Matrices and Vectors

The two-commodity market model (3.12) can be written—after eliminating the quantity variables as a system of two linear equations, as in (3.13'),

C]P] + CjPi = -co Y\ Pi + YiPi = -ft where the parameters c0 and y{) appear to the right of the equals sign. In general, a system of m linear equations in n variables (xux2i * ■ ■ ,xn) can also be arranged into such a format:

In (4.1), the variable appears only within the leftmost column, and in general the variable xj appears only in the jth column on the left side of the equals sign. The double-subscripted parameter symbol ai; represents the coefficient appearing in the ilh equation and attached to the /th variable. For example, «221 is the coefficient in the second equation, attached to the variable The parameter d, which is unattached to any variable, on the other hand, represents the constant term in the /th equation, hor instance, d\ is the constant term in the first equation. All subscripts arc therefore keyed to the specific locations of the variables and parameters in (4.1).

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