(a) The demand and supply functions of two interdependent commodities are given by Q D 1 40 3P 1 P 2 Q D 2 30 4P 1 0 5P 2 Q S 1 6 5P 1 Q S 2 5 2P 2 Show that the equilibrium prices satisfy Solve this system by calculating the inverse of the coefficient matrix (b) Use Cramers rule to find the value ...

(a) The demand and supply functions of two interdependent commodities are given by Q D 1 =...

Question:

(a) The demand and supply functions of two interdependent commodities are given by
Q_D₁ = 40 − 3P₁ −P₂
Q_D₂ = 30 − 4P₁ − 0.5P₂
Q_S₁ = −6 + 5P₁
Q_S₂ = −5 + 2P₂
Show that the equilibrium prices satisfy 1[P, 4 2.5 P2 46 35 Solve this system by calculating the inverse of the coefficient matrix.
(b) Use Cramer’s rule to find the value of y in the system: 3 5 12 1 3 -2 -20