| 摘要: | Hamilton et al. (1989)設立一個包括二家廠商在區位及銷售量競爭的空間歧視模 型，假設消費者平均分佈在一個線段且每個消費者均擁有相同的負斜率需求線，比較分 別在Bertrand 競爭及Cournot 競爭中所得到的結果。他們証明在Bertrand 競爭下的價格 較低；當運輸成本低時Cournot 競爭下的利潤較高，但當運輸成本高時Bertrand 競爭下 的利潤較高；在Bertrand 競爭下的社會福利則較高；此外，在Cournot 競爭下二廠商會 聚集在中點，而在Bertrand 競爭下則會分開，分別位於大約四分之一及四分之三處。 在本計畫中，我們假設二雙占廠商生產一種同質產品，消費者居住在二個分別位於 線段的相反二端點的隔絕市場中，此二市場之需求線並不一定相同。本計畫使用一個二 階段賽局，二廠商分別在第一階段選擇其利潤極大的區位；在第二階段則討論二個狀 況，一為二廠商分別在Cournot 競爭下決定最適產量，另一為二廠商分別在Bertrand 競 爭下決定最適價格。同樣的，我們分別求解這二種狀況下的結果，並與Hamilton et al. (1989)的結果做比較。 我們預期可得到一些與Hamilton et al. (1989)不一樣的結論。首先，若市場規模效 果凌駕空間地租效果，當運輸成本夠高時，在大市埸Bertrand 競爭下的均衡價格會高於 在Cournot 競爭。其次，當運輸成本低時Cournot 競爭下的利潤較高，而當運輸成本高 時Bertrand 競爭下的利潤較高，但當運輸成本夠高時Cournot 競爭下的利潤會再反轉為 較高。再者，當運輸成本夠高時，Cournot 競爭下的社會福利有可能會較高。最後，當 空間地租效果大於市埸規模效果時，在Cournot 競爭下二廠商會選擇分開位於線段的二 端點。 Hamilton et al. (1989) set up a model with two firms competing in location and sales for the case of spatial discrimination. Consumers are uniformly distributed along a line segment and have identical downward sloping demands. The results derived by two cases, the Bertrand and the Cournot competitions, are compared. They show that prices are lower under Bertrand competition than under Cournot competition. Profits are higher under Cournot competition for low transport costs, but the reverse holds for larger transport costs. Aggregate welfare is higher in the Bertrand competition case. The two firms agglomerate at the middle point of the line segment in the Cournot case, while taking apart in the Bertrand case. In this project, we assume that two duopolistic firms produce a homogeneous product. The consumers reside in two distinct markets, which locate at the opposite endpoints of a line segment, respectively, and the demand curves are not identical. A two-stage game is employed in which firms first choose locations to maximize their profits in the first stage. In the second stage, firms choose optimal outputs under Cournot competition in one case, while choose the prices under Bertrand competition in the other case. We solve these two cases and compare the results derived in this project with those in Hamilton et al. (1989). We expect to be able to obtain several different results contrasting to those in Hamilton et al. (1989). First of all, the equilibrium price of the larger market may be higher under Bertrand competition for high transport costs as the market-size effect outweighs the spatial-rent effect. Secondly, Profits are higher under Cournot competition for low transport costs, but the reverse holds for larger transport costs. Surprisingly, profits may be reversed again for sufficient high transport costs. Thirdly, aggregate welfare may be higher in the Cournot case for higher transport costs. Lastly, Firms may choose to locate apart under Cournot competition as the spatial-rent effect outweighs the market-size effect. |
