Suppose an economy has four sectors, Agriculture (A), Energy (E), Manufacturing (M), and Transportation (T). Sector A sells 10% of its output to E and 25% to M and retains the rest. Sector E sells 30% of its output to A, 35% to M, and 25% to T and retains the rest. Sector M sells 30% of its output to A, 15% to E, and 40% to T and retains the rest. Sector T sells 20% of its output to A, 10% to E, and 30% to M and retains the rest.

(a) Construct a diagram that shows the exchange between the three sectors.

(b) Determine the exchange table for this economy, where the columns describe how  the output of each sector is exchanged among the four sectors.

(c) Denote the prices of the total annual outputs of the sectors by pA, pE, pM and pT  respectively. Determine the equations that need to hold for the equilibrium prices  for the four sectors.

(d) Find the equilibrium prices, if they exist.