Inefficiency with a futures market. Prove the assertion in the text that when there are three states, two goods y and x and a spot and futures market for x then the rational expectations equilibrium...

Inefficiency with a futures market. Prove the assertion in the text that when there are three states, two goods y and x and a spot and futures market for x then the rational expectations equilibrium is not constrained Pareto efficient. (Hint: assume that the policy-maker can make a non-state-contingent transfer T and control z directly. Write down the four market clearing conditions for the spot and futures markets and totally differentiate them with respect to T and z and solve for the effects of T and z on the spot and futures prices. Then examine the derivative of the welfare function with respect to z at the level which would be chosen by the producer and show that the derivative will not in general be zero.)