Suppose that the government imposes a consumption tax of the rate t per unit of consumption of good 1, and spends the tax revenue for a lump-sum (meaning "fixed amount") transfer back to consumers equally. If t0) per unit of consumption of good 1, which is financed by a lump-sum tax on consumers equally. Specifically: p1dT=p1+t,=tiIx1i, where p1d is the demand price of good 1 for consumers, and T is the total amount of net transfer, which is divided equally to consumers. The second line represents the government budget constraint. Then (2) and (4) are replaced by, respectively: p1dx1i+p2x2ijmi;mip2e2i+jJijj+T/I,iIij=1j,=p1y1jp2z2j. (a) show that (9) is unchanged whenever (2) holds with equality. (b) show that (12) is unchanged, but TS is rewritten as TS=CS+PS+T, where p1 in CS is replaced by p1d. (c) show that an equilibrium allocation is not Pareto efficient for all t=0. (d) show that an equilibrium allocation is Pareto efficient for t=0. Suppose that the government imposes a consumption tax of the rate t per unit of consumption of good 1, and spends the tax revenue for a lump-sum (meaning "fixed amount") transfer back to consumers equally. If t0) per unit of consumption of good 1, which is financed by a lump-sum tax on consumers equally. Specifically: p1dT=p1+t,=tiIx1i, where p1d is the demand price of good 1 for consumers, and T is the total amount of net transfer, which is divided equally to consumers. The second line represents the government budget constraint. Then (2) and (4) are replaced by, respectively: p1dx1i+p2x2ijmi;mip2e2i+jJijj+T/I,iIij=1j,=p1y1jp2z2j. (a) show that (9) is unchanged whenever (2) holds with equality. (b) show that (12) is unchanged, but TS is rewritten as TS=CS+PS+T, where p1 in CS is replaced by p1d. (c) show that an equilibrium allocation is not Pareto efficient for all t=0. (d) show that an equilibrium allocation is Pareto efficient for t=0