Your task is to determine the cost (per low income family) of the two government propos-als, and to assess the impact of each of the three proposals (including the proposal from

the Institute for Cold-Hearted Economics) on family welfare. Finally, you are to consider

whether these policies may have unintended consequences for the rental market. Specif-ically, what impact might the schemes have on the equilibrium rents of acceptable and

substandard homes? And, what incentive do these price changes create for the landlords

of substandard housing? (Note: You do not need to model equilibria in the two rental

markets. Rather, you should explain how you expect prices to change given your knowledge of demand and supply.)

Each low income family receives a weekly payment of

$480 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=xy³,

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=y³ and MUy= 3xy²

.

Finally, the weekly rent on an acceptable family home is Px= $150 per week, and the price of the composite good is normalised to Py= 1. (You should interpretx < 1 as the family renting a home that does not meet the minimum acceptable standard.)

QUESTIONS:

Step 1: Derive the marginal rate of substitution for a low income family. (4 marks)

Step 2: Find the family's demands for acceptable housing, and for the composite good, as functions of the family's weekly income I and the price of housing Px . (Note: Do not substitute for family income or the price of housing at this step.) (16 marks)

Step 3: What is the lowest level of income at which a low income family's consumption of acceptable housing will meet the Government's target? What level of utility does the family experience at this level of income? (Hint: Use the price Px = $150 at this step.) (10 marks)

Step 4: What is the highest housing price at which a low income family's consumption of acceptable housing will meet the Government's target? What level of utility does the family experience at this price? (Hint: Use the income I = $480 at this step.) (10 marks)

Step 5: Find a low income family's optimal consumption basket when its income is a $330 payment, plus a $ 150 voucher redeemable for housing. What level of utility does the family experience in this case? (Hint: Use the price Px= $150 at this step.) (10 marks)