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 pe, pm, and pa, respectively. If possible: a. Find equilibrium prices that make each sector's income match its expenditures.
b. Find the general solution as a vector, with pa free.