(10 pts) The government is considering various subsidy and incentive programs to induce low-income families to live in better quality housing than they would otherwise live in. Three plans are i. Income subsidy: provide additional income I to a family that can be spent in any way. ii. Price subsidy: pay a fixed percentage p of a family's rent. iii. Voucher: pay an amount s toward a family's rent, provided the normal rent is at least R. Suppose commodities can be separated into housing (in amount x) and a general commodity representing all other goods (in amount z). Suppose a family has utility function U(x,z) = z4/5x1/5 And a monthly income of $500. The government wishes this family to live in a house that rents for at least $150. Suppose the prices are each $1.00 per unit. a. Without any subsidy, how much will the family spend on rent? b. Under each of the plans above, how much subsidy would be required to induce the family to live in a $150 house?