Consider the three-commodity market model given:

Q^d₁ = 15 - 2p₁ + 2p₂ + p₃ and Q^s₁ = 2p₁ - 7

Q^d₂ = 6 + 2p₁ - 2p_{2 -} p₃ and Q^s₂ = 2p₂ - 4

Q^d₃ = 4 + p₁ - p_{2 -} 3p₃ and Q^s₃ = 4p₃ - 6

(a) What is the relationship among the three goods? Are the goods substitutes or complements? Give a reason for your answer

(b) Write the equilibrium conditions for the model

(c) Use the substitution and elimination methods to find the equilibrium prices and quantities for the three goods