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2 Scenario The government of the island nation of Autarka has become concerned by recent reports that many low income families are residing in substandard housing, (Housing that is too small for the family, or that has significant defects.) The government has committed to implementing new policies to ensure that all families receiving welfare payments can afford housing that meets a "minimum acceptable standard", Two alternative schemes are under consideration: 1. Increase the weekly welfare payment made to low income families, to a level at which the families can afford to rent acceptable housing. 2. Subsidise the rents of families on welfare to bring the price of acceptable housing down to an affordable level. The Institute for ColdeHearted Economics has criticised both proposals for being too ex- pensive, They advocate converting $210 of the existing weekly welfare payment to a rental voucher, thereby forcing low income families to prioritise housing over other consumption, They claim that using a voucher in this way, would meet the government's goals without incurring additional expenditure. 2.1 Your task 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 ColdHearted 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.) 2.2 Household preferences 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=Xy2. 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 normalised to Py = 1. (You should interpret x