The demand and supply functions for two interdependent goods are given by Q D 1 50 2P 1 P 2 Q D 2 10 P 1 4P 2 Q S 1 20 P 1 Q S 2 10 5P 2 (a) Show that the equilibrium prices satisfy (b) Find the inverse of the 2 2 matrix in part (a) and hence find the equilibrium prices P 3 1 70 P2 1 20...

The demand and supply functions for two interdependent goods are given by Q D 1 = 50

Question:

The demand and supply functions for two interdependent goods are given by
Q_D₁ = 50 − 2P₁ + P₂
Q_D₂ = 10 + P₁ − 4P₂
Q_S₁ = −20 + P₁
Q_S₂ = −10 + 5P₂
(a) Show that the equilibrium prices satisfy P 3 -1 70 P2 -1 20 (b) Find the inverse of the 2 × 2 matrix in part (a) and hence find the equilibrium prices.