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 Cold-Hearted Economics has criticised both proposals for being too expensive. They advocate converting $150 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.

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.)

Step 1:

Marginal rate of substitution = y / 3x

Step 2:

Family's demand function for acceptable housing is x = I / 4 Px

Family's demand function for composite good is y = 3 * I / 4 * Py

Step 3:

Lowest level of income at which a low income family's consumption of acceptable housing will meet the Government's target is $600.

Utility = 91,125,000 utils

Step 4:

Highest housing price at which a low income family's consumption of acceptable housing will meet the Government's target is $120.

Utility = 46,656,000 utils

Step 5:

a low income family's optimal consumption basket when its income is a $330 payment, plus a $150 voucher redeemable for housing, Utility = 15,160,921.875 utils

Questions:

1.Introduction

In your introduction you should succinctly and accurately summarises the purpose of your report. You should also outline the methodology employed in your analysis, and your key findings. 200 w0rd

2.Discussion

In you discussion you should explain the significance of your analysis section findings in the context of the scenario. In this section you must address all the issues raised in the scenario. Be sure to base your discussion on the results in your analysis section and avoid assertions or speculation. Use economic terminology as appropriate. 400 w0rd

3.Conclusion

Your conclusion should succinctly and accurately summarises the findings of your analysis and the implications of these findings for the scenario. 200 w0rd