啞鈴模型與風險趨避廠商的區位選擇

BARBELL MODEL AND THE LOCATION CHOICE FOR A RISK－ AVERSE FIRM

在這篇文章裡我們將市場需求不確定的因素納入啞鈴模型的架構中，以重新檢視單一訂價與差別取價所產生之經濟效果的異同，包括廠商區位選擇的問題與社會福利大小的比較σ在將市場大小的角色允以中立化，並假設廠商具有風險趨避的特性下，我們的研究顯示了如下的重要發現：（i）在差別取價下，廠商會設定廠址在需求變異較小的市場，但在單一訂價下，只要各市場的需求變異不要差距太大，則廠址的位置就會落腳在連接市場的交通線上；（ii）在差別取價下，為了降低市場需求不確定性所帶來的風險損失，廠商對於遠端市場的訂價不一定會高於其在落腳市場的價格水準；（iii）當兩市場的相對需求變異程度差距較大或差距較小時，差別訂價下的市場期望總交易數量會小於單一訂價下的水準反之，差別訂價下的市場期望總交易數量會大於單一訂價下的水準；（iv）只要差別訂價下的市場期望總交易數量大於單一訂價下的水準，其相對應的社會期望福利水準就會高於單一訂價下的社會期望福利水準；（v）當差別訂價下的市場期望總交易數量小於單一訂價下的水準時，只要兩市場的相對需求變異程度差距小於特定水準，則差別訂價下社會期望福利水準仍會高於單一訂價下的社會期望福利水準。

In this article we highlight the role of demand uncertainty within the stylized frameworkof the Barbell model, which addresses the location problem of a monopolist firm which sellsits products to two geographically separated and demand-independent markets that areconnected by a highway. Our research reveals that market demand uncertainty is a crucialfactor in determining the firm’s location. In particular, under spatial uniform pricing, themonopoly may locate its plant at the interior post of the highway and stay away fromthe market with the greatest degree of demand uncertainty, whereas under discriminatorypricing, it will always locate at the market post with the least degree of demand uncertainty.Futhermore, we also find that the welfare under discriminatory pricing is greater than thewelfare with uniform pricing as long as the discrepancy in the degree of demand uncertaintyamong markets is large enough. Our results are sharply different from works that followthe Barbell model developed by Hwang and Mai (1990).