Suppose an economy consists of three sectors: Energy (E), Manufacturing (M), and Agriculture (A). Sector E sells 70% of its output to M and 30% to A. Sector M sells 30% of its output to E, 50% to A, and retains the rest. Sector A sells 15% of its output to E, 30% to M, and retains the rest. Denote the prices (dollar values) of the total annual outputs of the Energy, Manufacturing, and Agriculture sectors by P_e, P_m, and P_a, respectively. If possible, find equilibrium prices that make each sector's income match its expenditures. Find the general solution as a vector, with P_a free. [pe pm pa] = [0.465 pa 0.593 pa pa] [pe pm pa] = [0.308 pa 0.716 pa pa] [pe pm pa] = [0.356 pa 0.686 pa pa] [pe pm pa] = [0.607pa 0.481 pa pa]
Show transcribed image textSuppose an economy consists of three sectors: Energy (E), Manufacturing (M), and Agriculture (A). Sector E sells 70% of its output to M and 30% to A. Sector M sells 30% of its output to E, 50% to A, and retains the rest. Sector A sells 15% of its output to E, 30% to M, and retains the rest. Denote the prices (dollar values) of the total annual outputs of the Energy, Manufacturing, and Agriculture sectors by P_e, P_m, and P_a, respectively. If possible, find equilibrium prices that make each sector's income match its expenditures. Find the general solution as a vector, with P_a free. [pe pm pa] = [0.465 pa 0.593 pa pa] [pe pm pa] = [0.308 pa 0.716 pa pa] [pe pm pa] = [0.356 pa 0.686 pa pa] [pe pm pa] = [0.607pa 0.481 pa pa]
