THE OPTIMAL LOCATIONS OF BRANCH FACILITIES AND MAIN FACILITIES WITH CONSUMER SEARCH*

ABSTRACT. This paper examines the socially optimal locations of branch facilities (or small stores) and main facilities (or large stores) on a finite linear market that is uniformly populated from position 0 to position 1. Each consumer has a probability w of finding the desired service (or product) at a branch facility, and a probability 1 of finding the desired service (or product) at a main facility. Two types of consumer search are considered: phone search and visit search. Different assumptions are made about the numbers of branch facilities and main facilities (each involving one or two facilities of each type). Under visit search, the socially optimal locations of branch facilities tend to be closer to main facilities than under phone search, and this tendency is more pronounced for smaller values of w.     

Asymmetric Entrant Locaiton with a Discrete Consumer Distribution: Spatial Price Discrimination Versus Mill Pricing

In this paper I examine the profit-maximizing locations of entrants. Suppose that firms practice spatial price discrimination and consumer locations are discrete, such as five equally spaced towns on a roadway. With completely inelastic consumer demand an entrant between two existing firms is often indifferent between the symmetric (central) location and a continuum of asymmetric (noncentral) locations. However, downward-sloping consumer demand often causes the entrant to strictly prefer either of two asymmetric locations to any other location. These results are very different from those found in mill-pricing (free-on-board or f.o.b.-pricing) models.     

SPATIAL PRICE COMPETITION WITH CONSUIMERS ON A PLANE,AT INTERSECTIONS,AND ALONG MAIN ROADWAYS*

ABSTRACT. This paper examines two-dimensional price competition on a plane, with a block metric and a square grid of main roadways. One store is located at each intersection of main roadways. Consumer locations include a uniform distribution over the plane, linear concentrations along main roadways, and point concentrations at intersections. Bertrmd-Nash mill price competition is examined first. The equilibrium price depends on the relative numbers of consumers in the three types of locations (and on travel costs per mile and the spacing between stores). If too many consumers are in each point concentration, then the price equilibrium is undermined by a high-price strategy or by mill-price undercutting. Spatial competition with price discrimination is examined next, and compared to Bertrand-Nash mill price competition.     

THE OPTIMAL LOCATIONS OF MULTIPLE BRIDGES,CONNECTING FACILITIES,OR PRODUCT VARIETIES*

ABSTRACT This paper considers the optimal locations of two or more facilities, and the optimal number of facilities, when trips are made in pairs. The results are the same as standard models of spatial competition when there is perfect matching, but not when there is random matching. The first interpretation is bridges across a river, with residential locations on one side matched perfectly or randomly to jobs on the other side. The second interpretation is connecting facilities, such as tennis courts or restaurants where pairs of consumers meet. The third interpretation is product differentiation, with husbands and wives jointly choosing from among varieties.     

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.