Harmonic vectors and matrix tree theorems
نویسنده
چکیده
In this paper we prove a new result in graph theory that was motivated by considerations in mathematical economics; more precisely by the problem of price formation in an exchange economy [3]. The aggregate demand/supply in the economy is described by an n × n matrix A = (aij) where aij is the amount of commodity j that is on offer for commodity i. In this context one defines a market-clearing price vector to be a vector p with strictly positive components pi, which satisfies the equation ∑
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