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    Use the inverse matrix method to find the equilibrium prices and quantities where the supply and demand functions for each good are:

    Qd1 = 50 – 2p1 + 5p2 - 3p3
    Qd2= 22 + 7p1 – 2p2 + 5p3
    Qd3= 17 + p1 + 5p2 – 3p3

    Qs1 = 8p1 -5
    Qs2 = 12p2 -5
    Qs3 = 4p3 -1

    Thanks, could you also let me know what you got for your inverse and cofactor matix.

    The equations Qs1 = Qd1, Qs2 = Qd2, Qs3 = Qd3 can be written in matrix form as M p = c, where

    M = {{10, -5, 3}, {-7, 14, -5}, {-1, -5, 7}}
    p = {p1, p2, p3}
    c = {55, 27, 18}


    M^(-1) = (1/607)*{{73, 20, -17}, {54, 73, 29}, {49, 55, 105}}

    = M^(-1)c
    = {7, 9, 10}
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Updated: April 11, 2006
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