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, find equilibrium prices that make each sector's income match its expenditures. find the general solution as a vector, with pa free.