Fisher market

Fisher market is an economic model attributed to Irving Fisher. It has the following ingredients:

Each product ${\displaystyle j}$ has a price ${\displaystyle p_{j}}$; the prices are determined by methods that we describe below. The price of a bundle of products is the sum of the prices of the products in the bundle. A bundle is represented by a vector ${\displaystyle x=x_{1},\dots ,x_{m}}$, where ${\displaystyle x_{j}}$ is the quantity of product ${\displaystyle j}$ (the quantities are normalized such that the total quantity from each product is 1, i.e, ${\displaystyle x_{j}}$ is the fraction of product ${\displaystyle j}$ in the bundle); the price of a bundle ${\displaystyle x}$ is ${\displaystyle p(x)=\sum _{j=1}^{m}p_{j}\cdot x_{j}}$.

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