P [ B paa

which gives a system of reduced-form equations for the prices. The following 3x3 example illustrates and shows how to solve for a particular price (rather than the entire vector of prices) using Cramer's rule.

Example 9.22 Consider the markets for coffee, tea, and sugar. These goods are related in demand.

since the first two are often substitutes for each other while the third is often complementary with each of the other two goods. Ignoring any supply side links (which are. in any case, unlikely), we have as an example:

qf = 100-5 p,+3 pc - px qt = -10 + 2 p, q"r = 120- 8pe + 2 pi - 2p, <?; = -20 + 5 p, q's = 300 - 10p, - 5pt - ps ll = 15 Ps

Setting these pairs of equations equal to each other and arranging in matrix form gives the system for equilibrium prices:

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