Geodesic
Linear city model with exogenous Stackelberg competition
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 2, pp. 64-81

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The paper considers the linear city model of spatial competition with the exogenous Stackelberg competition. With low transport costs, firms' equilibrium locations are in the center of the market. The leader profit is twice as big as the follower's profit, the price is minimal and the quantity is maximal at the center of the market. With high transport costs, firms are differentiated and the market splits into two submarkets. Both the leader and the follower sell the largest share of their goods near their location. The price is minimal at the leader's location. Then transport costs are rising, while the price is increasing and the quantity of goods is decreasing.
Keywords: spatial competition, Stackelberg oligopoly, Hotelling linear city model. 
@article{MGTA_2013_5_2_a2,
     author = {Alexander M. Torbenko},
     title = {Linear city model with exogenous {Stackelberg} competition},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {64--81},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2013_5_2_a2/}
}
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Alexander M. Torbenko. Linear city model with exogenous Stackelberg competition. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 2, pp. 64-81. http://geodesic.mathdoc.fr/item/MGTA_2013_5_2_a2/