Each low income family receives a weekly payment of $600 from the government (this payment is their only source of income). Surveys of low income families suggest that their preferences are represented by the utility function, U = xy 2, where x represents the number of acceptable homes rented by the family, and y represents the quantity of the composite good consumed. The associate marginal utilities are, MUx = y2 and MUy = 2xy. Finally, the weekly rent on an acceptable family home is Px = $210 per week, and the price of the composite good is normalized to Py = 1. (You should interpret x < 1 as the family renting a home that does not meet the minimum acceptable standard.)

Q1 What is the lowest level of income at which a low income familys consumption of acceptable housing will meet the Governments target? What level of utility does the family experience at this level of income? (Hint: Use the price Px = $210 at this step.)

Q2 What is the highest housing price at which a low income familys consumption of acceptable housing will meet the Governments target? What level of utility does the family experience at this price? (Hint: Use the income I = $600 at this step.)

Q3 Find a low income familys optimal consumption basket when its income is a $390 payment, plus a $210 voucher redeemable for housing. What level of utility does the family experience in this case? (Hint: Use the price Px = $210 at this step.)