is proposed and illustrated with a numerical example.     

The Lösch System of Market Areas: Derivation and Extension

Certain aspects of Lösch's classic work on the network of markets and the system of networks have not yet been clearly explained in the literature. Lösch did not describe his derivation procedures in full, and apparent printing errors in certain förmulae confuse the issue further, with the result that several recent texts reproduce Lösch's diagrams but offer no explanation of how they are constructed. Accepting the network of hexagonal market areas for a continuous system of markets, given an even but discrete distribution of population, the derivation from first principles of the complete system of different market areas is presented. Apparent errors in the translated text of Lösch's work are corrected. Limitations in some other authors' work and accordance with earlier empirically derived formulae are mentioned. The production of “city-rich” and “city-poor” sectors is shown to be a constraint on, rather than a result of, the system, and Lösch's statement that the coincidence of centers is maximized is clarified. The extension of the Lösch system to the internal tertiary structure of the city is presented and attention drawn to the empirical attractiveness of this approach.     

METROPOLITAN AGGLOMERATION AND SECTORAL AGGREGATION*

ABSTRACT. This paper proposes a procedure with which sectoral production functions can be aggregated to metropolitan production functions in the presence of external economies of scale. The procedure specifies the production functions as part of general equilibrium models. Consistency of a one-sector and a two-sector general equilibrium model is defined in terms of equality of the distribution of a nation's population over its metropolitan areas in autarky.     

INTERDEPENDENT BEHAVIOR WITH RELOCATION COSTS: THE COMPARATIVE STATICS OF SPATIAL HISTORY*

Relocation costs are a form of sunk costs because they are relevant to new entrants, not to agents at their existing locations. With sufficiently high relocation costs, initial (historically given) locations and other conditions determine the equilibrium assignment of agents to locations. Comparative static results depend on initial conditions, i.e., history matters and historical persistence can be characterized. The model suggests empirically-relevant results which can be tested by collecting data on relocation and transportation costs. For example, appropriate levels of these costs imply that suburbanization always occurs with the entry of new firms. Sequential entry strategies may be adopted by existing firms which earn pure profits. This may be contrasted with traditional NUE models which predict changes in the boundaries of central zones.     

Place-to-Place Rent Comparisons among Canadian Cities

This paper estimates average monthly gross rents for comparable rented private-sector accommodation in Census Metropolitan Areas across Canada. By “gross rent” is meant the typical monthly payment in a CMA for a principal residence by a tenant of given traits under the conditions of a standard lease to a for-profit landlord in competitive market equilibrium for premises used exclusively for accommodation, in an arm's length transaction, and includes heating and utility expenses where paid separately by the tenant. A single average gross rent is estimated for each city for dwellings and households, each with specified characteristics. This paper reviews the application of hedonic price models for this purpose, identifies shortcomings of current research in the field, and suggests a new form for such models. This new model is estimated using microlevel data from a sample of renter households taken across the twenty-three largest urban areas in Canada. A classical version of the model is fitted first to renter data for individual cities, and its limitations assessed. A measure of “relative supply” is introduced to help explain city to city variations in the hedonic prices. Then an all-city new model is estimated which incorporates relative supplies. This all-city model is then used to derive place-to-place rent comparisons.     

Advances in the Theory of Market Areas

The purpose of the paper is to state general properties of theoretical market areas of cities. We consider two centers on the Euclidean plane, several models describing the spatial influence of a center, and a general, continuous, and strictly increasing transportation cost function. Derived properties of market areas concern area measure, topological bounds, emptiness, boundedness, connectedness, convexity, and the membership of a city to its own market area. In particular, it is shown how the shape of market areas changes with the transportation cost function. Finally, prospects for further research are presented.     

A Comparison of Simple Lattice Transport Networks for a Uniform Plain

The objective is to compare construction and transport costs for triangular, orthogonal, and hexagonal regular lattices as transport networks serving a uniform, unbounded plain. The lattices are standardized so that the average distance from the elementary area to the edge is the same for each. This standardization results in equal construction costs for the three networks; thus, the comparison can be made in terms of route factors, which favors the triangular lattice over the other two.     

The State of the Art in Modeling Migration in LDCS: A Comment

Early research on migration in LDCs, initially motivated by labor market postulates offered by Harris and Todaro, built upon general equilibrium models of interregional trade. In contrast, recent research on migration (such as Brueckner and Kim in this issue) builds upon a partial equilibrium analysis that is based on an urban land model. There are subtle differences between these models that complicate intermodel comparisons. The current paper, motivated by this complexity, has three purposes: (1) a mathematical explication of the state of the art in migration modeling, (2) a provision of further insights into the Todaro paradox, and (3) a suggestion for future research predicated on melding the urban land and interregional literatures.     

THE IMPACT OF RENT CONTROLS IN NON-WALRASIAN MARKETS: AN AGENT-BASED MODELING APPROACH

ABSTRACT.  We use agent-based models to consider rent ceilings in non-Walrasian housing markets, where bargaining between landlord and tenant leads to exchange at a range of prices. In the non-Walrasian setting agents who would be extramarginal in the Walrasian setting frequently are successful in renting, and actually account for a significant share of the units rented. This has several implications. First, rent ceilings above the Walrasian equilibrium price (WEP) can affect the market outcome. Second, rent ceilings that reduce the number of units rented do not necessarily reduce total market surplus. Finally, the distributional impact of rent controls differs from the Walrasian setting.     

Semi-parliamentary government in perspective: concepts,values, and designs

The article responds to four commentaries on the concept of semi-parliamentary government and its application to Australian bicameralism. It highlights four main points: (1) Our preferred typology is not more ‘normative’ than existing approaches, but applies the criterion of ‘direct election’ equally to executive and legislature; (2) While the evolution of semi-parliamentary government had contingent elements, it plausibly also reflects the ‘equilibrium’ nature of certain institutional configurations; (3) The idea that a pure parliamentary system with pure proportional representation has absolute normative priority over ‘instrumentalist’ concerns about cabinet stability, identifiability and responsibility is questionable; and (4) The reforms we discuss may be unlikely to occur in Australia, but deserve consideration by scholars and institutional reformers in other democratic systems.     

Scale-Economy Conditions for Spatial Variation in Farm Size

Given the usual neoclassical assumptions of economic rationality, perfect competition, long-term spatial equilibrium, a Thunian context, and perfectly divisible labor and capital, this paper expresses economies of scale in farming in terms of the yield derived from a given level of intensity. If yield increases as farm scale increases, there are economies of scale. If yield decreases, there are diseconomies of scale. The literature on scale economies in agriculture suggests that scale economies accrue from increases in capital inputs, but diseconomies occur as a result of increases in farm area. The models of the spatial structure of agriculture, with farm size included, show the following: 1. Unless there are economies of scale giving way to diseconomies of scale with increases in farm size, no optimal farm area or farm scale can be defined; 2. If the optimal intensity for farming does not vary over space, the optimal farm scale or area should be constant over space; 3. If intensity varies spatially, and if the optimal economies of scale are a function of area only, farm areas should not vary spatially, and sales volume per farm should increase as market access and fertility increase; 4. It is only if intensity varies spatially and optimal scale economies are a function of both area and total quantities of nonland inputs per farm that farm area should increase as distance to market increases or fertility decreases. In this last case, quantities of nonland inputs per farm should also decrease, and usually sales volume per farm should decrease also.