I hope someone can help me solving the following issue. I want to solve via MATLAB for the equilibrium of a multi-sector economy.
More particularly, I have many sectors (and even more agents) that differ in type. If I take some particular vector of prices p of sectors, I can solve the sectoral choice of agents, get some goods supply for each sector. I know how goods demand should look like, hence I get say between sector i and sector 1, the excess demand. Thus I know how the price of sector i has to move vis-a-vis sector 1. The problem is that there are not only two sectors (then I could do a simple bisection), but many sectors. And therefore it is not clear that if price ratio between sector i and 1 has to be bigger if all other prices are p_j , this still holds if the prices are p_k for all other sectors.... Thus I cannot use a simple bisection.
Does anyone have an idea how to solve that?
In other words: Say I have vector of 10 variables, to be determined jointly. As all variables depend on each other, I cannot use a simple bisection (as an equation might be positive if other variables are say equal to X, but negative if all other variables are equal to Y). How can I try to solve this?
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