Scenario

The government of the island nation of Autarka has become increasingly concerned about

the health and wellbeing of low income households. Medical experts stress the importance

of a healthy diet in this regard. They have determined that, ideally, a household would

consume at least 10kg of fresh fruit and vegetables each week.

The government has proposed implementing a new voucher scheme to ensure that the

10kg per week consumption target is met. Under the government's proposal, the vouchers

would be redeemable for fresh fruit and vegetables, but could not be used for other types

of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme,

the value of the vouchers sent to a household would be linked to the household's income.

Community groups in Autarka have expressed concern that a voucher scheme is unnec-

essarily paternalistic; depriving low income households of the choice of how to spend their

income. These groups argue that the government's consumption targets could be met

just as well using transfers (monetary payments from the government to the low income

households). Transfers, they argue, would empower low income households to make their

own consumption decisions.

Your task

Your task is to determine the optimal voucher value as a function of household income.

The voucher must implement the government's target of 10kg of fresh fruit and vegetables

consumed per week, while minimising the cost of the vouchers to the government. You

are also to assess the community groups' claim that a transfer scheme would implement

the government's targets just as well.

Do you think that the community groups are

motivated by the health outcomes associated with a good diet? Or might they have

another objective?

Household preferences

Using data from household surveys, you have determined that the 'typical' household's

preferences are represented by the utility function,

U= (x+ 36)y ,

where x represents the quantity of fruit and vegetables consumed, and y represents the quantity of the composite good consumed. The associate marginal utilities are,

MUx = y and MU y = x + 36.

The price of fruit and vegetables is P x = $12 per kg, and the price of the composite good is normalised to Py = 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. The introduction has a 200 word limit.

Analysis

In the analysis section you must complete each of the steps detailed below. The required

analysis draws on content covered in lectures 1-5. When completing the steps you must:

Type all equations using the 'Insert Equation' function (or equivalent).

Show all of your working and include sufficient written description for the reader to

follow your process.

Note that hand draw figures and equations are not acceptable. There is no word/page

limit for the analysis section.

Step 1: Derive the marginal rate of substitution for the typical household. (4 marks)

Step 2: Find the household's demands for 'fruit and vegetables', and for the composite

good, as functions of the household's weekly income /. Hint: There is a critical income

level below which the household's optimal consumption basket is a corner solution. (23

marks)

Step 3: What is the lowest level of income at which a household's consumption of fruit

and vegetables will meet the Government's target? (5 marks)

Step 4: Suppose that the government decides to implement its target consumption of

fruit and vegetables using transfers. How much would the government need to transfer to

a household each week to achieve the 10kg consumption target? Hint: Your answer will

be a function of the household's income /. You should assume that transfers cannot be

negative. (4 marks)

Step 5: Suppose that, instead of transfers, the government decides to use vouchers re-

deemable for fruit and vegetables. What value of voucher would the government need in

order to achieve the 10kg consumption target? Hint: Your answer will be a function of

the household's income/. You should assume that vouchers cannot have a negative value.

(14 marks)

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.

Conclusion

Your conclusion should succinctly and accurately summarises the findings of your analysis

and the implications of these findings for the scenario.

Type a