Purchase tax policy. Show that it is possible to achieve a restricted Pareto efficient level of z by means of a purchase tax t on the producer’s output with the proceeds of the purchase tax Hs  tfs...

Purchase tax policy. Show that it is possible to achieve a restricted Pareto efficient level of z by means of a purchase tax t on the producer’s output with the proceeds of the purchase tax Hs  tfs being returned to the producer as a lump-sum payment in each state. (Hint: the producer’s income in state s is #s  T  Hs  (ps t)fs(z). Show that her input choice satisfies Evsy ( #s  T  Hs  (ps t)fs(z*),z*)(ps  t)f′ s(z*)  Evsz( #s  T  Hs  (ps  t)fs(z*),z*)  0 What level of t must be set so that satisfaction of this equation implies that [D.17] is equal to zero?)