Question 4. Liz Lemon has a utility function over condominium floor space (good x, measured in squared feet) and other stuff (good y), given by U(x,y) = xzy. Liz's income is $30,000, and the initial price ofx is $100, and the price of y is $1. 4.1 Find Liz's optimal consumption bundle of floor space and other goods. Find Liz's utility level. The city government has two alternative housing programs that Liz is eligible for. For each program, determine (i) what Liz's optimal bundle would be; (ii) Liz's utility level; and (iii) how much it costs the government to offer Liz this program. 4.2 Program 1: a lump-sum cash payment of $3,000, regardless of the size of condominium purchased. 4.3 Program 2: a $20 subsidy on the price of condominiums, so that the price per square foot is $80. 4.4 Now draw a picture with x on the horizontal and 31 on the vertical. On that picture, draw three budget constraints, one each for parts a, b and c. Then, draw three indifference curves that go through the three optimal consumption bundles. You may wish to use three colors to distinguish between parts a, b and c. 4.5 If you were the government, what would you have to think about if you wanted to choose between implementing Program 1 or Program 2