Assume an economy has 3 goods with the following supply and demand curves:
q1s = 2 + p1 + p2 q1d = 5 + 2p2 – p3
q2s = -2 – p1 + p2 + 2p3 q2d = 6 + p1 – 2p2
q3s = -1 + p3 q3d = 5 + p1 – p3
Set up a 3×3 matrix equation that can be solved for equilibrium prices p1, p2, and p3. (equilibrium occurs when quantity supplied is equal to quantity demanded. In this case each good needs to be in equilibrium.
Using Cramers Rule, Gaussian Elimination or Matrix Inversion, find the equilibrium price for all three goods.