Nonnegative Solutions for Dominant Diagonal Matrices with Both Signs in the Off-Diagonals

正負非對角項並存下優勢對角矩陣非負解的探討

張鐸瀚(To-Han Chang) ； 張明宗(Ming Chung Chang)

《經濟論文叢刊》 31卷3期 (2003/09) Pp. 381-400

https://doi.org/10.6277/ter.2003.313.4

摘要

線性體系在各領域的應用十分廣泛，譬如說經濟學中比較靜態的探討可以轉述成一個線性體系求解的問題。為保證線性體系的解為非負，文獻上通常假設該體系的係數矩陣是梅滋勒矩陣，也就是說矩陣中非對角項的係數設定為非負值。本文放鬆這個假設求得非負解的充分條件，並應用至多產品獨占廠商利潤極大化定價的探討。

關鍵字

優勢對角矩陣 ； 線性體系 ； 網路接續定價 ； 利潤最大化定價 ； 藍氏定價

並列摘要

This paper considers a well-known linear system that is in widespread use. Any comparative statics exercise that is often employed in economics can be represented by a linear system. In order to guarantee that the solution to this linear system is nonnegative, previous research assumed that the coefficient matrix in this linear system was a Metzler matrix, i.e. each off-diagonal entry of this matrix was nonnegative. In this paper we relax this assumption, and apply this mathematical technique to study the profit-maximization pricing of a multi-product monopolist.

並列關鍵字

dominant diagonal matrix ； linear system ； network-access pricing ； profit-maximization pricing ； Ramsey pricing

參考文獻

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